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For a continuous time signal with spectrum $$X_c(j\Omega)=1 \quad\text{for} \quad10\pi < |\Omega| < 50 \pi$$

Choose the minimum sampling frequency so that there is no overlap in the spectrum of replicas.

I want to know the formula for calculating minimum sampling frequency using the frequency range given above to avoid aliasing.

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First, let's exclude the process of quadrature sampling as a solution. Notice that you signal's lowest frequency is smaller than the signal's bandwidth. As such, bandpass sampling is not possible to avoid aliasing. So, ...standard lowpass sampling is your only choice in which case you should merely apply the Nyquist Criterion to your problem. (Also, note that your problem's given signal frequency dimensions are radians/second and not cycles/second.)

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  • $\begingroup$ Having been doing lots of image processing lately -- you just assume it's radians per second. It could be radians/year, radians/screen, radians/cubit, etc. $\endgroup$
    – TimWescott
    Nov 13, 2022 at 17:30

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