[1] A low-pass filter is to be designed to have a 3-dB bandwidth of 4 kHz and an attenuation of at least 30 dB at 6 kHz. What order of Butterworth filter is needed? [2] A low-pass filter is to be designed to have a 3-dB bandwidth of 200 Hz and an attenuation of 50 dB at 400 Hz. Determine the order of the Butterworth filter required. [3] Determine the order of a low-pass Butterworth filter that is to provide 40 dB attenuation at $frac{omega}{omega_0} = 2$. [4] Design a state-variable filter with Chebyshev characteristics and a centre frequency of 40 kHz. What is the bandwidth of the bandpass output?
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The magnitude response of a Butterworth filter is given by: \[ |H(j\omega)| = \frac{1}{\sqrt{1 + (\frac{\omega}{\omega_c})^{2n}}} \] where \(\omega_c\) is the cutoff frequency, and \(n\) is the filter order. Show more…
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