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:  

 

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)