Problem 2. (50 points) Develop a computer-based algorithm for computing a moving average filter and determine its effects on a signal described by: y(t) = sin(14.5t) + 0.25 cos(400.5t) + 0.1sin(980) Two seconds of this signal were recorded with a sampling rate of 10 kHz. For this signal determine the following: a) Since we know the signal sinusoids, use a hand calculator to provide the values of the frequency components present in the signal. b) Is this signal aliased? c) Represent the signal in time domain, i.e. time-domain signal plot. d) Represent the signal in the frequency domain, i.e. plot its Fourier Transform (its spectrum) a. Did you need to use zero padding to improve the frequency resolution? e) Provide a plot with your best results of filtering out (removing the highest frequency component a. Adjust the window size to remove only the highest frequency component without affecting the other two. i. Could you tune the window size of the filter to remove only the highest component? Explain your conclusion