Operations and Principles
docsity.com
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
DFT Operation And Principles part 1-Digital Signal Processing-Lecture Slides, Slides of Digital Signal Processing
Prof. Gunaratna Setty delivered this lecture at Gujarat Ayurved University for Digital Signal Processing course. It includes: Operation, Principles, Digital, Signal, Processing, Aperiodic, Spectrum, Continuous
Typology: Slides
2011/2012
1 / 15
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download DFT Operation And Principles part 1-Digital Signal Processing-Lecture Slides and more Slides Digital Signal Processing in PDF only on Docsity!
Operations and Principles
Signal(Time)
Spectrum(Freq)
Periodic
Periodic and discrete
Aperiodic
Aperiodic and continuous
Time Domain
Frequency
Domain
Signal Sampled
Replicas appear
Spectrum Sampled
Computer doesn’t know continuous thingssuch as DTFT.
In order to perform Linear Filtering, we need tohave spectrum stored in the computer for e.g Circular Convolution
N o w w e can say d ivid e th e ran g e - in to in fin ite p erio d s each w ith len g th
, g o t th at!
(
)
(
)
(
)
(
)
(
)
L et u s su b stitu te
k
k
lN
N
j
n
j
n
N
N
s
n
l
n
lN
k
lN
N
j
n
N
s
l
n
lN
n
N
X
k
x n e
x n e
X
k
x n e
n
, th en
(
)
(
)
(
)
(
)
W e k n o w rearran g e th e o rd er o f su m m atio n.
(
)
(
)
(1 )
k
N
j
n
lN
N
s
l
n
k
N
j
n
N
s
l
n
k
N
j
n
N
s
n
l
n
lN
X
k
x n
lN
e
X
k
x n
lN
e
X
k
x n
lN
e
Now
(
) is a periodic signal
(
) with
period
.
According to fourier series analysis equation
1
(
)
and it can be compared with eq(1)
(
)
(
)
l
p
l
k
N
j
n
N
k
p
n
N
s
n
l
x n
lN
x
n
N
c
x
n e
N
X
k
x n
lN
(1)
(
)
and according to fourier series synthesis equation
1
(
)
(
)
k
j
n
N
k
s
k
k
N
N
j
n
j
n
N
N
p
k
s
k
k
e
c
X
k
x
n
c e
X
k
e
N
When DTFT is sampled, it becomes discreteand we called it as
Discrete Fourier
Transform
. It is described as
( )
( )
, ,
,....
N
kn
N
n j
N
N
X k
x n W
k
N
where W
e
1
0
2
0 1 2
1
1
2
1
2
4
2(
3
6
3(
1
2(
(
1)(
1
1
1
.
.
.
1
(0)
(0)
1
.
.
.
(1)
(1)
1
.
.
.
(2)
(2)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
.
.
.
(
(
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
X
x
W
W
W
X
x
W
W
W
X
x
W
W
W
W
W
W
X N
x N
docsity.com
( )
p
x
n
(
p
x
n
(
p
x
n
(
p
x
n
Circular shift of a sequence is given as
'( )
(
, mod
)
'( )
((
))
Circular shift is same as performing rotationon a signal.
N
x
n
x n
k
N
x
n
x
n
k