I appreciate any help with the following questions: (1) You are given an input s

Question

I appreciate any help with the following questions:

(1) You are given an input signal with a maximum input frequency of 1 kHz. Also, given that the Nyquist criteria of a minimum sampling frequency is two times the highest input frequency, are there any potential problems of sampling the input signal at a sampling rate of exactly 2 kHz?

What if there is no antialiasing input filter and the input signal exceeds the Nyquist sampling frequency criteria to a value of 0.6 times fs ? What affect would this have on the output?

(2) Given a real-time digital signal processing system, how do the sampling frequency and the number of bits used in performing the analog-to-digital conversion of an analog input signal impact the design and performance of the system? What features of the system are affected by these two factors?

How are the memory requirements for the real-time digital signal processing system affected by the sampling frequency, f s ? For example, if f s is increased by a factor of 2, what affect does this have on the system memory requirements?

Explanation / Answer

(1) If the sampling rate is exactly 2 KHz, then the condition is fs=2fm. According to sampling theorem no guard band exists at this condition. So the signal can be recovered from its samples by using only an ideal low pass filter with sharp cutoff. This is practically may not be possible.

fm>0.6fs means fs<2fm. At this condition the output signal cannot be recovered properly from its samples.

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