An analog signal consisting of a sum of sinusoids was sampled with a sampling rate of fs = 10000 samples/s to obtain x[n] = xc(nT ). Four spectrograms showing the timedependent Fourier transform |X[n, λ)| were computed using either a rectangular or a Hamming window. They are plotted in Figure P10.32. (A log amplitude scale is used, and only the top 35 dB is shown.)

(a) Which spectrograms were computed with a rectangular window? (a) (b) (c) (d)

(b) Which pair (or pairs) of spectrograms have approximately the same frequency resolution? (a&b) (b&d) (c&d) (a&d) (b&c)

(c) Which spectrogram has the shortest time window? (a) (b) (c) (d)

(d) To the nearest 100 samples, estimate the window length L (in samples) of the window in spectrogram (b).

(e) Use the spectrographic data in Figure P10.32 to assist you in writing an equation (or equations) for an analog sum of sinusoids xc(t), which when sampled at a sampling rate of fs = 10000, would produce the above spectrograms. Be as complete as you can in your description of the signal. Indicate any parameters that cannot be obtained from the spectrogram.