Find the inverse discrete time Fourier transform (impulse response) of an ideal filter with magni tude responseH()1 and linear phase response m for the following cases: (a) Low pass filter (b) High pass filter (e) Band pass filter (d) Band stop filter 2: In problem 1, the impulse response responses are IR filter coefficients. In each case truncate the impulse responses to length N sequences, so that you will obtain FIR filter coefficients, Further, fix m (a) Provide stem plots for the filter coefficients for each filter (low pass, high pass, band pass, and band stop) for N-I1,N-21,N-41 and N- 61 (b) Now compute the discrete time Fourier transform for each filter and each N indicated in part a, and provide the magnitude spectrum in graphical form. (e) Did you observe improvement in the filter design as N increases d) Calculate Ap- pass band ripple and A. stop band attenuation in dB for each filter and each N : This question deals with windowing techniques. Consider the following window functions Bartlett window, Hanning window, Hamming window, Blackman window, and Kaiser window. (a) Pro- vide stem plots for each window for the values of N for,21, 41, and 61 (b) Modify your filter coefficients with the aid of ufn for each window and each N and provide stem plots. (c) Recalculate discrete time Fourier transform for each modified filter coefficients and provide the magnitude spectrum in graphical form. (d) For each case calculate A, and A, and tabulate them write your own conclusions in each case you observed in question 3