Auto correlation(corrected) on dsp. .pdf

Dsp

1. WELCOME
To our presentation

2. Saroar Hossain
ID: 2002221
Md.MahbubHasan
ID:2002271
Presented By
Presented to
Prof. Dr. Md. Zamil Sultan
Chairman
Dept. of EEE
Rimu Rahman Munna
ID: 2002267
Rakibul Hasan
ID:2002280

3. AUTO CORRELATION IN
DIGITAL SIGNAL PROCESSING
1

4. 2
In digital signal processing (DSP), correlation is a
fundamental operation used to measure the
similarity between two signals.
Correlation
Types of Correlation
There are two main types of correlation in DSP
1.Auto Correlation
2.Cross Correlation

5. 3
Auto correlation measures the similarity of a signal with itself at different
time shifts.
Auto correlation of signal x[n] is defined as:
Rxx(??????)=σ
??????=−∞
∞
??????????????????(??????−??????)
Where ??????= 0, ±1, ±2……
Auto Correlation

6. 4
Auto Correlation
0
0.5
1
1.5
2
2.5
0 1 2 3 4
Transmitted Signal
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6
Received Signal
???????????? ????????????−??????

7. 5
Auto Correlation of the discrete time(DT) signal
Let compute auto correlation of the DT signal x[n] = {−1, 2, 1}
We know that autocorrelation of x[n]
Rxx(??????)= σ
??????=−∞
∞
??????????????????(??????−??????)
For ??????= 1;
Rxx(-1)=σ
??????=−∞
∞
??????????????????(??????+1)
=σ
??????=−∞
∞
[0,−2,2]
= 0
??????= 1
= 0
−1 2 1
−1 2 1
−2 2

8. For ??????= 2;
Rxx(-2)=σ
??????=−∞
∞
??????????????????(??????+2)
= σ
??????=−∞
∞
[0,0,−1]
= −1 ??????= 2
= −1
For ??????= 0;
Rxx(0) = σ
??????=−∞
∞
??????????????????(??????)
= σ
??????=−∞
∞
[1,4,1]
= 6
6
−1 2 1
−1 2 1
−1

9. ??????= 0
= 6
For ??????= -1;
Rxx(1)= σ
??????=−∞
∞
??????????????????(??????−1)
= σ
??????=−∞
∞
[−2,2,0]
= 0 ??????= -1
= 0
7
−1 2 1
−1 2 1
1 4 1
−1 2 1
−1 2 1
-2 2

10. For ??????= -2;
Rxx(2)= σ
??????=−∞
∞
??????????????????(??????−2)
= σ
??????=−∞
∞
[−1,0,0]
= −1
??????= -2
=−1
Thus Rxx(??????) = {−1, 0, 6, 0,−1}
8
−1 2 1
−1 2 1
−1

11. 9
clc;
close all;
clear all;
x = [-1, 2, 1]
t = 0:length(x)-1;
subplot(2,1,1);
stem(t, x,'linewidth',2);
auto_corr= xcorr(x);
lag = -length(x)+1:length(x)-1; % Lag values for xcorrresul
subplot(2,1,2);
stem(lag, auto_corr,'linewidth',2 );
disp('Rxx:');
disp(auto_corr);
Auto Correlation Using MATLAB

12. 10

13. 11
•The maximum value of the auto-correlated signal is obtained when
time-shift is zero that is at ??????= 0. Becauseat ??????= 0 the overlapping signal
best matches the given signal.
•Rxx(??????) is a symmetric function, that is Rxx(??????) = Rxx(-??????)
Important Feature of Auto Correlation

14. 12
•Auto-correlation is used to identify repeating patterns within a signal
•Speech processing
•Signal synchronization incommunication systems
•Radar system
•Weather forecasting
•Security system
Applications of Auto Correlation

15. THANK YOU