A continuous-time signal x 0 (t) is band limited to 5 kHz, i.e., x 0 (t) has a spectrum X a(I) that is zero for |f| > 5 kHz. Only 10 seconds of the signal has been recorded and is available for processing. We would like to estimate the power spectrum of xa(t) using the available data in a radix-2 FFT algorithm, and it is required that the estimate have a resolution of at least 10 Hz. Suppose that we use Bartlett's method of periodogram averaging.
(a) If the data is sampled at the Nyquist rate, what is the minimum section length that you may use to get the desired resolution?
(b) Using the minimum section length determined in part (a), with 10 seconds of data, how many sections are available for averaging?
(c) How does your choice of the sampling rate affect the resolution and variance of your estimate? Are there any benefits to sampling above the Nyquist rate?