ENG201: Define a row vector v = (10 7 4 1 -2) using colon operator: Linear Systems Analysis & Design Individual Lab Report, SUSS, Singapore

Question 1

(a) Define a row vector v = (10 7 4 1 -2) using colon operator.

(b) Convert the vector generated in Question 1(a) into a column vector.

(d) Use one command to indicate only the third columns of matrix A defined in Question 1(c).

Question 2
Let the discrete-time signal

Use the MATLAB commands fft and fftshift to numerically calculate and plot the DTFT of the following signals in the frequency range from –π to π radians: (a) x[n]
(b) y[n] = x[2n]
(c) z[n] = x[4n]

Question 3
Use MATLAB to determine the output of the given LTI system where the input is x[n] = −u[n] + 2u[n − 3] − u[n − 6]
and the system’s impulse response is
h[n] = u[n +1] − u[n −10].

Question 4
Solve for the partial-fraction expansion for Y(z) where