Hi Guys,
I was referred to this thread by Serafino Di Rosario, and I will test this PD patch for performing ESS measurements. Everything is very interesting for me, and it seems that Katja did a very good job!

Regarding the problems encountered, I give you these infos:

1. sine-phase-matched sweep. This method is very useful when performing distortion measurements, or computing multiple-order IRS to be used in not-linear convolution processor (for emulating the nonlinearities of a device). For the method to work, it is mandatory that the sine sweep is sine-phased not only at the beginning, but also at the end of each octave. This way, each harmonic-order IR will be phase matched with the linear IR. The provided formulation solves this problem, and it is very good to see it explained here so simply.
   The importance of using a phase-synced exponential sweep was first discovered by Antonin Novak, a Ph.D. student of the universities of Prague and Le Mans.

2. The ripple at low frequencies can be controlled by proper fade-in. The choice of the "optimal" fade law is still a big subject under scientific discussion. Hann windowing is just a very initial, suboptimal approach. I plan to investigate further the choice of the optimal fade law, and publish something on this topic, soon.

3. The concept of cutting away everything before the arrival of the direct sound is wrong, in my opinion. The "silence" before the arrival of the direct sound has a very important physical meaning, it is the "time-of-flight" of the sound, and provides an accurate measurement of the distance between the source and the receiver. Furthermore, it contains "background noise", which is a very important quantity to know, for example when deriving STI from the IR measurement.
   So PLEASE, do not cut away this initial silence! If the IR has to be used as a filter for a convolution-based reverb plugin, the plugin must be intelligent enough for analyzing the IR, and giving the user the possibility to keep this initial silence or cut it away. For example, IR-1 from Waves gives these possibilities. In any case, a measured IR of a room should always contain the time-of-flight... Publishing "pre-cutted" IRs is wrong, and in the long run will cause a lot of troubles...

4. The "Fractional delay", for the same reasons, should NOT be corrected! If the time-of-flight is fractional, good, let's stay with this fact. As pointed out, cutting (time-shifting) improperly the measured IR can alter its spectrum. So, please, keep every measured IR as it comes out from the convolution with the inverse sweep... If the higher-order distortion products are not needed, it make sense to only keep the linear part only, but always starting from the true "zero time". Let's make an example: I generate a 20s-long IR at 48 kHz, that is 960,000 samples.
   The inverse sweep will also be 960,000 samples long.
   I play the sweep, and record the room response for, say, 1,200,000 samples, for being sure of capturing the complete reverberant tail even at the higher frequencies.
   Now I convolve the recorded signal (1,200,000 samples) with the inverse sweep (960,000 samples), and I get a convolved signal which is long 2,159,999 samples.
   If I want to keep a 4s long IR, containing only the linear response, you should throw away the first 959,999 samples, and keep the following 192,000 samples.
   As this signal starts from the true "zero time", the main peak will not be at the very beginning, but delayed of an amount corresponding to the source-receiver distance. If it was 10m, it will be 10/340=0.0294 seconds...

5. For performing efficiently convolution of very long filters (in the example above, the Inverse Sweep was nearly 1 million points) it is advisable to employ a partitioned convolution scheme. That is, the filter is splitted in a number of blocks, so that instead of performing a single, very long FFT , a number of shorter FFTs is performed instead. On my web site you find a couple of papers explaining the partitioned convolution algorithm. This is the same algorithm employed in the well-known BruteFIR open-source program by Anders Torger.

Bye!

Angelo Farina