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Unformatted text preview: ECE-501 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, finite-length 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 0.5-10 10 20 30 40 time amplitude-500-400-300-200-100 100 200 300 400 500 0.2 0.4 0.6 0.8 1 1.2 1.4 frequency magnitude (b) The least-squares design produces a linear-phase finite impulse response (FIR) filter of the specified duration by minimizing the integrated squared error between the design and specified magnitude response. For piece-wise 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 0.5-10 10 20 30 40 time amplitude-500-400-300-200-100 100 200 300 400 500 0.2 0.4 0.6 0.8 1 1.2 1.4 frequency magnitude The LPFs designed using the MATLAB built-in routines yield magnitude responses that are generally much closer to ideal than the truncated-sinc LPF. The passband from firls is very flat, while that from the truncated-sinc 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 truncated-sinc 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 window-based 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