We wish to design a discrete Butterworth filter that can be used in filtering a continuous-time signal. The frequency components of interest in this signal are between 0and 1 kHz, so we would like the filter to have a maximum passband attenuation of 3 dB within that band. The undesirable components of the input signal occur beyond 2 kHz, and we like to attenuate them by at least 10 dB. The maximum frequency present in the input signal is 5 kHz. Finally, we would like the dc gain of the filter to be 10. Choose the Nyquist sampling frequency to process the input signal. Use MATLAB to design the filter. Give the transfer function of the filter, plot its poles and zeros, and its magnitude and unwrapped phase response using an analog frequency scale in kHz.