1 a. A signal is sampled with a sampling frequency of 44.1 KHz. A design enginee

Question

1 a. A 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.
i. The band limiting low pass filter frequency response is zero for all frequencies above 16KHz.
ii. he band limiting low pass filter frequency response is zero for all frequencies above 26KHz.
iii. The band limiting low pass filter frequency response is zero for all frequencies above 22.05 KHz.

Explanation / Answer

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

sampling frequncy = 44.1 kHz

44.1/2 = 22.05

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

false

given that ,for a low pass pass filter has 16 kHz , it means that frequencies more than 16 kHz are not reconstructed

. hence this is not valid

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

true

given that ,for a low pass pass filter has 16 kHz , that is it allows upto 26 kHz ,as the max is 22.05 kHz ,

therfore it can be used for reconstruction

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

given that ,for a low pass pass filter has 22.05 kHz . as this is ideal filter but it is not possible for reconstruction, so practically it is not used.

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