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Let x(t) be a continuous-time, real valued signal band-limited to F Hz. The Nyquist sampling rate in Hz, For y(t) =x(0.5t) +x(t)-x(2t) is

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Let x(t) be a continuous-time, real valued signal band-limited to F Hz. The Nyquist sampling rate in Hz, For y(t) =x(0.5t) +x(t)-x(2t) is

(a) F

(b) 2F

(c) 4F

(d) 8F

The question was posed to me during an interview for a job.

The above asked question is from Spectrum Analysis of Sampling Process topic in chapter Digital Control Systems of Control Systems

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Right choice is (c) 4F

The best explanation: Expansion in time domain in compression in frequency domain and vice-versa. So, the maximum frequency component in given signal is 2F Hz. And according to sampling theorem.

Nyquist rate =2fm =4F Hz.

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