Fourier Transform e^(-t)

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himesh
himesh 2015-4-9
回答： hategekimana shadrack 2021-12-14
Hi. Why in MATLAB, why do we have to add a Heaviside function when doing Fourier transforms? For example when doing a Fourier transform of something simple, e.g. e^(-t), I get an error.
.
%%Error code
syms x w X
f = exp(-x)
X=fourier(f, x, w)
ezplot(X)
.
To fix this I need to write f = exp(-x)*heaviside(x);
Why is this?

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回答（3 个）

Torsten
Torsten 2015-4-10
Because your f is not integrable over IR, but only over IR+.
Or what is integral_{t=-oo}^{t=0} exp(-t) dt ?
Best wishes
Torsten.
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Torsten
Torsten 2015-4-10
I mean that
integral_{t=-oo}^{t=00} exp(-t) dt
does not exist, but only
integral_{t=0}^{t=oo} exp(-t) dt.
For the Fourier transform to exist, it would be necessary that
integral_{t=-oo}^{t=00} exp(-t) dt < oo
which is not the case.
Best wishes
Torsten.
himesh
himesh 2015-4-11
Thanks. I also have one last question and that is when plotting these, I have to write
ezplot(abs(X))
Why are there errors when I get rid of the abs() in the ezplot statement?
Many thanks

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sarath sai krishna babu gunupudi
Display the expression after computing Fourier Transform of u(t).
Save u(t) function in variable x and Fourier transform in variable xf.
hategekimana shadrack
Use matlab to calculate the Fourier series of the following periodic signals.
a. Draw the Amplitude spectrum of signal.

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