Use Matlab function 'firpm to design (a) Low-pass 31-order filter hi[n], with pass band 0-2 kHz. (b) Low-pass 127-order filter h12[n], with pass band 0-2 kHz. Use Fs - 15 kHz. The firm command gives the impulse response time domain) of the filter. The Fourier Transform of the impulse response is called the Transfer Function of the filter. Plot the magnitude of the transfer function for each filter. Allow about 200 Hz transition for each filter. From your answers to (a) and (b), what can you infer about the effect of the filter order on the "sharpness" of the magnitude? Generate a signal x[n) as the sum of two sine waves, at frequencies 1 kHz and 3 kHz, respectively. Use the sampling frequency of 15 kHz and generate the signals such that they are about 300 samples long. Plot the magnitude of the Fourier Transform for this signal. 3. Convolve the signal in (2) with the impulse response in (1b). Plot the magnitude of the Fourier Transform of the filtered output. You should see the higher frequency component (3 kHz) suppressed in the output. Use Matlab function 'firpm to design (a) Low-pass 31-order filter hi[n], with pass band 0-2 kHz. (b) Low-pass 127-order filter h12[n], with pass band 0-2 kHz. Use Fs - 15 kHz. The firm command gives the impulse response time domain) of the filter. The Fourier Transform of the impulse response is called the Transfer Function of the filter. Plot the magnitude of the transfer function for each filter. Allow about 200 Hz transition for each filter. From your answers to (a) and (b), what can you infer about the effect of the filter order on the "sharpness" of the magnitude? Generate a signal x[n) as the sum of two sine waves, at frequencies 1 kHz and 3 kHz, respectively. Use the sampling frequency of 15 kHz and generate the signals such that they are about 300 samples long. Plot the magnitude of the Fourier Transform for this signal. 3. Convolve the signal in (2) with the impulse response in (1b). Plot the magnitude of the Fourier Transform of the filtered output. You should see the higher frequency component (3 kHz) suppressed in the output