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Unformatted text preview: ECE501 Introduction to Analog and Digital Communications Autumn 2011 Homework #2 Oct. 10, 2011 HOMEWORK SOLUTIONS #2 1. The code and plots for the lowpass filter designs are shown below. (a) The impulse response truncation method starts with a delayed, sampled version of the ideal impulse reponse, then truncates to obtain a causal, linear phase, finitelength impulse re sponse. Observe the ringing in the magnitude response due to the truncation. 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510 10 20 30 40 time amplitude500400300200100 100 200 300 400 500 0.2 0.4 0.6 0.8 1 1.2 1.4 frequency magnitude (b) The leastsquares design produces a linearphase finite impulse response (FIR) filter of the specified duration by minimizing the integrated squared error between the design and specified magnitude response. For piecewise linear magnitude response, the optimization is simple and is computed by the Matlab routine firls . 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510 10 20 30 40 time amplitude500400300200100 100 200 300 400 500 0.2 0.4 0.6 0.8 1 1.2 1.4 frequency magnitude The LPFs designed using the MATLAB builtin routines yield magnitude responses that are generally much closer to ideal than the truncatedsinc LPF. The passband from firls is very flat, while that from the truncatedsinc filter is flat except for severe ringing near the passband edge. The stopband from firls is essentially zero over the desired range; the stopband of the truncatedsinc filter is also zero except near the stopband edge. A more detailed view of the stopband responses can be seen in a semilog plot, freqz(h,1,8096,1/Ts) . Details of filter design are a topic covered in an introductory course on Digital Signal Processing; other design techniques include equiripple firpm and windowbased fir2 ....
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This note was uploaded on 11/11/2011 for the course ECE 501 taught by Professor Schniter,p during the Fall '08 term at Ohio State.
 Fall '08
 Schniter,P

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