An FIR filter has coefficients b = [ 1.0000 -0.6387 1.0214 0.8210 -0.7470 1.0920 ]
(a) Find H(z) for the filter and plot its frequency response (magnitude and phase) using subplot.
(b) For an input of x(t) =5 cos(100πt) sampled at fs=250Hz, plot the input and the output of the filter on a single plot. Use a sample input vector of 100 points. Annotate the plot showing the gain and phase shift caused by the filter. State how these values relate to the plot of part (a).
(c) Submit your source code and subplots.
(a) Using Matlab, find and plot the magnitude of the DTFT of 10 samples of x(n) for n=[0:1:9] of x(n) = cos(2*pi*f1*n) + cos(2*pi*f2*n) for f1=0.22 and f2=0.24 and pad zeros to get 100 samples. Let the frequency axis run from 0 to 2 in pi units. Use 500 frequency points to plot the DTFT.
(b) Using Matlab, overlay on the plot the magnitude of the DFT coefficients X_{k} vs frequency in pi units for a 100 point transform of this set of samples.
(c) Find the DFT frequency resolution. On the plot, indicate where f1 and f2 are on the frequency axis.
(d) Now use 100 sample points of the waveform with no zero padding in the DFT magnitude plot. Annotate this plot and indicate the frequencies f1 and f2 present in the wave form.
(e) Title the plots and label the axes appropriately. Submit the plots along with the source code.