MatLAB Answers

Determine a and b for which f(x) = a sin(πx/2) + b cos(πx/2) fits the following data in the least-squares sense:-

(solve using MATLAB with steps).

x = −0.5, −0.19, 0.02, 0.20, 0.35, 0.50.

y =−3.558 , −2.874 , −1.995 , −1.040, −0.068, 0.677.

The formula for normalizing data-in a vector x-into the range [0,1] is given by

Z1=(x1-min(x))/(max(x)-min(x))

implement the formula above in a function

Plot the following functions on the same graph for x values from -π to π. selecting spacing to create a smooth plot: y1 = sin (x) y2 = sin(2x) y3 = sin(3x)

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.