8.3. Exercises


Plot the rectangular, triangular, Hanning, Hamming, Blackman and Kaiser windows using MATLAB functions boxcar, bartlett, hanning, hamming, blackman and kaiser. Calculate and plot the magnitude of their spectra. Emphasize the sidelobe level and the bandwidth of these spectra. Conclude about the effect of these windows on a FIR filter design.


Using the properties of the four classes of FIR filters summarized in Table 8.1, find the appropriate applications for each of them from the following list: lowpass filter, bandpass filter, highpass filter, stopband filter, Hilbert transformer and derivative filter.


Calculate the coefficients of a 25th order derivative filter using the LS method, for a sampling frequency fs = 20 kHz. Plot its transfer function, impulse response and zeros. Imagine a possible application for this filter.


a. Use H(4, 4) = 0 in exercise 8.7 and observe the effect on the original image. Can you explain the results obtained?

b. Perform a highpass filtering of the same image using an appropriate transfer function.

c. Repeat exercise 8.7 for a “salt and pepper” and then a “speckle” noise. Compare the effectiveness of the lowpass filtering in the three cases.


Design a 120th order FIR highpass filter using the frequency sampling method. Consider a cutoff frequency fc = 6 kHz, and a sampling frequency fs = 20 kHz. Plot the filter transfer function. Compare its order to that of an IIR ...

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