Paarmann L.D.
Chapter 9
FREQUENCY TRANSFORMATIONS - all with Video Answers
Educators
Chapter Questions
Similar to Example 9.1, determine the transfer function of 3rd-order Butterworth lowpass filter with $\mathrm{an}_c$ of $5000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the transfer function of a 3rd-order Chebyshev Type I lowpass filter with $A_p=1.5 d B$ and $\omega_p=1000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Repeat Problem 9.2 for $\omega_c=1000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the poles for the transfer function of Problem 9.1.
Check back soon!
Determine the poles for the transfer function of Problem 9.2.
Check back soon!
Determine the poles for the transfer function of Problem 9.3.
Check back soon!
Given that the desired specifications of a Butterworth lowpass filter are as follows: $\quad A_p=3 \mathrm{~dB}, \quad A_s=70 \mathrm{~dB}, \quad \omega_p=2,500 \mathrm{rad} / \mathrm{s}, \quad$ and $\omega_s=10,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=3 d B, A_s=70 d B$, $f_p=6,500 \mathrm{~Hz}$, and $f_s=26 \mathrm{kHz}$.
Check back soon!
Given that the desired specifications of a Chebyshev Type I lowpass filter are as follows: $A_p=1.2 \mathrm{~dB}, \quad A_s=75 \mathrm{~dB}, \quad \omega_p=3,500 \mathrm{rad} / \mathrm{s}, \quad$ and $\omega_s=7,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=1.2 d B, A_s=75 d B$, $f_p=6,500 \mathrm{~Hz}$, and $f_s=13 \mathrm{kHz}$.
Check back soon!
Determine the Filter Selectivity, $F_S$, for each of the two filters in Problem 9.7.
Amit Srivastava
Numerade Educator
Determine the Filter Selectivity, $F_S$, for each of the two filters in Problem 9.8.
Amit Srivastava
Numerade Educator
Determine the Shaping Factor, $S_a^b$, for each of the two filters in Problem 9.7, where $a=3 d B$ and $b=70 d B$.
Check back soon!
Determine the Shaping Factor, $S_a^b$, for each of the two filters in Problem 9.8, where $a=1.2 d B$ and $b=75 d B$.
Check back soon!
Indicate how Figure 3.8 could be used to obtain the plot of phase delay for each of the two filters in Problem 9.7.
Check back soon!
Indicate how Figure 3.9 could be used to obtain the plot of group delay for each of the two filters in Problem 9.7.
Check back soon!
Indicate how Figure 3.10 could be used to obtain the plot of the unit impulse response for each of the two filters in Problem 9.7.
Check back soon!
Indicate how Figure 3.11 could be used to obtain the plot of the unit step response for each of the two filters in Problem 9.7.
Check back soon!
Similar to Example 9.2, determine the transfer function of 3rd-order Butterworth highpass filter with an $\omega_c$ of $5000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the transfer function of a 3rd-order Chebyshev Type I highpass filter with $A_p=1.5 d B$ and $\omega_p=1000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Repeat Problem 9.18 for $\omega_c=1000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the poles and zeros for the transfer function of Problem 9.17.
Check back soon!
Determine the poles and zeros for the transfer function of Problem 9.18.
Check back soon!
Determine the poles and zeros for the transfer function of Problem 9.19.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.17.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.18.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.19.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the highpass filter of Example 9.3.
Check back soon!
Given that the desired specifications of a Butterworth highpass filter are as follows: $A_p=3 d B, \quad A_s=70 d B, \quad \omega_{s_{H P}}=2,500 \mathrm{rad} / \mathrm{s}, \quad$ and $\omega_{p_{H P}}=10,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=3 d B, A_s=70$ $d B, f_{s_{H P}}=6,500 \mathrm{~Hz}$, and $f_{p_{H P}}=26 \mathrm{kHz}$.
Check back soon!
Given that the desired specifications of a Chebyshev Type I highpass filter are as follows: $A_p=1.2 \mathrm{~dB}, \quad A_s=75 \mathrm{~dB}, \quad \omega_{s_{d I P}}=3,500 \mathrm{rad} / \mathrm{s}$, and $\omega_{p_{H P}}=7,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specífications. Repeat the above for $A_p=1.2 \mathrm{~dB}, A_s=75 \mathrm{~dB}$, $f_{s_{H P}}=6,500 \mathrm{~Hz}$, and $f_{p_{H P}}=13 \mathrm{kHz}$.
Check back soon!
Determine the Filter Selectivity of the highpass filter of Problem 9.17 in two ways: (a) by use of (9.14) and (3.7), and (b) computationally, using MATLAB.
Check back soon!
Determine the Filter Selectivity of the highpass filter of Problem 9.18 in two ways: (a) by use of (9.14) and (4.9), and (b) computationally, using MATLAB.
Check back soon!
Determine the Filter Selectivity of the highpass filter of Problem 9.19 in two ways: (a) by use of (9.14) and (4.9), and (b) computationally, using MATLAB.
Check back soon!
Determine the Shaping Factor of the highpass filter of Problem 9.17 in two ways: (a) by use of (9.15) and (3.10), and (b) computationally, using MATLAB.
Check back soon!
Determine the Shaping Factor of the highpass filter of Problem 9.18 in two ways: (a) by use of (9.15) and (4.12), and (b) computationally, using MATLAB.
Check back soon!
Determine the Shaping Factor of the highpass filter of Problem 9.19 in two ways: (a) by use of $(\mathbf{9 . 1 5})$ and (4.12), and (b) computationally, using MATLAB.
Check back soon!
For the Butterworth highpass filter of Problem 9.17, determine a closed-form expression for the group delay, similar to Example 9.4. Using MATLAB, plot the response of your expression. For comparison, determine and plot the group delay response as obtained by computational manipulation of the phase response (the traditional computational approach).
