SIR SYED UNIVERSITY OF ENGINEERING & TECHNOLOGY DEPARTMENT OF ELECTRONIC ENGINEERING (021) 34988000‐5, http://www.ssuet.edu.pk DIGITAL SIGNAL PROCESSING PRACTICE PROBLEM 2 1. Determine the DFT of the sequenceݔ() = {1, 0, 0, 1}. Let data sequence be sampled at 8KHz. Determine the magnitude and phase calculations and also sketch them. Verify your answer result by calculating IDFT of the sequence. 2. Compute the DFT of the 4-point sequence by matrix method. x(n) = {0, 1, 2, 3} 3. Convolve the given sequence by circular method. i. ݔଵ () = {2,1,2,1} ݔଶ () = {1,2,3,4} ii. ℎ() = {0, 1, 2, 3} () = {1, 0.5, 1, 0.5, 1, 0.5, 1, 0.5} 4. Calculate the DFT of the data sequence by using the direct DFT method and also by using the DIT Radix-2 method. i. ݔ() = {2,2,1,1} ii. ݕ() = {0,2,4,1} 5. Compute the DFT of the 8-point sequence by direct DFT method and also by using the Radix-2 method. ℎ() = {−3, 2, 6, 2, 2, 5, 2, −7} 6. Determine the IDFT of the following sequences. i. () = (6 − 2 + 2 −2 − 2 − 2) ii. () = (6 1− 0 1 + ) 7. Given a sequence ݔ() for 0 ≤ ≤3 where ݔ(0) = 1, ݔ(1) = 2, x(2)=3 and x(3)=4. We have computed four DFT co-efficients () for 0 ≤ ≤ 3 as (0) = 10, (1) = −2 + 2, (2) = −2, (3) = −2 − 2. If the sampled rate is 10Hz; a. Determine the sampling period, time index, sampling time instant for a digital sample ݔ(3) in time domain. b. Determine the frequency resolution and highest frequency in the spectrum.