HW10 - Revision history

Joshua.Sarris at 06:33, 3 December 2009

2009-12-03T06:33:12Z

← Older revision		Revision as of 23:33, 2 December 2009
Line 9:		Line 9:
	About cross correlation:		About cross correlation:
	First of all correlation is defined as<br>		First of all correlation is defined as<br>
	[[image:Img1204.png]]		[[image:Img1204.png]]<br>
	We may interpret the correlation operator as		We may interpret the correlation operator as

Line 15:		Line 15:
	which is <math>\|\|x\|\|^2=N </math> times the coefficient of projection onto x of y advanced by n samples (shifted circularly to the left by n samples). The time shift n is called the correlation lag, and the function is called a lagged product.		which is <math>\|\|x\|\|^2=N </math> times the coefficient of projection onto x of y advanced by n samples (shifted circularly to the left by n samples). The time shift n is called the correlation lag, and the function is called a lagged product.

	This is then used to define cross correlation as		This is then used to define cross correlation as <br>
	[[image:Img1541.png]]		[[image:Img1541.png]]

Line 24:		Line 24:
	The DFT of the cross-correlation may be called the cross-spectral density, or ``cross-power spectrum,'' or even simply ``cross-spectrum'': <br>		The DFT of the cross-correlation may be called the cross-spectral density, or ``cross-power spectrum,'' or even simply ``cross-spectrum'': <br>
	[[image:Img1544.png]]		[[image:Img1544.png]]

			Matlab has a cross correlation function "xcorr()" but I am not familiar with it and could only find an example on Matlab's website using the following format, it was different in that it didnt have any example signals but gave an outline on defining the matrix's and how they should relate to one another to work.

Joshua.Sarris at 06:30, 3 December 2009

2009-12-03T06:30:35Z

← Older revision		Revision as of 23:30, 2 December 2009
Line 23:		Line 23:

	The DFT of the cross-correlation may be called the cross-spectral density, or ``cross-power spectrum,'' or even simply ``cross-spectrum'': <br>		The DFT of the cross-correlation may be called the cross-spectral density, or ``cross-power spectrum,'' or even simply ``cross-spectrum'': <br>
	[[image:~~Img15544~~.png]]		[[image:Img1544.png]]

Joshua.Sarris at 06:29, 3 December 2009

2009-12-03T06:29:49Z

← Older revision		Revision as of 23:29, 2 December 2009
Line 6:		Line 6:

	I decided to show a cross correlation example using MATLAB.		I decided to show a cross correlation example using MATLAB.

			About cross correlation:
			First of all correlation is defined as<br>
			[[image:Img1204.png]]
			We may interpret the correlation operator as


			which is <math>\|\|x\|\|^2=N </math> times the coefficient of projection onto x of y advanced by n samples (shifted circularly to the left by n samples). The time shift n is called the correlation lag, and the function is called a lagged product.

			This is then used to define cross correlation as
			[[image:Img1541.png]]

			The term ``cross-correlation'' comes from statistics, and what is defined here is more properly called a ``sample cross-correlation.''

			This definition of a sample cross-correlation is only valid for stationary stochastic processes, e.g., ``steady noises'' that sound unchanged over time. The statistics of a stationary stochastic process are by definition time invariant, thereby allowing time-averages to be used for estimating statistics such as cross-correlations. For brevity below, we will typically not include ``sample'' qualifier, because all computational methods discussed will be sample-based methods intended for use on stationary data segments.

			The DFT of the cross-correlation may be called the cross-spectral density, or ``cross-power spectrum,'' or even simply ``cross-spectrum'': <br>
			[[image:Img15544.png]]

Joshua.Sarris at 06:22, 3 December 2009

2009-12-03T06:22:11Z

← Older revision		Revision as of 23:22, 2 December 2009
Line 26:		Line 26:
	sigC = real(ifft(sigA.*sigB));</pre>		sigC = real(ifft(sigA.*sigB));</pre>

	~~''To be completed later tonight''~~		cross correlatoin of same wave<br>
			[[image:Same_wave.jpg]]

			cross correlation with 90degree delay<br>
			[[image:90degree_shift.jpg]]

			cross correlation with 45 degree delay<br>
			[[image:45shift.jpb

			cross correlation with <math>\frac{\pi}{1000}</math><br>
			[[image:Pi_onethousanths_shift.jpg]]

Joshua.Sarris at 01:03, 3 December 2009

2009-12-03T01:03:33Z

← Older revision		Revision as of 18:03, 2 December 2009
Line 25:		Line 25:
	sigB = fft([sig2 Zmat]);		sigB = fft([sig2 Zmat]);
	sigC = real(ifft(sigA.*sigB));</pre>		sigC = real(ifft(sigA.*sigB));</pre>

			''To be completed later tonight''

Joshua.Sarris at 01:03, 3 December 2009

2009-12-03T01:03:12Z

← Older revision		Revision as of 18:03, 2 December 2009
Line 8:		Line 8:


	close all		<pre>close all
	clear all		clear all
	f = 2; % sine wave frequency		f = 2; % sine wave frequency
Line 24:		Line 24:
	sigA = fft([sig1 Zmat]);		sigA = fft([sig1 Zmat]);
	sigB = fft([sig2 Zmat]);		sigB = fft([sig2 Zmat]);
	sigC = real(ifft(sigA.*sigB));		sigC = real(ifft(sigA.*sigB));</pre>

Joshua.Sarris at 01:00, 3 December 2009

2009-12-03T01:00:37Z

← Older revision		Revision as of 18:00, 2 December 2009
Line 6:		Line 6:

	I decided to show a cross correlation example using MATLAB.		I decided to show a cross correlation example using MATLAB.


			close all
			clear all
			f = 2; % sine wave frequency
			tmax = 2; % go to 2 seconds
			theta = pi/4;
			T = 0.01;
			t = 0:T:tmax;
			N = length(t);
			Nmat = 0:N-2;
			Zmat = Nmat *0;
			sig1 = sin(2pif*t); % A alpha signal
			sig2 = sin(2pif*t); % A beta signal
			c= conv(sig1,sig2); %test of matrix size
			%zeropad both vectors to length N1+N2-1 to avoid cyclic convolution
			sigA = fft([sig1 Zmat]);
			sigB = fft([sig2 Zmat]);
			sigC = real(ifft(sigA.*sigB));

Joshua.Sarris: New page: '''Problem Statement''' Present an Octave (or MATLAB) example using the discrete Fourier transform (DFT). '''Solution''' I decided to show a cross correlation example using MATLAB.

2009-12-03T00:58:40Z

New page: '''Problem Statement''' Present an Octave (or MATLAB) example using the discrete Fourier transform (DFT). '''Solution''' I decided to show a cross correlation example using MATLAB.

New page

'''Problem Statement'''

Present an Octave (or MATLAB) example using the discrete Fourier transform (DFT).

'''Solution'''

I decided to show a cross correlation example using MATLAB.