A bandlimited continuous-time signal has a bandlimited power spectrum that is zero for || 2(10 4 ) rad/s. The signal is sampled at a

A bandlimited continuous-time signal has a bandlimited power spectrum that is zero for |Ω| ≥ 2π(10⁴) rad/s. The signal is sampled at a rate of 20,000 samples/s over a time interval of 10 s. The power spectrum of the signal is estimated by the method of averaging periodograms as described in Section 10.6.3.

(a) What is the length Q (number of samples) of the data record?

(b) If a radix-2 FFT program is used to compute the periodograms, what is the minimum length N if we wish to obtain estimates of the power spectrum at equally spaced frequencies no more than 10 Hz apart?

(c) If the segment length L is equal to the FFT length N in part (b), how many segments K are available if the segments do not overlap?

(d) Suppose that we wish to reduce the variance of the spectrum estimates by a factor of 10 while maintaining the frequency spacing of part (b). Give two methods of doing this. Do these two methods give the same results? If not, explain how they differ.