Fourier Transform using MATLAB Symbolic Math toolbox only of

Fourier Transform (using MATLAB Symbolic Math toolbox only) of

and

Solution

Solutions:

Functions can be directly defined using symbolic tool box.

\'syms\' command defines a symbol.

\'fourier(f)\' directly gives the symbolic fourier transform of f

e^-at will not have fourier transform. Insted we used e^-atU(t) by using heaviside function of MATLAB.

The MATLAB CODE is given below

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syms t
a=3;
w0=20*pi;
f1 = exp(-a*t)*heaviside(t);
F1=fourier(f1)
f2=sin(w0*t);
F2=fourier(f2)

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The output (shown below) gives F1 and F2 which are fourier transforms of given functions respectively.

>> fourier_symb

F1 =

1/(w*i + 3)


F2=

-pi*(dirac(w - 20*pi) - dirac(20*pi + w))*i

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dirac means unit impulse function