Determine the 32 point Walsh transform, and the SAL, CAL, and power spectrum for the following data, generated from the MATLAB statements given. The data is sampled over a period of 8 seconds. For each case determine the predominant sequency of the data. Is the data based on an even (CAL) or odd (SAL) function?

a. Generate the data from p = [1 1 -1 -1]; x = [ p p p p p p p p];

b. Generate the data from p = [1 1 -1 -1]; x = [1 -1 -1 p p p p p p p 1];

Consider the function  y(t)=0.2cos(2πf1t)+0.35sin(2πf2t)+0.3sin(2πf3t)

where _{f1 =}20 Hz, f₂ =50 Hz, and f₃ =70 Hz. 512 equispaced samples of the function are taken over 2 seconds. Determine the Walsh power spectrum of the data. The function is closely related to the function of Example 8.2. How does the Walsh power spectrum compare with the Fourier power spectrum, shown in Fig. 8.6? Repeat the above analysis for the function:

y(t)=0.2sign(cos(2πf1t))+0.35sign(sin(2πf2t))+0.3sign(sin(2πf3t))

and again compare the Walsh and Fourier power spectra.