ENGR2722_8722 - Analysis of Engineering Systems - MATLAB - Engineering Assignment Help

ENGR2722_8722:  Analysis of Engineering Systems Assignment Help

Assignment Task:

2) Calculate signal x(t) as the summation of the three signals x1(t) , x2(t) , x3(t)

3) Use subplot to plot the signal x(t) and signals x1(t) , x2(t) , x3(t)

4) Calculate the discrete Fourier transform of the signals x(t) ,x1 (t), x2 (t), x3 (t) using command fft.

5) Use subplot to plot the magnitude of the calculated discrete Fourier transform of the signals.

6) Use subplot to plot the phase of the calculated discrete Fourier transform of the signals. Hint: for parts 5 and 6, the x-axis is frequency and can be defined as;

f = linspace( 0, fs, numel( t)); Use the command abs(.) for plotting magnitude and command unwrap(angle(.)) for phase

7) If we consider only the middle frequency to be of interest, find the frequency response H(jω) of an LTI system that filters out the higher and lower frequencies.
Hint: you can apply an input X(jω) = X1 (jω)+X2(jω) + X3

(jω) to the system, and the output must be of the form Y(jω) = X2 (jω).

Then Fourier transform multiplication property: Y(jω) = H(jω) × X(jω) allows you to solve for H(jω).

8) Plot the magnitude and phase of the frequency response.

9) Calculate the impulse response as the inverse Fourier transform of the frequency response h(t) = F −1

{H(jω)} using command ifft.

10) Plot the impulse response of the system.

11) Calculate the convolution between the impulse response and the input x(t) to find the expected output of the system, using command Conv.

12) Compare the output of your system with the expected output.

Hint: use the subplot command and plot expected output, and output of the system.

Remember when we convolve two sequences of length N1 andN2, the result is of length N1 + N2 − 1. In our exampleN1 = N2 = 1001. If the two sequences range over intervals t1: ?t:t2 and t3: ?t:t4, then the result of the convolution will range over t1 + t3: ?t:t2 + t4. Thus, we plot the expected output using:

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