Problem 8 (30 points): Below is a general algorithm for plotting the magnitude response of a filter:  Generate a 1 Hz input signal for a large number of samples.  Pass it through the filter and obtain the output.  Compute the ratio of the "rms value of the output sequence" and the "rms value of the input sequence". This ratio is the magnitude response of the filter at 1 Hz.  Repeat this process for 2 Hz, 3 Hz, etc.  Plot the magnitude response (in Y-axis) vs. frequency (in X-axis using a log scale). An N-sample moving average FIR filter is given by, y n = 1 x n − i −1 i=0 , an IIR filter with smoothing parameter, , is given by, y n = 1 − x n + y n − 1 , and a difference filter is given by, y n = x n − x n − 1