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1. Let x(n) = 0.35cos(0.2πn), n = 0, 1, ..., 99.?Downsample x(n) by the following factors (a) M = 2 (b) M = 4 (c) M = 8. In each case, plot the sequence and the magnitude of its frequency response. In addition, plot x(n) and the magnitude of its frequency response.

2- Let x(n) = 0.25cos(0.4πn), n = 0, 1, ..., 99.?Upsample x(n) by the following factors (a) L = 3 (b) L = 6 (c) L = 9.?In each case, plot the sequence and the magnitude of its frequency response. In addition, plot x(n) and the magnitude of its frequency response.

3. Let x(n) = 0.35cos(0.2πn) + 0.25sin(0.4πn), n = 0, 1, ..., 99.

Obtain the samples of the sequence y(n) =  861_1.png

Plot y(n) and the magnitude of its frequency response.?In addition, plot x(n) and the magnitude of its frequency response.

B- THEME: D.T. Filter Design:

4. ?Design a D.T. FIR filter to only pass a band of frequencies 20 kHz wide from the frequencies between 10 kHz and 30 kHz. The center frequency of the band lies at 20 kHz and the sampling frequency is 200 kHz. Use the Hamming window.

5. Design a D.T. FIR band stop filter to remove the frequency of 50 Hz from a signal sampled at 1 kHz. Use the Hamming window to design a low pass filter with pass band edge at 30 Hz and a high pass filter with pass band edge at 70 Hz.

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