The Fourier transform of x2(t) is X2(w) and that of x3(t) is X3(@). If Â3(w) = X_(3w – 3wo) then c. express x3 (t) in terms of x2(t).

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Fourier Series and Transform
4nn
2nnt'
The Fourier series for a periodic signal x(t) shown below is x(t) =+
6
sin
cos
10
10
-9 -8
-3 -2 -1 0 1 2 3 4 5 6
8 9 10
-7 -6
-5
-4
Calculate the Fourier series for the periodic waveform x, (t) shown below in sine/cosine form.
а.
x1(t)
9 * -1 6 5 4 3 2 -1 0 1 2 3 4 5 6 7 8 9 10
b.
Calculate the Fourier series for the periodic waveform x1(t) shown in part (a) in complex exponential
form.
The Fourier transform of x2(t) is X,(w) and that of x3(t) is X3(@). If X3(@)
X2(3w – 3wo) then
с.
express x3(t) in terms of x2(t).
If the Fourier transform of x4(t) is X4(w), what is the Fourier transform of
y(t) = x4(-2t) * x4(2t), where * represents convolution? [Hint: Use Fourier transform properties]
d.
Transcribed Image Text:Fourier Series and Transform 4nn 2nnt' The Fourier series for a periodic signal x(t) shown below is x(t) =+ 6 sin cos 10 10 -9 -8 -3 -2 -1 0 1 2 3 4 5 6 8 9 10 -7 -6 -5 -4 Calculate the Fourier series for the periodic waveform x, (t) shown below in sine/cosine form. а. x1(t) 9 * -1 6 5 4 3 2 -1 0 1 2 3 4 5 6 7 8 9 10 b. Calculate the Fourier series for the periodic waveform x1(t) shown in part (a) in complex exponential form. The Fourier transform of x2(t) is X,(w) and that of x3(t) is X3(@). If X3(@) X2(3w – 3wo) then с. express x3(t) in terms of x2(t). If the Fourier transform of x4(t) is X4(w), what is the Fourier transform of y(t) = x4(-2t) * x4(2t), where * represents convolution? [Hint: Use Fourier transform properties] d.
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