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In this lab, you will use different methods to design a filters that satisfy the following gain specifications (note that gains are specified in dB): 20 log1o (H(e)"I/<-50 w <0.1m 2 < 20 log1o [H(er)I<4 0.2m < E <0.4x 2010g10 0.5m < w <0.6m 1 < 20 logio 0.7% 20 log1o 0.9m swst For each of the following design methods, find the minimam length filter that meets the specifi- cations. Demonstrate graphically that your filter satisfies the given specifications (i.e., show plots that zoom in on the various transition regions with a grid). 1. Windowing method (you can use any window) 2. Frequency sampling method 3. Matlab's fir1 algorithm. 4. Parks-McClellan algorithm (firpe). 5. Parallel combination of elliptical IIR filters. For this last approach, plot the phase response and group delay of your design, and discuss the resulting phase distortion of the filter.

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