Solutions_Assignment5_w2010

Solutions_Assignment5_w2010 - Carleton University Dept of...

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April 13, 2010 1 Carleton University Dept of Systems and Computer Engineering SYSC-4405: Digital Signal Processing Winter 2010 ________________________________________________________________________ Assignment 5 Due: Apr 7th, 2010 (by 4 p.m.) Question 1 It is desired to design a bandpass filter, with a lower cut-off frequency of 500 Hz and an upper cut-off frequency of 1000 Hz. The sampling frequency is 16000 Hz. a) What is the center frequency of the desired filter? What is the cut-off frequency of the equivalent lowpass filter? Give you answers in terms of both the digital frequency ( ω ) and analog frequency (f). Recall that b) Design the equivalent lowpass filter. Use N= number of coefficients = 21, and a rectan- gular window. c) From the lowpass equivalent, calculate the coefficients of the desired bandpass filter. d) Plot the frequency response of the bandpass design. How does this response differ from the desired ideal bandpass response?( you may use matlab as a calculator to compute the frequency response based on your own formulation) Solution a) Center frequency=(1000+2000)/2=1500 Hz. The Equivalent lowpass has a cutoff frequency of (2000-1000)/2=500 Hz. In terms of digital frequencies; b) The coefficients of the equivalent lowpass are given by ; The lowpass coefficients for n=0 to 10 are: ω 2 π f f s -------- = ω c ω u ω l () 2 2 π 16000 -------------- 1000 500 2 ------------------------------- π 32 ----- == = ω 0 ω u ω l + 2 2 π 16000 500 1000 + 2 3 π 32 ------ = h lp n ω c π ω c n sin ω c n ---------------------- ⎩⎭
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Solutions_Assignment5_w2010 - Carleton University Dept of...

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