MATLAB: Error using plot Vectors must be the same length.

autocorrelationMATLABmatlab coder

good evening family I was calculating the autocorrelation of the function cos (wt) but every time I compile I get an error like Error using plot Vectors must be the same length.

Help me please.

this is my code :

function autocorrx
f0=20; N=1000  ;
k=5; Tmax=k/f0;
t=0/2:Tmax/N:Tmax;
x=cos(2*pi*f0*t); 
subplot(1,1,1);
plot(t,x);
axis([0 0.1 -1 1]);grid;
xlabel('t(s)');
ylabel('cos(wt)');
C = xcorr(x,x)*Tmax;
subplot(2,2,2) ; plot(t,C) ;
axis([-0 0.1 -1 1]);
grid
xlabel ('t') ;
ylabel ('Cxx(t)') ;
title ('autocorrelation ')
end

Best Answer

The cross correlation function xcorr() will produce an output with 2*M-1 elements where M is the number of elements in the input. Perhaps you want to plot the results as a function of the lag.

[C,lags]= xcorr(x,x);
C = C*Tmax;  % <--- this is from your code; 
plot(lags,C);

Note that your subplots are not defined correctly. Assuming you want two vertically stacked subplot, the subplot definitions should be

subplot(2,1,1)
subplot(2,1,2)

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MATLAB: Fourier Transformation HELP PLEASE

clear all; close all; clc;
incrm = 0.01;
t = incrm:incrm:10;
xt = cos(2*t);
plot(t,xt,'LineWidth',3)
hold on
grid on
xlabel('t')
ylabel('x(t)')
legend('x(t)')
set(gca,'FontSize',13)
%%Fouier Series Approximation of x(t)
%---Fourier Coefficients---%
T0 = pi;
w0 = 2*pi/T0;
a0 = (1/T0) * trapz(t(1:1+T0/incrm), xt(1:1+T0/incrm), 2);
for nn = 1 : 17
    an(nn) = (2/T0) * trapz(t(1:1+T0/incrm-1), xt(1:1+T0/incrm-1).*cos(nn*w0*t(1:1+T0/incrm-1)), 2);
    bn(nn) = (2/T0) * trapz(t(1:1+T0/incrm-1), xt(1:1+T0/incrm-1).*sin(nn*w0*t(1:1+T0/incrm-1)), 2);
end
%---Fourier Series Approximation---%
sumk=cell(1,17)
sumk{1} = 0;
for nn = 1 : 17-1
    sumk{nn+1} = sumk{nn} + an(nn)*cos(nn*w0*t) + bn(nn)*sin(nn*w0*t);
end
xt_FS = a0 + [sumk{:}]
figure;
plot(t, xt, 'LineWidth', 3)
hold on
grid on
xlabel('t')
ylabel('x(t)')
plot(t,xt_FS(1:numel(t)),'r','LineWidth',1.5)
ylim([-1,1])
legend('x(t)','FS Approximation')
set(gca,'FontSize',13)
%%Fourier Coefficients for Frequency Plot
%---Problem 3---%
w = w0 * (1 : 17);
%---Problem 4---%
figure%('Position', [50,100,1200,400]);
subplot(1,2,1)
stem(w,an,'MarkerSize', 14,'LineWidth', 2)
grid on
box on
xlabel('\omega')
ylabel('a_n')
set(gca,'FontSize', 13)
xlim([0 17])
ylim([-0.5 2])
ax = gca;
ax.XTick = 0:1:17;
ay = gca;
ay.YTick = -0.5:0.5:2;
subplot(1,2,2)
stem(w,bn, 'MarkerSize', 14, 'LineWidth', 2)
grid on 
box on
xlabel('\omega')
ylabel('b_n')
set(gca, 'FontSize', 13)
xlim([0 17])
ylim([-0.5 2])
ax = gca;
ax.XTick = 0:1:17;
ay = gca;
ay.YTick = -0.5:0.5:2;

MATLAB: Isn’t the autocorrelation of rand a delta function

As described in detail here, http://en.wikipedia.org/wiki/Autocorrelation, there is more than one convention when calculating autocorrelation. In signal processing, autocorrelation of a sequence is often calculated without subtracting off the mean. As described in the documentation, this is indeed what XCORR does:

http://www.mathworks.com/help/signal/ref/xcorr.html

By default, xcorr computes raw correlations with no normalization.

If you generate the uniform random numbers with no bias (subtract 0.5), you will indeed get a result that looks like a delta function.

x=rand(1,100,1)-0.5; Rxx=xcorr(x); subplot(2,1,1); plot(Rxx); grid; title('Autocorrelation function of rand'); xlabel('lags'); ylabel('Autocorrelation');
x=randn(1,100,1); Rxx=xcorr(x); subplot(2,1,2); plot(Rxx); title('Autocorrelation function of randn'); xlabel('lags'); ylabel('Autocorrelation');

Best Answer

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MATLAB: Fourier Transformation HELP PLEASE

MATLAB: Isn’t the autocorrelation of rand a delta function

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