(TCO 7) You are sampling a signal which consists of a mixture of 86, 87 and 88 H

Question

(TCO 7) You are sampling a signal which consists of a mixture of 86, 87 and 88 Hz sinusoids and which you want to resolve in your FFT. If you are storing 4096 samples, what is the range of sampling frequencies you can use such that you don’t violate Nyquist theorem and still meet or exceed the needed resolution when you perform the FFT operation on the full set of collected data

any frequency greater than or equal to 176Hz
       less than or equal to 8132 Hz but greater than 176 Hz
       less than or equal to 16384 but greater than 176 Hz
       less than or equal to 4096 Hz but greater than 176

Explanation / Answer

sampling a signal consists of a mixture of 86, 87 and 88 Hz

sampling rate fs= 2 fmax

=2 x 88 Hz =176 Hz

according to Nyquist theorem the range of sampling frequencies should be less than or equal to 4096 Hz but greater than 176 Hz to perform the FFT operation on the full set of collected data

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