correlation of dts by er. sanyam s. saini me (reg) 2012-14
TRANSCRIPT
Presented By-
Er. Sanyam S. SainiME (I&CE) (Regular)
2012-14
Presented To-
Dr. Lini MathewAssociate Prof. (Electrical Deptt.)
NITTTR, Chandigarh
Correlation of Discrete-Time Signals
• Correlation gives a measure of similarity between two data sequence.
• Correlation is a comparison process.
• The correlation between two functions is a measure of their similarity.
• Correlation techniques are widely used in signal processing with
many applications in telecommunications, radar, medical
electronics, physics, astronomy, geophysics, fingerprint matching
etc.
Radar Target Detection
Reflected Signal, y(n)
y(n) = αx(n-D) + w(n)Here,y(n) = Sampled version of Received signalx(n) = Sampled version of transmitted signalw(n) = Noise that picked up by Antenna & noise
generated by electronic comp. & amp. In front of radar. (Additive Noise)
D = Round Trip Delayα = Attenuation factor (Loss in round trip transmission of x(n) )
Properties of Correlation
Detect wanted signal in the presence of noise or other unwanted signals.
1.
2.
3.
Example free space, various materials, solids, liquids, gases etc .
Recognise patterns within analogue, discrete-time or digital signals.
Allow the determination of time delays through various media.
Cross correlation Sequences
• In cross correlation, two ‘separate’ signals are compared.
.......3,2,1,0l
lnynxrn
xy
.......3,2,1,0l
nylnxrn
xyOr
If, we reverse the order of x(n) & y(n)
.......3,2,1,0l
lnxnyrn
yx
.......3,2,1,0l
nxlnyrn
yxOr
..........(i)
..........(ii)
On comparison
lrlr yxxy
Numerical on Cross correlation
Determine the cross correlation sequence of the following,
1,0,0,1nx 1,2,3,4ny&
Solution: lnynxrn
xy
Sr . l=0,±1, ±2,
1. l= 0 5
2. l= ±123
3. l= ±232
4. l= ±341
nynxrn
xy 0
Expression for rxy (l)
11 nynxrn
xy
rxy (l)
22 nynxrn
xy
33 nynxrn
xy
Auto correlation Sequences
When y(n) = x(n) , the cross correlation function become auto correlation function
.......3,2,1,0l
lnynxrn
xy
We know that
if y(n) = x(n)
therefore
.......3,2,1,0l
lnxnxrn
xx
.......3,2,1,0l
nylnxrn
xyOr
.......3,2,1,0l
nxlnxrn
xxOr
Auto correlation Sequences
In dealing with finite duration sequences, it is necessary to express the auto-correlation & cross correlation in terms of the finite limits on the summation
The correlation & auto correlation may be expressed as:
lnynxrkN
ln
xy
1
lnxnxlrkN
in
xx
1
If , x(n) & y(n) are causal sequences of length ‘N’ (i.e., x(n)=y(n)=0 for n<0 &n>N).
i=l , k=0 for l>=0
Where,
i=0 , k=l for l<0&
Compute the auto correlation of the signal
10, anuanx n
Since x(n) is an infinite- duration signal, its auto correlation also has infiniteduration.
solution
Considering two cases,
Numerical on Auto correlation
If , l>=0
0 0
2
0 n n
nllnn
n
xx aaaalnxnxlr
l
xx aa
lr21
1Hence
Numerical on Auto correlationx(n)
n
x(n-l)
nl
1
0-2 -1 0 1 2 ..
1
If , l<0
on
lnl
n
xx aa
aalnxnxlr2
2
0 1
1
x(n-l)
n l
1
-2 -1 0 1 2 . . .l o
1l<0
l>=0
l
xx aa
lr21
1
We can observe that, lrlr xxxx
Correlation of Periodic Sequences
Let x(n) & y(n) be two periodic signals.
1
0
1 N
n
xy lnynxN
lr
Their correlation sequences is defined as ,
if, x(n) =y(n)
1
0
1 N
n
xx lnxnxN
lr
Application of Correlation
Radar Target Detection
Thank You