Problem 3 This question concerns evaluating the bandwidth of a signal. There are many different definitions on how bandwidth should be measured. In...
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Problem 3 This question concerns evaluating the bandwidth of a signal. There are many
different definitions on how bandwidth should be measured. In this question we adopt the 3-dB
bandwidth. Suppose that the given signal g(t) is lowpass. The 3-dB bandwidth for a lowpass signal
is defined as the separation between f = 0, at which the amplitude spectrum is assumed to attain
its peak value, and a frequency point f = Br, at which the amplitude spectrum drops to 1/v2 of
its peak value. Mathematically we may write
IG(BT)I
IG(0)|
V2
where G(f) is the Fourier transform of the signal. The value By obtained is the 3-dB bandwidth.
(a) (15%) Find the 3-dB bandwidth of the lowpass signal
g(t) = 1 0,
e-20nt t > 0
t<0
(b) (15%) What would you say about the 3-dB bandwidth of the following bandpass signal
g (t) = 0,
e-20nt cos(27 fct), t> 0
t<0
where the frequency fc > 0 is very large. Note that you may slightly change the definition of
the 3-dB bandwidth to fit this problem better.

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