Question

me) = est ult-2) (Please do fourier transform then plot) and m(t) e 3t uct-2) cos (2ooort)

I would like to have a better understanding of how to do Fourier transformations on Matlab.

If this is possible. Please show me how to:

1. have Matlab FIND the Fourier transformation of the two functions above. They do not have to be in the same program or anything. I just want to understand the syntax and semantics better.

2. THEN plot the Fourier transform that you found
VIA MATLAB.

The main thing that I am trying to do is to be able to check to see if my Fourier transformations solved on paper are correct to make things easier in the future. comments in the code would be greatly appreciated!

Thank you.

Answer 1

First I am giving you basic example of Fourier Transform

1  

We know that Fourier Transform of dirac(t) =1

Now Using MATLAB

clc
syms t % symbolic t
f = dirac(t);
f_FT = fourier(f) % Symbolic Fourier Transform

Result:

f_FT =
1

clc syms t symbolic t f = dirac(t); f_FT = fourier (f) Symbolic Fourier Transform Command Window f_FT =

2.

Now Check for Unit Step

$\bg_white \fn_jvn \large F\left (u(t) \right )=\frac{-j}{\omega }+\pi *dirac\left ( t \right )$

Using MATLAB CODE

clc
syms t % symbolic t
f = heaviside(t); % Heaviside is unit step function
f_FT = fourier(f) % Symbolic Fourier Transform

Result:

f_FT =
pi*dirac(w) - 1i/w

Now coming to given Problems

1.

f= exp(-3*t)*u(t-2)

MATLAB CODE

syms t % symbolic t
f = exp(-3*t)*heaviside(t-2);
f_FT = fourier(f) % Symbolic Fourier Transform

RESULT:

f_FT =
exp(- w*2i - 6)/(3 + w*1i)
>>

syms t symbolic t f = exp(-3*t) heaviside (t-2); f_FT = fourier (1) Symbolic Fourtier Transform Command Window f FT = exp (- W*2i - 6)/(3 + w*li)

2.

f= exp(-3*t)*u(t-2)*cos(2000*pi*t)

MATLAB CODE

syms t % symbolic t
f = exp(-3*t)*heaviside(t-2)*cos(2000*pi*t);
f_FT = fourier(f) % Symbolic Fourier Transform

RESULT:

>> symbolic_fft
f_FT =
exp(- w*2i - 6)/(2*(w*1i - pi*2000i + 3)) + exp(- w*2i - 6)/(2*(w*1i + pi*2000i + 3))

syms t symbolic t f = exp(-3*t) *heaviside (t-2) *COS (2000*pi*t); f_FT = fourier(1) Symbolic Fourier Transform Command Window >> symbolic_fft f FT = exp(- w2i - 6)/(2* (w*li - pi*2000i + 3)) + exp(- w*2i - 6)/(2* (w li + pi*2000i + 3)) fx >>

If you have any doubt ,please feel free to ask in comment section.

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