Scribd
Upload
365 views11 pages

DTFT Presentation

The document discusses the discrete-time Fourier transform (DTFT). It provides definitions of the DTFT, including that it operates on discrete data samples and produces a periodic summation of the continuous Fourier transform. The document outlines properties of the DTFT, differences between the DTFT and discrete-time Fourier series, and applications of representing signals in the time and frequency domains using the DTFT.

Uploaded by

AAYUSH RIJAL
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
365 views11 pages

DTFT Presentation

The document discusses the discrete-time Fourier transform (DTFT). It provides definitions of the DTFT, including that it operates on discrete data samples and produces a periodic summation of the continuous Fourier transform. The document outlines properties of the DTFT, differences between the DTFT and discrete-time Fourier series, and applications of representing signals in the time and frequency domains using the DTFT.

Uploaded by

AAYUSH RIJAL
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 11

Group: F

● Shadab Nafis (1604239)


● Aayush Rijal (1604241)
Discrete Time ● Shreyasi Mazumder (1604242)

Fourier ● Shubhangi Suman (1604244)


● Soham Roy (1604246)
Transform ● Sombit Ghosal (1604247)
● Soumalya Chakrabarti (1604248)
History of DTFT
● The Discrete-Time Fourier Transform (DTFT) tells us that from a discrete
set of samples of a continuous function, we can find periodic summation of
Fourier transform of the samples.
● Under certain theoretical conditions, described by the sampling theorem, the
original continuous function can be recovered perfectly from the DTFT and
thus from the original discrete samples.
● That famous theorem is called the Nyquist-Shannon sampling theorem.
● The term discrete-time refers to the fact that the transform operates on
discrete data (samples) whose interval often has units of time.
● From only the samples, it produces a function of frequency that is a periodic
summation of the continuous Fourier transform of the original continuous
function.
● The DTFT itself is a continuous function of frequency.
Definition of DTFT
The discrete-time Fourier transform is a form of Fourier analysis that is applicable
to the uniformly-spaced samples of a continuous function. The term discrete-time
refers to the fact that the transform operates on discrete data whose interval often
has units of time. The Discrete Time Fourier Transform (DTFT) is the member of
the Fourier transform family that operates on aperiodic, discrete signals.
Analysis and Synthesis Equations
Properties Of DTFT:-
Difference between DTFT and DTFS
. Fourier Series gives the harmonic content of a periodic time function.

.Fourier Transform gives the frequency information for an aperiodic signal.


DISCRETE TIME FOURIER SERIES DISCRETE TIME FOURIER
(DTFS) TRANSFORM (DTFT)

Time domain Discrete and periodic Discrete and aperiodic

Frequency spectrum Discrete and periodic Continuous and periodic

Determination
Time Domain And Frequency Domain Representation
Applications of DTFT
● The DTFT is defined to process an infinitely long signal (sum from
-infinity to infinity).
● The DTFT spectrum is continuous.
● Since it is impossible to process an infinite number of samples the
DTFT is of less importance for actual computational processing; it
mainly exists for analytical purposes.
● Instead of DFT is used as it is defined to process a periodic signal
(the periodic part being of finite length) and the DFT spectrum is
discrete.
CONCLUSION
So far we have studied analysis and synthesis equation for DTFT, properties of
DTFT, difference between DTFT and DTFS and represented spectral analysis of
DTFT along with some real life applications.

You might also like