Check back soon!
Using MATLAB, plot the magnitude frequency response, phase response, phase delay response, group delay response, unit impulse response, and unit step response for a 10th-order Chebyshev Type I highpass filter with $A_p=1 d B$ and $\omega_{p_{H P}}=1000 \mathrm{rad} / \mathrm{s}$. That is, confirm the results plotted in Figure 9.1 through ${ }^{\text {HPp }}$ Figure 9.7 (Example 9.6).
Check back soon!
Similar to Example 9.11, determine the poles and zeros of an 8th-order Butterworth bandpass filter, with $\omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the poles and zeros of a 6th-order Chebyshev Type I bandpass filter, with $1 \mathrm{~d} B$ of ripple, $\omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.37.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.38.
Check back soon!
Given that the desired specifications of a Butterworth bandpass filter are as follows: $\quad A_p=3 d B, \quad A_s=70 d B, \quad B_p=2,500 \mathrm{rad} / \mathrm{s}, \quad$ and $B_s=10,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=3 d B, A_s=70$ $d B, B_p=6,500 \mathrm{~Hz}$, and $B_s=26 \mathrm{kHz}$.
Check back soon!
Given that the desired specifications of a Chebyshev Type I bandpass filter are as follows: $A_p=1.2 \mathrm{~dB}, A_s=75 \mathrm{~dB}, \quad B_p=3,500 \mathrm{rad} / \mathrm{s}$, and $B_s=7,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=1.2 \mathrm{~dB}, A_s=75 \mathrm{~dB}$, $B_p=6,500 \mathrm{~Hz}$, and $B_s=13 \mathrm{kHz}$.
Check back soon!
Determine the Filter Selectivity of the bandpass filter in Problem 9.41 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.31) and (3.7), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.43 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Filter Selectivity of the bandpass filter in Problem 9.42 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.31) and (4.9), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.45 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Shaping Factor of the bandpass filter in Problem 9.41 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.32) and (3.10), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.47 for $\omega_0=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Shaping Factor of the bandpass filter in Problem 9.42 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.32) and (4.12), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.49 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using the closed-form procedure of Example 9.14 , compute the group delay of a 6th-order Butterworth bandpass filter at $\omega_{p_1}, \omega_{p_2}$, and $\omega_o$ where $\omega_o=5000 \mathrm{rad} / \mathrm{s}$ and $B_p=500 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using MATLAB, plot the magnitude frequency response, phase response, phase delay response, group delay response, unit impulse response, and unit step response for a 10th-order Chebyshev Type II bandpass filter with $A_p=3 \mathrm{~dB}, A_s=80 \mathrm{~dB}, \omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$. That is, confirm the results plotted in Figure 9.8 through Figure 9.14 (Example 9. 15).
Check back soon!
Similar to Example 9.20 , determine the poles and zeros of an 8th-order Butterworth bandstop filter, with $\omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the poles and zeros of a 6th-order Chebyshev Type I bandstop filter, with $1 \mathrm{~dB}$ of ripple, $\omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.53.
Check back soon!
Using MATLAB, plot the magnitude frequency response and the phase response for the filter of Problem 9.54.
Check back soon!
Given that the desired specifications of a Butterworth bandstop filter are as follows: $\quad A_p=3 \mathrm{~dB}, \quad A_{\mathrm{s}}=70 \mathrm{~dB}, \quad B_{\mathrm{s}}=2,500 \mathrm{rad} / \mathrm{s}, \quad$ and $B_p=10,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=3 d B, A_s=70$ $d B, \quad B_s=6,500 \mathrm{~Hz}$, and $B_p=26 \mathrm{kHz}$
Check back soon!
Given that the desired specifications of a Chebyshev Type I bandstop filter are as follows: $A_p=1.2 \mathrm{~dB}, \quad A_s=75 \mathrm{~dB}, \quad B_s=3,500 \mathrm{rad} / \mathrm{s}$, and $B_p=7,000 \mathrm{rad} / \mathrm{s}$, determine the minimum required filter order to meet or exceed these specifications. Repeat the above for $A_p=1.2 d B, A_s=75 d B$, $B_s=6,500 \mathrm{~Hz}$, and $B_p=13 \mathrm{kHz}$.
Check back soon!
Determine the Filter Selectivity of the bandstop filter in Problem 9.57 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.45) and (3.7), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.59 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Filter Selectivity of the bandstop filter in Problem 9.58 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.45) and (4.9), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.61 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Shaping Factor of the bandpass filter in Problem 9.57 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.46) and (3.10), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.63 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Determine the Shaping Factor of the bandpass filter in Problem 9.58 with $\omega_o=15,000 \mathrm{rad} / \mathrm{s}$ in two ways: (a) by use of (9.46) and (4.12), and (b) computationally, using MATLAB.
Check back soon!
Repeat Problem 9.65 for $\omega_o=10,000 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using (9.48), and the procedure in Example 9.22, compute the group delay of a 6th-order Butterworth bandstop filter at $\omega_{p_1}, \omega_{p_2}$, and $\boldsymbol{D C}$, where $\omega_o=5000 \mathrm{rad} / \mathrm{s}$ and $B_p=500 \mathrm{rad} / \mathrm{s}$.
Check back soon!
Using MATLAB, plot the magnitude frequency response, phase response, phase delay response, group delay response, unit impulse response, and unit step response for a 10th-order elliptic bandstop filter with $A_p=1 d B$, $A_s=80 \mathrm{~dB}, \omega_o=1000 \mathrm{rad} / \mathrm{s}$, and $B_p=200 \mathrm{rad} / \mathrm{s}$. That is, confirm the results plotted in Figure 9.15 through Figure 9.21 (Example 9.23).
Check back soon!