Chapter 4, Problem 21
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (2)](https://i0.wp.com/www.numerade.com/static/ace-animation-pdp/video_6.d86d01139302.gif "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (2)")
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Using the MATLAB functions cheblap, impulse and step:
(a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with $\omega_p=1$, $A_p=1.2 d B$, and $N=6$.
(b) Determine the impulse response and the step response for the filter of part (a).
(c) By multiplying the pole vector found in part (a) by $2 \pi 1000$ determine the transfer function of a Chebyshev Type I filter with $f_p=1000 \mathrm{~Hz}$, $A_p=1.2 d B$, and $N=6$.
(d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in $d B$ and a linear horizontal scale from 0 to $5000 \mathrm{~Hz}$. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase.
(e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by $1 /(2 \pi 1000)$, and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of $2 \pi 1000$.
(f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d).
(g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): $t_{g d}(n) \cong-[\phi(n)-\phi(n-1)] / S_s$, where $\phi(n)$ is the phase in radians at step $n$, and $S_s$ is the step size in $\mathrm{rad} / \mathrm{s}$.
Video Answer
![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (3)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy84NzNkMzdlMjI1ZDU0OTk1OTc5ODRkY2I5ZjYxYjU0MC5qcGVnIiwgImVkaXRzIjogeyJyZXNpemUiOiB7IndpZHRoIjogMjU2LCAiaGVpZ2h0IjogMjU2fX19 "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (3)")
![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (4)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy84MmEwNTBjYzUzNmY0NDRkODkzZjQ0OGJkMTI3M2FlYi5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0= "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (4)")
![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (5)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy9mOTZmZjFmOGY4Njc0YjIxOGQ5ZjdjYmM0NDAzODg4My5wbmciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0= "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (5)")
![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (6)](https://i0.wp.com/www.numerade.com/static/logos/logo-full-royal-on-white.ac63bc8717eb.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (6)"){kind=logo}
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (7)](https://i0.wp.com/www.numerade.com/static/icons/close-x.0ceebab0a1bd.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (7)"){kind=icon}
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Using the MATLAB functions cheblap, impulse and step:(a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with $\omega_p=1$, $A_p=1.2 d B$, and $N=6$.(b) Determine the impulse response and the step response for the filter of part (a).(c) By multiplying the pole vector found in part (a) by $2 \pi 1000$ determine the transfer function of a Chebyshev Type I filter with $f_p=1000 \mathrm{~Hz}$, $A_p=1.2 d B$, and $N=6$.(d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in $d B$ and a linear horizontal scale from 0 to $5000 \mathrm{~Hz}$. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase.(e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by $1 /(2 \pi 1000)$, and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of $2 \pi 1000$.(f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d).(g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): $t_{g d}(n) \cong-[\phi(n)-\phi(n-1)] / S_s$, where $\phi(n)$ is the phase in radians at step $n$, and $S_s$ is the step size in $\mathrm{rad} / \mathrm{s}$.
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Your personal AI tutor, companion, and study partner. Available 24/7. Ask unlimited questions and get video answers from our expert STEM educators. Millions of real past notes, study guides, and exams matched directly to your classes. ![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (8)](https://i0.wp.com/www.numerade.com/static/newbookpage/Group_29.dade2cbbb916.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (8)")
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (9)](https://i0.wp.com/www.numerade.com/static/newbookpage/Answers.7cde04c4d430.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (9)")
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (10)](https://i0.wp.com/www.numerade.com/static/newbookpage/ntp-v2.17ba9743d61b.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (10)")
Ace Chat![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (11)](https://i0.wp.com/www.numerade.com/static/newbookpage/ntp-v3.9ed6fbf06b85.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (11)")
Ask Our Educators![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (12)](https://i0.wp.com/www.numerade.com/static/newbookpage/ntp-v4.6da2a3990184.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (12)")
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (17)](https://i0.wp.com/www.numerade.com/static/loading.b2df72ce9ed3.gif "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (17)")
![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (18)](https://i0.wp.com/s3-us-west-1.amazonaws.com/com.numerade/books/51a2c2c3-b276-4b55-9811-d5b64888205d.jpg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (18)")
Design and Analysis of Analog Filters: A Signal Processing Perspective
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Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21
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![Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (19)](https://i0.wp.com/www.numerade.com/static/comments/Student_Info.322cc5589342.svg "Using the MATLAB functions cheblap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles, of a Chebyshev Type I filter with =1, Ap=1.2 d B, and N=6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector found in part (a) by 2 π1000 determine the transfer function of a Chebyshev Type I filter with fp=1000 Hz, Ap=1.2 d B, and N=6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in d B and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap to display the smooth phase response rather than the principle phase. (e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by 1 /(2 π1000), and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of 2 π1000. (f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d). (g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): tg d(n) ≅-[ϕ(n)-ϕ(n-1)] / Ss, where ϕ(n) is the phase in radians at step n, and Ss is the step size in rad / s. | Numerade (19)")
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