Hello Bassik and Katjav,

Kirkeby inverse function creates inverse chirp from forward chirp, before all the trouble begins....

A long sweep from f1to f2has no more bandwidth than a short sweep from f1to f2. Seemingly small FFT can do a lot of windowing. Here is study of room transfer function using FFT bandwidth limited sweeps:

http://waveformfidelity.com/

The windowing produces super smooth spectrum at expense of computational noise, which of course is well below that of the room, speakers, and microphone. The extra fade in method is very quiet, but has a little ripple.... I had not found this prior to the above investigation.

Barleywater

Hello Katjav,

I have been chasing the swept sine technique with Farina's Aurora tools on the Cool Edit/Adobe Audition platform. I too found that octave extension of low frequency side only to use as fade in made possible much better result. Also small fade out at the end for non zero end state and all was greatly improved. But applied to getting IR of sound card loopback produces wrong answer. AC coupling of output and input stages produces min phase Butterworth type answer and swept sine with fades always contaminates with its sinc like IR. MLS gives correct answer, but of course brings its own baggage.

Your webpage: http://www.katjaas.nl/expochirp/expochirp.html shows IR result that I've seen on many of my screens while working on the fade issue. Very nicely done indeed.

Farina released plugins for Audacity for convolution and sweep generation. Audacity display doesn't provide zoom tools for display of fine detail. The plugins do provide ready reference.

The solution to the fade issue is to not use them in producing the sweep pair. The answer is in generating at least one of the sweeps in the frequency domain.

Here is link to a great paper covering some of this: "Transfer Function Measurement with Sweeps," SWEN MÜLLER and PAULO MASSARANI I found it here: http://www.melaudia.net/zdoc/comparisonMesure.PDF

Chapter 5 has got the goods.

Turns out that Kirkeby inverse is perfect tool for the job, and many more! To bad it is trapped in Cool Edit/Audition domain. Perhaps Farina will liberate it soon. The perfect place to apply it is before all the trouble begins. An arbitrary broadband signal of 2^n length may be inverted with Kirkeby, and convolution of the pair returns extremely good result. Samples directly next to pulse of 1e-6 easy to obtain. Starting with white noise, results emulating MLS are possible. Starting with exponential sweep a sweep is returned by Kirkeby with circular convolution properties: To get right convolution result, two copies of forward sweep need to be used and cropped to central result. Alternately Kirkeby may be directed to return result 4x longer for direct convolution. I found that a 2x long Kirkeby result produced artifacts. One may also use 2 copies of a 1x Kirkeby to recover IR with single instance of the seed wave.

I communicated this with Farina, and he honored me by placing his confirmations to: http://pcfarina.eng.unipr.it/Public/Wolkoff/

There are six wave files: 2^20 sample length forward sweep and inverse sweep generated without fades; and 1x,2x,4x Kirkeby inverses of the forward sweep. Additionally a time shift Kirkeby is posted. This is a hack I proposed as a partial work around for straight convolution. It is simply cutting first half of 1x Kirkeby and pasting it back at the end. Fading the ends controls bandwidth, and provides kernel for auralization applications.

Cheers!