I created two signals in the time domain: signal A which is a square wave, and signal B which is a right-angled triangle wave, as shown in the picture below.
I took the FFT of these signals, multiplied channel 1 FFT with the conjugate of channel 2 FFT. Then I inverse-FFT'd to observe it back in the time domain, and I observed this:
Now, instead if I did the correlation directly in the time domain using signal in Python like this:
txcorr = signal.correlate(wave1, wave2, mode = 'same', method='direct')
I see this output:
So, my assumption is taking the conjugate of a signal in the frequency domain reverses the time axis? Could someone give me a more mathematical background or where I could read to understand what is happening exactly in the frequency domain? Of course, when I simply do the multiplication in the frequency domain without taking the conjugate of a signal, it produces the shape expected
Additionally, this is probably the biggest confusion: Why is the "maximum point" of the cross-correlated signal in the time domain not at 0.3s? This is what I expected from what cross-correlation page in wikipedia showed: