Design an IIR digital filter to reduce the amount of noise in the two sinusoidal components in Experiment 1.3. Evaluate your specifications by processing x_noisy, as defined in that experiment, with the designed filter and verifying the output signal-to-noise ratio.

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Experiment 1.3 Suppose the signal x(t) = 5 cos(251) + 2 cos(250r), sampled with Fs = 1000 samples per second, as shown in Figure 1.25a, is corrupted by a small amount of noise, forming the signal shown in Figure 1.25b generated by the following commands: amplitude 1 = 5; freq 1 = 5; amplitude 2 = 2; freq 2 = 50; F_s = 1000; time = 0:1/F_s: (1-1/F_s); sine 1 = sine_2 noise = amplitude 1*sin(2*pi*freq 1. *time); amplitude 2*sin(2*pi*freq 2. *time); randn (1, length (time)); x_clean sine_1 + sine_2; x_noisy = x_clean + noise; figure(1); plot (time, x_clean); figure (2); plot (time, x_noisy); In particular, the randn command generates the specified number of samples of a pseudo- random signal with Gaussian distribution with zero mean and unit variance. We can minimize the noisy effect by averaging N successive samples of x(n) = x_noisy, implementing the following difference equation: y(n) = x(n)+x(n1)+...+x(nN+1) N (1.242)