# 1d correlation / convolution

Started by August 12, 2018
``` I have the absolute amplitude of a digital signal that I want to
auto correlate with self , also cross correlate with a different
digital signal [ absolute magnitude ] .

I'm using a complex  1d fft to implement this .

I only have the absolute values of the spectra to work with ; where
the absolute value is defined as : square root of (Real^2 + Imaginary^2).

After multiplying the absolute spectra together I have a unique
spectra , again this is an absolute valued spectra.
So at this stage does the very first value , sometimes known as the
d.c term , contain the magnitude of the correlation ; or some indication thereof .

Now applying the fft to the previous product of the spectra we obtain a digital signal , again we only use the absolute value of this.
At the first sample the maximum value seems to appear ; is this indicating the amount of correlation .
In some instances I find a value that's greater than that of the
auto correlation , therefore I'm also wondering if a better indication of correlation is a value that tends to equal that of
the auto correlation ; rather than being less than or greater than.

To date I haven't extensively examined shifted signals , I'm of the
belief that the results will be similar .

Note absolute values of all signals , complex fft only ; no inverse
fft , of any type , is used .

```
```Am 12.08.2018 um 21:56 schrieb quintin9g@gmail.com:
>   I have the absolute amplitude of a digital signal that I want to
> auto correlate with self , also cross correlate with a different
> digital signal [ absolute magnitude ] .
>
>   I'm using a complex  1d fft to implement this .
>
>   I only have the absolute values of the spectra to work with ; where
> the absolute value is defined as : square root of (Real^2 + Imaginary^2).

You won't get lucky here. The time information required for cross
correlation is in the phase. And the phase is lost by taking the
absolute value, i.e. the time information is lost.

All you can do with this kind of information is to identify signal with
similar spectral distribution.

>   Now applying the fft to the previous product of the spectra we obtain a digital signal , again we only use the absolute value of this.
>   At the first sample the maximum value seems to appear ; is this indicating the amount of correlation .

No, this is something different.
See -> Cepstrum or -> autocepstrum respectively.

Marcel
```