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8 Discrete Time Signals In Frequency Domain
8
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The output of a linear system to a sinusoidal input is a sinusoid of the same frequency but
with a different magnitude and phase
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This information is called the system's frequency response
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Given one, you can calculate the
other
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8
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X(ejω) can alternately be expressed in the form

The quantity |X(e ejω)| is called the magnitude function and the quantity θ(ω) is called the phase
function
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The DTFT X (ejω) is a periodic continuous function in ω with a period 2π
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MATLAB Commands:
For complex Z, the magnitude R and phase angle theta are given by:
R = abs (Z)
Theta = angle (Z)

Y = fft(X) returns the discrete Fourier transform of vector X, computed with a fast Fourier
transform (FFT) algorithm
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Y = fft(X, n)

Fast Fourier Transform:

The Fast Fourier Transform (FFT) is just a computationally fast way to calculate the DFT
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Use the FFT (Fast Fourier
Transform) function
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Determine the Fourier transform of the following sequence
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Compute the discrete Fourier transform of the following function analytically and
then
Plot the magnitude and phase
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Given below is the frequency response of the system,
H(ejw) =

1+e-jw

1-e-jw+0
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Taking w = -4*pi:8*pi/511:4*pi;

34 | P a g e



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