A speech signal is sampled with a sampling rate of 16,000 samples/s (16 kHz). A window of 20-ms duration is used in time-dependent Fourier analyses of the signal, as described in section 10.3, with the window being advanced by 40 samples between computations of the DFT. Assume that the length of each DFT is N = 2^v.

(a) How many samples are there in each segment of speech selected by the window?

(b) What is the “frame rate” of the time-dependent Fourier analysis; i.e., how many DFT computations are done per second of input signal?

(c) What is the minimum size N of the DFT such that the original input signal can be reconstructed from the time-dependent Fourier transform?

(d) What is the spacing (in Hz) between the DFT samples for the minimum N from part (c)?