A random signal is generated by passing zero-mean white Gaussian noise with unit varianc...

A random signal is generated by passing zero-mean white Gaussian noise with unit variance through a filter with system function

(a) Sketch a typical plot of the theoretical power spectrum for a small value of the parameter a (i.e., 0 < a < 0.1). Pay careful attention to the value of the two spectral peaks and the value of

(b) Let a = 0.1. Determine the section length Al required to resolve the spectral peaks of when using Bartlett's method.

(c) Consider the Blackman-Tukey method of smoothing the periodogram. How many lags of the correlation estimate must be used to obtain resolution comparable to that of the Bartlett estimate considered in part (b)? How many data points must be used if the variance of the estimate is to be comparable to that of a four-section Bartlett estimate?

(d) For a = 0.05, fit an AR(4) model to 100 samples of the data based on the Yule-Walker method and plot the power spectrum. Avoid transient effects by discarding the first 200 samples of the data.

(e) Repeat part (d) with the Burg method.

(f) Repeat parts (d) and (e) for 50 data samples and comment on similarities and differences in the results.