Regarding Autocorrelation function in an application

So i've got an audio file (trying to remove echo) i load in via y=wavread('echo.wav'); and then calculated the autocorrelation xcorr(y,y); and plotted it, centering the single peak at 0. This yields two peaks on either side at +/- 930 which is the sample delay for the echo.

Next I'm trying to find the echo amplitude constant 'a', but I need to do it via relation of the autocorrelation of y and autocorrelation of x. The equation is y(n) = x(n) + a*x(n-no) this yields, (where r_yy is autocorr of y, and r_xx is autocorr of x) : r_yy(k) = r_xx(k) + a^2*r_xx(k) + a*r_xx(k+no) + a*r_xx(k-no)

Now it is aparent that at k=0 I have the value of r_yy(0) and r_xx(0) available from the graph. However my issue is, what then will r_xx(930) = r_xx(-930)= ? If I know that I can calculate 'a'.

Thanks

Answer 1

[Daniel Shub]

There is no way to know apriori what r_xx(930) is going to be. You need to know more about what x is. If x is a sine wave with period 930 and amplitude 1 then r_xx(930) will be 1. If x has a period of 1860, then r_xx(930) will be -1. If x is a impulse, then r_xx(930) will be 0. If x is a segment of a white noise process, then r_xx(930) will be a random value that approaches zero as the length of the segment increases.