## Time alignment by windowed chirp

Dahlberg
Posts: 90
Joined: 19 Oct 2019 23:46

### Time alignment by windowed chirp

After having learnt (sort of) time alignment by sine wave convolution, this has also come up in some discussion as an alternative.

I was searching for information about it and came up with this:
Abstract
A new signal-adaptive joint time–frequency distribution for the analysis of nonstationary signals is proposed. It is based on a fractional-Fourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms. Improvement over the standard time–frequency representations is achieved when the principal axes of a signal (defined as mutually orthogonal directions in the time–frequency plane for which the width of the signal's fractional power spectrum is minimum or maximum) do not correspond to time and frequency. The computational cost of this fractional-domain realization is the same as the computational cost of the realizations in the time or the frequency domain, since the windowed Fourier transform of the fractional Fourier transform of a signal corresponds to the short-time Fourier transform of the signal itself, with the window being the fractional Fourier transform of the initial one. The appropriate fractional domain is found from the knowledge of three second-order fractional Fourier transform moments. Numerical simulations confirm a qualitative advantage in the time–frequency representation, when the calculation is done in the optimal fractional domain. The approach can be generalized to the time–frequency distributions from the Cohen class.

Looks like this and there is no sound when you generate it. I was a bit worried about that
I seriously have no clue on how to use this so anyone who has can pitch in at any time
Best regards. Bengt
UliBru
Posts: 433
Joined: 19 Oct 2019 13:58

### Re: Time alignment by windowed chirp

Bengt,

the windowed chirp is introduced here as a test signal similar to the sinewave convolution.
Indeed two days ago I have used it for detection of the polarity of a speaker driver.

The basic idea: you create a windowed chirp with the frequency of your interest and convolve the chirp with a given pulse response. You may also convolve the chirp with an ideal pulse response for comparison. The result will show up a different gain, a polarity switch, a phase/time-shift and/or all kind of ringing.

The chirp is a very short signal and if has a soft fade-in/out different to the sinewave you have recently worked with. The chirp signal is usually way too short to be used as a signal for listening.

The chirp can also be helpful for time-alignment of speaker drivers. But I highly recommend to also check the chirp result with the original XOs to better understand the result.
Stay well tuned
Uli

Moderator
Acourate system: JRiver/Roon -> AcourateConvolver -> miniDSP U-DIO8 -> TacT M/S2150 amps -> DIY horn speakers
Dahlberg
Posts: 90
Joined: 19 Oct 2019 23:46

### Re: Time alignment by windowed chirp

So if I for instance would like to time align my system in this way. Would I then be supposed to convolve a 70hz windowed chirp to both the subwoofer and midbass xo files first. Followed by the same procedure for the midbass and tweeter at 350hz ? Or maybe the other way around in a similar fashion as used with the sinewave convolution ? And the chirp would be visible in the pulse response ?
Best regards. Bengt
Dahlberg
Posts: 90
Joined: 19 Oct 2019 23:46

### Re: Time alignment by windowed chirp

So I did this What I did can read below the chart If it's useful in any way
Best regards. Bengt
UliBru
Posts: 433
Joined: 19 Oct 2019 13:58

### Re: Time alignment by windowed chirp

Exactly nothing!
The time domain chart is the important chart.
Please also keep in mind that the frequency response chart does not contain any time information, it just shows a steady state.
Stay well tuned
Uli

Moderator
Acourate system: JRiver/Roon -> AcourateConvolver -> miniDSP U-DIO8 -> TacT M/S2150 amps -> DIY horn speakers
Dahlberg
Posts: 90
Joined: 19 Oct 2019 23:46

### Re: Time alignment by windowed chirp

UliBru wrote:
20 Nov 2020 15:51
Exactly nothing!
Best regards. Bengt
Dahlberg
Posts: 90
Joined: 19 Oct 2019 23:46

### Re: Time alignment by windowed chirp

So now I'm at least in the right window

Midbass drivers are EQ'd, I suppose that's why that pulse is not symetrical.

Best regards. Bengt