Let\'s assume we were given an x(n) discrete-time sequence, whose sample rate is

Question

Let's assume we were given an x(n) discrete-time sequence, whose sample rate is 20KHz, and its IX(f)l spectral magnitude is shown below. We were asked to design a linear-phase low-pass FIR filter to attenuate the undesired high-frequency noise, as seen in the spectral magnitude plot. Assume we already designed the filter and the frequency magnitude response of our filter is also shown below. 10 To be "filtered out de 10 (a) 20 -40 Freq (kHz) t/2) dB 20 -40 Freq (kHz) (t/2) Sometime later, we unfortunately learned that our original sequence x(n) had actually been obtained at 40KHz sampling rate and not at 20KHz! So do we need to do anything with our low-pass filter coefficients h(k)'s which were originally obtained based on the assumption of 20KHz sampling rate so that our filter still attenuates the high-frequency noise when the sample rate is actually 40KHz? If yes, what? If no, why not? Please discuss.

Explanation / Answer

Because of sampling, the the each frequency spectrum of original spectrum(before samplig)will Shift by sampling. If the Sampling frequency is greater than twice of maximum frequency present in the signal.

So The filtered out signal is greater than fm = fs / 2 = 4kHz.

As fs >>>fm

So the designed filter, still will work.because the desired frequency range is 0-4kHz.

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