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DIGITAL SIGNAL PROCESSING PRACTICE PROBLEM 2

1. Determine the DFT of the sequence() = {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. () = {2, 1, 2, 1} () = {1, 2, 3, 4}

ii. () = {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. () = {2, 2, 1, 1} ii. () = {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.

() = {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 () for 0 3 where (0) = 1, (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 (3) in time domain.

b. Determine the frequency resolution and highest frequency in the spectrum.

8. A speech signal is sampled at 8KHz. A DFT is computed of a block of 1024

samples of the data. a. What is the duration of the block? b. What is the frequency resolution of DFT? c. If only 512 samples were taken but the block was zero bedded to

restore the size to 1024, what would be the new answer to a & b?

DSP Practice Problem 2DSP Practice Problem 2 - Solution