Digital Signal Processing Practice (EC3002)
Experiment 3: Frequency Domain Analysis
September 5, 2023
1. Verify the frequency shifting property of the Discrete Time Fourier Transform for the following
signals
nπ ; 0 ≤ n ≤ 100
x(n) = cos
2
jπn
y(n) = e 4 x(n)
Note: Plot magnitude and phase of both signals x(n) and y(n) at 501 equispaced points between
[0, π] to verify.
2. An LTI system is described by the difference equation
y(n) = 0.8y(n − 1) + x(n)
1. Determine H e
jω
.
2. Calculate and plot the steady-state response yss (n) to the input signal
x(n) = cos(0.005n)u(n)
Note: Plot magnitude and phase of both signals x(n) and yss (n) at 101 equispaced points to verify.
3. Consider the filter described by the difference equation
√
1
y(n) = √ y(n − 1) − x(n) + 2x(n − 1)
2
Plot the magnitude and the phase response of this filter, and verify the type of filter.
Note: Plot magnitude and phase of the filter at 501 equispaced points between [0, π] to verify.
4. A system is described by the difference equation
y(n) = 0.81y(n − 2) + x(n) − x(n − 2)
Plot the magnitude and the phase response of this filter, and verify the type of filter.
Note: Plot magnitude and phase of the filter at 501 equispaced points between [0, π] to verify.
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