PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

504 Practical MATLAB® Applications for Engineers

ANALYTICAL Solution

R 11 (0) = [0 1 2 1 2 0 1 0]. * [0 1 2 1 2 0 1 0] = [0 1 4 1 4 0 1 0] = 11

R 11 (1) = [0 1 2 1 2 0 1 0]. * [1 2 1 2 0 1 0 0] = [0 2 2 2 0 0 0 0] = 6

R 11 (2) = [0 1 2 1 2 0 1 0]. * [2 1 2 0 1 0 0 0] = [0 1 4 0 2 0 0 0] = 7

R 12 (0) = [0 1 2 1 2 0 1 0]. * [0 1 2 3 4 5 6 7] = [0 1 4 3 8 0 6 0] = 22

R 12 (1) = [0 1 2 1 2 0 1 0]. * [1 2 3 4 5 6 7 0] = [0 2 6 4 10 0 7 0] = 29

R 12 (2) = [0 1 2 1 2 0 1 0]. * [2 3 4 5 6 7 0 0] = [0 3 8 5 12 0 0 0] = 28

MATLAB Solution

% Script file: auto _ cross

fn1=[0 1 2 1 2 0 1 0]; fn2 = [0 1 2 3 4 5 6 7];

auto _ corr=xcorr(fn1);cross _ corr = xcorr(fn1,fn2);cross _ corrx =

xcorr(fn2,fn1);

disp(‘******************* R E S U L T S ***************************’)

disp(‘The auto-correlation coefficients of f1(n)are:’)

auto _ corr

disp(‘The cross-correlation coefficients of f1(n) with f2(n) are:’)

cross _ corr

disp(‘***************************************************************’)

n=-7:7;

subplot(3,1,1)

bar(n,auto _ corr)

title(‘Auto-correlation of f1(n)’)

xlabel(‘time index n’)

ylabel(‘Amplitude’)

subplot(3,1,2)

bar(n,cross _ corr)

title(‘Cross-correlation of f1(n) with f2(n)’)

xlabel(‘time index n’); ylabel(‘Amplitude’)

Subplot(3,1,3)

bar(n,cross _ corrx)

title(‘Cross-correlation of f2(n) with f1(n)’)

xlabel(‘time index n’); ylabel(‘Amplitude’)

********************** R E S U L T S *************************

The auto-correlation coefficients of f1(n)are:

auto _ corr =

Columns 1 through 8

-0.0000 -0.0000 1.0000 2.0000 3.0000 7.0000 6.0000 11.0000

Columns 9 through 15

6.0000 7.0000 3.0000 2.0000 1.0000 -0.0000 -0.0000

The cross-correlation coefficients of f1(n) with f2(n) are:

cross _ corr =

Columns 1 through 8

-0.0000 7.0000 20.0000 24.0000 34.0000 28.0000 29.0000 22.0000

Columns 9 through 15

15.0000 9.0000 5.0000 2.0000 1.0000 -0.0000 0

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