Highlights
1. The analog signal x(t) is band-limited to 40 Hz. Suppose the signal is sampled at the rate of 100 samples per second and that at this rate 200 samples are collected. 200 zeros are appended to the 200 samples to form a 400-point vector. Then the 400-point DFT of this vector is computed to get X(k) for0 ≤ k ≤ 399.
a) Which DFT coefficients are free of aliasing?
b) The DFT coefficient X(50) represents the spectrum of the analog signal at what frequency f? (Give your answer in Hz).
2. Analog touch tone push-button telephones use a system called dual-tone multi-frequency signaling (DTMF) to communicate to the telephone switch which button is being pressed. Each button produces a combination of two sine tones:
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