Chapter 6, Problem 36
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Question
Answered step-by-step
An IIR bandstop digital filter that satisfies the requirements:
$$
\begin{aligned}
0.95 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 1.05, \quad 0 \leq|\omega| \leq 0.25 \pi \\
0 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 0.01,0.35 \pi \leq|\omega| \leq 0.65 \pi \\
0.95 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 1.05,0.75 \pi \leq|\omega| \leq \pi
\end{aligned}
$$
can be obtained using the following MATLAB script:
```
wp = [0.25,0.75]; ws = [0.35,0.65]; delta1 = 0.05; delta2 = 0.01;
[Rp,As] = delta2db(delta1,delta2);
[N, wn] = cheb2ord(wp, ws, Rp, As);
[b,a] = cheby2(N,As,wn,'stop');
```
The filter coefficients $b_k$ and $a_k$ are in the arrays $\mathrm{b}$ and $\mathrm{a}$, respectively, and can be considered to have infinite precision.
1. Using infinite precision, provide the log-magnitude response plot and the pole-zero plot of the designed filter.
2. Assuming direct-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function.
3. Assuming cascade-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function.
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An IIR bandstop digital filter that satisfies the requirements:$$\begin{aligned}0.95 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 1.05, \quad 0 \leq|\omega| \leq 0.25 \pi \\0 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 0.01,0.35 \pi \leq|\omega| \leq 0.65 \pi \\0.95 & \leq\left|H\left(e^{j \omega}\right)\right| \leq 1.05,0.75 \pi \leq|\omega| \leq \pi\end{aligned}$$can be obtained using the following MATLAB script:```wp = [0.25,0.75]; ws = [0.35,0.65]; delta1 = 0.05; delta2 = 0.01;[Rp,As] = delta2db(delta1,delta2);[N, wn] = cheb2ord(wp, ws, Rp, As);[b,a] = cheby2(N,As,wn,'stop');```The filter coefficients $b_k$ and $a_k$ are in the arrays $\mathrm{b}$ and $\mathrm{a}$, respectively, and can be considered to have infinite precision.1. Using infinite precision, provide the log-magnitude response plot and the pole-zero plot of the designed filter.2. Assuming direct-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function.3. Assuming cascade-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function.
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![An IIR bandstop digital filter that satisfies the requirements: 0.95 ≤|H(e^j ω)| ≤1.05, 0 ≤|ω| ≤0.25 π 0 ≤|H(e^j ω)| ≤0.01,0.35 π≤|ω| ≤0.65 π 0.95 ≤|H(e^j ω)| ≤1.05,0.75 π≤|ω| ≤π can be obtained using the following MATLAB script: “` wp = [0.25,0.75]; ws = [0.35,0.65]; delta1 = 0.05; delta2 = 0.01; [Rp,As] = delta2db(delta1,delta2); [N, wn] = cheb2ord(wp, ws, Rp, As); [b,a] = cheby2(N,As,wn,'stop'); “` The filter coefficients bk and ak are in the arrays b and a, respectively, and can be considered to have infinite precision. 1. Using infinite precision, provide the log-magnitude response plot and the pole-zero plot of the designed filter. 2. Assuming direct-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function. 3. Assuming cascade-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function. | Numerade (13) An IIR bandstop digital filter that satisfies the requirements: 0.95 ≤|H(e^j ω)| ≤1.05, 0 ≤|ω| ≤0.25 π 0 ≤|H(e^j ω)| ≤0.01,0.35 π≤|ω| ≤0.65 π 0.95 ≤|H(e^j ω)| ≤1.05,0.75 π≤|ω| ≤π can be obtained using the following MATLAB script: “` wp = [0.25,0.75]; ws = [0.35,0.65]; delta1 = 0.05; delta2 = 0.01; [Rp,As] = delta2db(delta1,delta2); [N, wn] = cheb2ord(wp, ws, Rp, As); [b,a] = cheby2(N,As,wn,'stop'); “` The filter coefficients bk and ak are in the arrays b and a, respectively, and can be considered to have infinite precision. 1. Using infinite precision, provide the log-magnitude response plot and the pole-zero plot of the designed filter. 2. Assuming direct-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function. 3. Assuming cascade-form structure and a 12-bit representation for filter coefficients, provide the log-magnitude response plot and the pole-zero plot of the designed filter. Use the Qcoeff function. | Numerade (13)](https://i0.wp.com/www.numerade.com/static/loading.b2df72ce9ed3.gif)
Digital Signal Processing Using Matlab: A Problem Solving Companion
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