MatLAB Answers

Compute the 8-point DFT of a sequence x(n) = {1/a, 1/b, 1/c, 1/d, 0, 0, 0, 0} using radix-2 

DIT FFT

Compute Z-transform of the following signals along with the RoC and verify the result with MATLAB result and attach screen shot of code and results:

(a) 𝑥(𝑛) = (1/𝑅𝐹) 𝑛𝑢(𝑛) + (1/𝑅𝐿) 𝑛𝑢(𝑛)

where RF = 12 RL = 56

Also take inverse Z-transform of computed X(z) and verify the result on page as well as in MATLAB.

Compute 4-point DFT of following signal using (a) metrices method (b) DIT FFT:

x(n) = last four digits of your registration number

Hint: let’s your registration number is 11204316 then x (n) = { 4, 3, 1, 6}

Compute Z-transform of the following signals along with the RoC and verify the result  with MATLAB result and attach screen shot of code and results:

(a) 𝑥(𝑛) = (1/𝑅𝐹)

𝑛𝑢(𝑛) + (1/𝑅𝐿)

𝑛𝑢(𝑛)

where RF = First two digits of your Registration Number

RL = last two digits of your Registration Number

Also take inverse Z-transform of computed X(z) and verify the result on page as well 

as in MATLAB.

Compute the linear convolution and cross correlation of following two signals x(n) and 

h(n) on page and in MATLAB and attach screen shot of code and results: 

x(n) = First four digits of your Registration Number

h(n) = Last four digits of your Registration Number

Hint: let’s your registration number is 11204316 then x (n) = {1, 1, 2, 0} and h(n) = {4, 3, 1, 6} 

If x1(n) = 5Sin(2πf1n) and x2(n) = 5Cos(2πf2n), then plot following signals in MATLAB  and attach screen shots of code and result 

(a) y1(n) = x1(n) + x2(n) (b) y2(n) = x1(n) – x2(n) 

note: f1 = f2 = Last two digits of your Registration Number

Hint: If last two digits of your registration number are 00 then take first two digits of your registration 

number as R (if last digits are say 05, then consider R = 5)

Plot the following signals on page and in MATLAB, considering x(n) = your 

registration number:

(a) x(n-2)

(b) x(n+3)

(c) x(-n+2)

(d) x(-n-3)

Hint: let your registration number be 11204316 then x (n) = {1, 1, 2, 0, 4, 3, 1, 6}, and 4th sample value 

will be at n = 0 time.

 Use your program to find the 200-point DFT of the following sequences:

(i) x(n) = 2cos(2πn/10) + cos(2πn/5)

(ii) x(n) = n

Plot the magnitude response of these sequences. The horizontal axis must be scaled appropriately to represent the interval (0, π). Also Comment on the validity of your results.

Write a program to compute the circular convolution of two length-N sequences via the DFT ap-

proach. Use your DFT and IDFT programs for this purpose.

Use your programs (using calling function) to

nd the circular convolution of the following pairs of sequences:

(i) x(n) = [1; 3;-2; 4; 7], h(n) = [3; 1; 21;-3]

(ii) x(n) = n; h(n) = (0:5)^n, 0 < n <10

Write a program to compute the N-point inverse-DFT (IDFT) of a sequence. DO not use the inbuilt command. Test your program on the DFTs of the sequences in the previous part.