signal is sampled with a sampling frequency of 44.1 KHz. A design engineer claim

Question

 signal is sampled with a sampling frequency of 44.1 KHz. A design engineer claim that the sampled signal is perfectly reconstructed by low pass filter in each of the following cases: Whether his claim is correct? Give justifications.

band limiting low pass filter frequency response is zero for all frequencies above 16KHz.

band limiting low pass filter frequency response is zero for all frequencies above 26KHz.

band limiting low pass filter frequency response is zero for all frequencies above 22.05KHz.

Explanation / Answer

Given sampling frequency = 44.1 KHz.

According to the Nyquist Theorem, the sampling rate must be at least 2fmax, or twice the highest analog frequency component.

sampling rate must = 2fmax

fmax = sampling rate / 2

       = 44.1 kHz / 2

       = 22.05 kHz

Case 1 : -

If band limiting low pass filter has frequency of 16KHz, then frequncies above 16 kHz are not reconstructed. Therefore it is not a valid case.

Case 2 : -

If band limiting low pass filter has frequency of 26KHz, it can be used to reconstruct te sample signal of 44.1 kHz. Therefore it is a valid case.

Case 3 : -

If band limiting low pass filter has frequency of 22.05KHz, it can be used to reconstruct the sample signal of 44.1 kHz.

It should be the ideal filter , but it is not possible, So practically it is not used.

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