a A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc The filter operates at a sampling frequency of 20 kHz b A continuous time signal is given to the input of the system in Figure The signal is given as follows with f 10 kHz, f 20 kHz, and f3 40 kHz i Compute the resultant discrete time signal ii Use the notch filter designed in part (a), as the LTI system, to process the input signal x n III Construct the output y(t), assuming ideal reconstruction 1 x(t) 2 cos(2nft) cos(2nft) cos(2nfat)

Question: a. A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc. The filter operates at

a. A notch filter is required to be designed, that produces a null at 5 kHz and unity gain at dc. The filter operates at a sampling frequency of 20 kHz.

b. A continuous time signal is given to the input of the system in Figure. The signal is given as follows with f₁ = 10 kHz, |f₂ = 20 kHz, and f3 = 40 kHz:

1 x(t) = 2 cos(2nft) - cos(2nft) += cos(2nfat)

i. Compute the resultant discrete-time signal?

ii. Use the notch filter designed in part (a), as the LTI system, to process the input signal x[n].

III. Construct the output y(t), assuming ideal reconstruction.

1 x(t) = 2 cos(2nft) - cos(2nft) += cos(2nfat)

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