What is the maximum distortion (% in amplitude and in time delay) that affects a low-pass...
What is the maximum distortion (% in amplitude and in time delay) that affects a low-pass signal of 1 Khz bandwidth, when it is transmitted through a channel with impulse response h(t)=300e-1000tu(t)
Homework Answers
The Fourier transform of the impulse response function is nothing but the frequency response of the system.
The Fourier transform is given by H(jw) = FT{300exp(-1000t)u(t)}
H(jw) = 300 / (jw + 1000)
The amplitude distortion at 1 kHz is given by
|H(j2pi1000)| = |300 / (j2*pi*1000 + 1000)| = 0.0472
Therefore the maximum amplitude distortion is given by (0.0472-1)/0.0472*100 = 2018%
Frequency of oscillation corresponding to 1kHz bandwidth is 1KHz
time period of oscillation is 1/1KHz = 1 ms. (this corresponds to 2*pi radians)
Phase delay is given by <H(j2pi1000) = 80.9 deg
time deay is given by Td = 1 ms * 80.9/360 = 0.224 ms
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