Design a linear phase FIR low pass filter with cut off frequency wc= 1 rad/sample and phase delay of T = 4 and at least 40 dB attenuation in the stopband. Also obtain the magnitude/frequency response of the filter. a) Find the closed form of ha[n]. b) What is the best window function that optimizes this filter? Why? c) Find closed form of the impulse response h[n] and all filter coefficients based on the window function that you chose in part (b). d) Find the mathematical equation of frequency response H[2] of the filter you designed in parts (a) through (c). Use Matlab to draw the frequency response magnitude. e) Use Matlab and your findings in parts (a) through (d) to prove that your filter works. Apply a sine wave input within the passband and stopband and show what output is being produced by the filter you designed.