A 10 kHz sinusoid is sampled at 15 k samples/s. The sampled signal passes through an ideal low-pass filter with 25 kHz cutoff. Find the maximum output frequency component in kHz.
Sampling produces replicas at frequencies $|kf_s\pm f_0|$ for integer k. With $f_s=15$ kHz and $f_0=10$ kHz, nonnegative components include 5, 10, 20, 25, 35, 40 kHz and higher. The ideal filter retains those up to its stated cutoff, so the greatest is 25 kHz, under the question’s inclusive cutoff convention.
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