Question

1. Using the windowing functions discussed in class, design a low-pass FIR filter with a cutoff frequency of 2 kHz, a minimum stop band attenuation of 40 dB, and a transition width of 200 Hz. The sampling frequency is 10 kHz 2. Using the windowing functions discussed in class, design a high-pass FIR filter with a cutoff frequency of 15 kHz, a minimum stop band attenuation of 55 dB, and a transition width of 500 Hz. The sampling frequency is 50 kHz 3. Using the windowing functions discussed in class, design a band-pass FIR filter centered at 20 MHz with a bandwidth 30 Mzinimum stop band attenuation of 30 a iminimuim s dB, and a transition width of 1 MHz. The sampling frequency is 80 MHz, 4. Given the following filter design for a signal with Fs = 1 kHz, answer the questions given below: sin [0.2π (n-86] 10.54 +0.46cos ( Brin-86) -12 cos(0.5mn), n = 0 . . . 172 (1) (a) What type of windowing function was used? What is the stop band attenuation and mim imum pass band gain? (b) What is the center frequency of this filter? Is it low-pass, high-pass, or band-pass? (c) If low/high-pass, what is the cutoff freqency? If band-pass, what is the bandwidth? (d) What is the transition width? 5. Implement the filters designed in Problem-1, Problem-2 and Problem-3 using MATLAB. Plot the magnitude response in dB and verify that the desired specifications were satisfied. In each case, plot the magnitude response for Rectangular windowing on the same plot (see examples of superimposed plots included in the lecture slides). Notes on Matlab Problem 5: Write a brief Report using a word processor summarizing the objectives, approach and make observations based on the simulation results. » Add appropriate titles, labels and legends to all the plots for your report. . A Dropbox has been created for Homework-9 on Course Pilot . Submit the Report and attach matlab code printout in class on the due date. Also submit the matlab m-files in Pilot-Dropbox designated for Homework-9 on the due date.

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