Design of Raised Cosine Matched Filters

The impulse response of a pair of matched filters that results in a raised cosine spectrum is given in Eq. (7.5.2). A simple way to design these filters is to window the sampled version of the filter impulse response and design an FIR filter with the windowed sampled impulse response. In this project we examine the time and frequency response of this approach for a particular design specification. Assume that the rolloff factor of the raised cosine pulse is 0.1, the length of each FIR filter is 23 taps, and the sampling rate is T /4, with 1/T the transmission rate of the pulses.

(a) If the design uses a rectangular window, sketch the overall back-to-back impulse response of the transmitter and receiver filters. What is the variance of the ISI caused by the filter if the center tap is normalized to 1?

(b) Using MATLAB or an alternative computation tool, calculate and plot the frequency response of the filter. What is the minimum attenuation in the sidelobes and the percentage of power in the main lobe?

(c) Repeat parts (a) and (b) for a triangular window.

(d) If the design criterion is to minimize the out-of-band component of the spectrum, which window is your choice? If the design criteria is to minimize the ISI, which window is your choice?