Table 13.18 shows the multiplier coefficients of a scaled Chebyshev filter designed with the following specifications

\[\begin{aligned}A_{\mathrm{p}} & =0.6 \mathrm{~dB} \\A_{\mathrm{r}} & =48 \mathrm{~dB} \\\Omega_{\mathrm{r}} & =3300 \mathrm{rad} / \mathrm{s} \\\Omega_{\mathrm{p}} & =4000 \mathrm{rad} / \mathrm{s} \\\Omega_{\mathrm{s}} & =10000 \mathrm{rad} / \mathrm{s} .\end{aligned}\]

The structure used is the cascade of second-order direct-form structures.

(a) Plot the output-noise RPSD in decibels.

(b) Determine the filter coefficient wordlength, using the sign-magnitude representation, that obtains at most \(1.0 \mathrm{~dB}\) as the passband ripple.

(c) Plot the filter magnitude response when the filter coefficients are quantized with the number of bits obtained in item (b). Compare the results with the nonquantized magnitude response.

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Table 13.18. Coefficients of a Chebyshev filter. Scaling factor: X = 2.6167 x 10-2. Coefficient Section 3 Section 1 Section 2 0.0252 0.0883 -0.0503 -0.1768 1.0000 -2.0000 12 0.0252 0.0883 1.0000 171) 1.5751 1.6489 1.5465 1711 0.7809 0.7012 0.9172