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Lab 5 CS

The document outlines an experiment focused on the MATLAB implementation of the Continuous Time Fourier Transform (CTFT). It details objectives, introduces the Fourier Transform concepts, and provides MATLAB functions and steps for computation and plotting of various signals' Fourier Transforms. Additionally, it lists specific lab tasks involving different pulse functions and their Fourier Transforms.

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maliha khan
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14 views3 pages

Lab 5 CS

The document outlines an experiment focused on the MATLAB implementation of the Continuous Time Fourier Transform (CTFT). It details objectives, introduces the Fourier Transform concepts, and provides MATLAB functions and steps for computation and plotting of various signals' Fourier Transforms. Additionally, it lists specific lab tasks involving different pulse functions and their Fourier Transforms.

Uploaded by

maliha khan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Experiment # 5

MATLAB Implementation of Continuous Time Fourier Transform

5.1 Objective

 To understand and implement the CTFT using MATLAB.

5.2 Introduction to Fourier Transform

The Fourier Transform expresses the signal (or function) g(t) in the frequency domain, the signal
is described by a function G(f). The Fourier Transform is denoted by the symbol F[.] and inverse
Fourier Transform is represented as F-1[.], as

G(f) = F[g(t)] and g(t) = F-1[G(f)]

g(t)  G(f)

To recapitulate,

where w=2 π f

5.3 MATLAB Functions

 fourier(): to calculate Fourier Transform


 ifourier(): to calculate inverse Fourier Transform
 int(): for symbolic integration

Steps:

 Define t and w as symbolic variable.


 Define function for which fourier transform has to be calculated.
 Calculate fourier transform by using in-built function or by using the definition of Fourier
transform with the help of int() function.
 Define the range of frequency w.
 Substitute value of w in above calculated Fourier Transform function using command
“subs()”.
 Plot w.r.t frequency w. To plot magnitude, use abs(X), for phase use angle(X), for real
and imaginary part use real(X), imag(X) respectively.

5.4 Lab Tasks

1. Compute and plot the Fourier Transform of the rectangular pulse and find inverse Fourier
transform of rectangular pulse.

Hint: Use bulit-in function heaviside() or rectangularPulse() to define rectangular pulse

2. Compute and plot the Fourier Transform of the triangular pulse.

Hint: Use built-in function triangularPulse() to define triangular pulse.


2
3. Compute and plot the Fourier Transform of the function e−t .
4. Compute and plot the Fourier Transform of the impulse function. Use dirac() to define
impulse function.
5. Compute and plot the Fourier Transform of the function of cos 2 π f0t and sin 2 π f0t.
6. Compute the Fourier transform of the signal e−t u(t) and compare the results with previous
task. Plot magnitude, angle, real and imaginary part
Hint: To define u(t) use built-in function heaviside()
7. Compute and plot the Fourier Transform of the function sinc(x) = sin( π x)/ π x and
calculate inverse Fourier of sinc function.

5.5 Conclusion
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