Signals using MatLab

Result should look like this:

The FIR filter of the previous problem had linear phase and therefore, its phase-delay was constant indepen- dent of frequency. For many filters, the phase delay. T(w) =-LH(w)/w" is a non-trivial function of w. and therefore, input components of different frequencies suffer different amounts of delays (and attenuations) as they go through the filter. Consider a peaking filter (see Appendix (13)) with peak frequency wo and bandwidth parameter B. Its derivation will be given later in the course. Here, we simply use the result of (13). The frequency response is obtained by setting z into (13): 2ju The corresponding numerator and denominator coefficient vectors are Show analytically (you may use MATLAB's symbolic toolbox) that H(w) can also be written as (5 points) H (w) = cou- It follows that H(wo) = 1. Thus, an input sinusoid 2(n)-sin(won) will suffer no phase delay or amplitude modification. From (9), it follows that the phase delay is: cos w-COS WO arctan (10) = 3 sin w Next, consider an input sinusoid at some side frequency wi near wo 2(n) = sin(win) The corresponding steady-state output is given by y(n) = H, sin(win + ), where, H, = lH(w1)0, = ArgH(w), or, H(w1)-H, ejel Now consider the following four problems, example plots for which are given in Fig. 3 Problem 2.1 (5 points). Consider the following values, ao 0.2, = 0.1, and wi = 0.05m. Make a plot (2.5 points) of the magnitude response of the filter, H (w), over the range 0