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Units at the Correlator Output

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afr123

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Hello,

I have a confusion about a very basic question I guess.

I have a pulse of a known waveform measured in volts. I use a matched filter to detect the presence of the waveform in the singal. The impulse response of the matched filter as we know is the time-reversed version of the transmitted waveform. The following equation is used to correlate the transmitted signal with the reference (matched filter).

g[n] = IFFT {FFT(x[n]) . FFT(h[n])}

So my question is: what is the unit of g[n]?

Thanks
 
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weetabixharry

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So my question is: what is the unit of g[n]?

Why do you want to know? If you're trying to get some meaningful idea of how "strong" the correlation is, I think it's far better to compute the normalised correlation coefficient. This then takes (unitless) values with magnitude between 0 and 1, where 1 denotes perfect correlation (regardless of the scaling of x[n]). If you don't normalise your correlation value, then simply increasing and decreasing the magnitude of x[n] proportionally increases and decreases the (unnormalised) correlation -- which seems to me like a silly property for a "correlation" measure to have.

Having said that, in many practical situations, you're essentially just going to assign some arbitrary threshold to choose between "detected" and "not detected" ... so if you find a threshold that works for you, then this is often sufficient regardless of units, normalisation or anything else.

g[n] = IFFT {FFT(x[n]) . FFT(h[n])}

You need to be very careful here. I hope you understand the difference between linear and circular convolution. Computing linear convolutions and correlations in the frequency domain requires correct handling of the circular wrap.
 

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