Answer Happy

Let the signal to be filtered be the first 100 samples from MATLAB's "train" signal. To this signal add some Gaussian noise to be generated by randn, multiply it by 0.1, and add it to the 100 samples of the train signal. Design three discrete filters, each of order 20, and a half frequency (for Butterworth butter) and passband frequency (for the Chebyshev filters) of W, = 0.5. For the design with cheby1 let the maximum passband attenuation be 0.01 dB, and for the design with cheby2 let the minimum stopband attenuation be 60 dB. Obtain the three filters and use them to filter the noisy "train" signal. Use MATLAB plot the following for each of the three filters: a. Using fft function compute the DFT of the original signal, the noisy signal and the noise and plot its magnitude. Is the cut-iff frequency of the filters adequate to get rid of the noise? Explain. Compute and plot the magnitude and poles & zeros for each of the three filters. Comment on the differences in the magnitude responses. (20 Marks) b. Use the filter function to obtain the output of each of the filters. Also, plot the original noiseless signal and filtered signal. Compare them. (15 Marks)