21. Consider a ninth-order analog Butterworth lowpass filter H(s) with 3 dB cutoff frequency of 10 Hz. (a) Determine and graph the pole locations ofH(s). (b) Plot the magnitude and

log-magnitude[0, 100] Hz range.responses over (c) Determine frequencies at which the attenuation is 30 dB, 40 dB, and 50 dB. \mathrm{VG} \simeq \sum_{k=0}^{K}|h[n]|^{2} . \quad K \gg 1 \mathrm{VG}=R_{0}^{2}+\sum_{k=1}^{N} \sum_{k=1}^{N} \frac{R_{k} R_{\ell}^{*}}{1-p_{k} p_{\ell}^{*}}