Biomedical Engineering > GATE 2023 > Sampling
A continuous time, band limited signal x(t) has its Fourier transform described by:
The signal is uniformly sampled at a sampling rate of 600 Hz. The Fourier transform of the sampled signal is Xs(f). What is the value of Xs(600)/Xs(500)? (Round off the answer to one decimal place.)
Correct : 0.5
The correct answer is 0.5.
Here, the signal x(t) is band-limited and sampled uniformly at fs = 600 Hz. When a signal is sampled, the Fourier transform of the sampled signal Xs(f) is given by the superposition of the original spectrum X(f) shifted by multiples of the sampling frequency fs.
So, Xs(f) = (1/T) Σ X(f - nfs), where T = 1/fs.
At f = 500 Hz, only one shifted copy of X(f) contributes a non-zero value. But at f = 600 Hz, the overlapping shifted copies together contribute a value that is exactly half of what we get at f = 500 Hz.
Therefore, Xs(600) / Xs(500) = 0.5.
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