### Notice

Please note that most of the software linked on this forum is likely to be safe to use. If you are unsure, feel free to ask in the relevant topics, or send a private message to an administrator or moderator. To help curb the problems of false positives, or in the event that you do find actual malware, you can contribute through the article linked here.
Topic: Looking for explanation / visualization of echoes in frequency and phase domain (Read 953 times)
0 Members and 1 Guest are viewing this topic.

## Looking for explanation / visualization of echoes in frequency and phase domain

##### 2016-02-12 07:30:12
It is known that any given snippet of audio can be transformed from waveform representation into frequency and phase representation via Fourier transform.

It is often very useful to do this with impulse responses, to visualize the effect that passing general music through an audio system has on the music's frequency response.  From such a visualization one can predict many of the colorations one would hear from the system.  One can do even better, by applying corrections via equalizer (for amplitude response) or full-blown inverse filters (for amplitude+phase response) to go quite some way towards removing those colorations.

What I do not understand, in the above picture, is where ECHOES stand in this grand scheme of things.  To my naive understanding, ECHOES (of certain frequencies, or broad band) would seem to entail that the same frequency (that is echoed) appears both in the initial impulse and in the time interval where the echo occurs.  How one represents this phenomenon in terms of a single phase angle for such a frequency, is quite beyond the understanding of this feeble mind.

Even further out for me is what the inverse filter for a system with an echo would look like, in frequency+phase representation or in waveform terms.  Intuitively I imagine there being a delayed inverse phase impulse required to cancel out the original echo--then, because the delayed inverse phase impulse elicits its own delayed inverted echo, a further delayed positive phase impulse (of much smaller amplitude now).  Then an infinite series of further delayed impulses, each of opposite phase to the one before, and of exponentially decreasing amplitude...--but I have never SEEN an inverse filter that looks anything like this.

Help?

## Re: Looking for explanation / visualization of echoes in frequency and phase domain

##### Reply #1 – 2016-02-12 15:52:46
T = time delay between a signal and its echo.
Then echo frequencies are 1/T, 2/T, 3/T... (or 2π/T, 4π/T, 6π/T...)