Bangalore School Of Audio

Two full-range loudspeakers in a delay system The alignment of two full-range systems in time isn’t so easy, as the real world loudspeakers aren’t so perfect as the one represented by the Dirac in the wrapped phase section above. Most sound reinforcement loudspeakers have a low frequency cut-off around 35Hz or above. The curves above are both filtered by a high-pass filter around 50Hz. The measurement is often influenced by reflections from the room as seen in the blue curve above. The next graph shows the wrapped phase curves from the two systems in the top graph and the ETC in the bottom graph. Very often mistakes are made when trying to match the wrapped phase. The phase can became several turns off, with time smearing and side-lobe errors as results. The reason is often the cut-off frequency, which makes an increasing group-delay at low frequency and will bend the low frequencies of the phase. This is very hard to see in the phase graph, but if we look at the group delay instead we can see how the curves divert below 150Hz
If the high-pass slope or the LF cut-off is very steep its very important to raise the start frequency of the FFT. Otherwise the phase calculation will start down in the noise floor with invalid results. In this graph the FFT start frequency is raised to 50Hz. It’s obvious that it helps when trying to find the match to the wraps. As seen in the wrapped phase above, there are some extra oscillations due to the reflections in one of the IR. If a strong reflection is present close to the desired IR, there is a risk that one aligns to the reflection instead. It is therefore very important to window the time graph so the measurement will be anechoic. In the time graph below Multiple windows are applied to clean the IR.

Bävholm & Grenander ”

A not so common calculation, but very useful is the Cepstrum analysis. The benefits over PIR view is that the noise is suppressed, so reflections are clearly visible [19, 20]. This is very useful for setting the time windows. Cepstrum is the inverse FFT of the logarithmic magnitude with the phase preserved. As the logarithmic scale doesn’t contain negative values, the time domain will be “rectified”. The peak is normalized to one. (Cepstrum is a spectrum of a spectrum and the word is coined by paraphrasing Spectrum. Other words in the Cepstrum domain are Quefrency (Frequency) and Rahmonics (Harmonics)).

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The feature here is that the sub-bass is visible and it can be seen how the energy is smeared
out in time.

Wavelets con’t Wavelets analysis is very similar to Multiple time windowing. The wavelets analysis usually starts with a Gaussian window (here a symmetric window). Each time slice in the scalogram is made up of merged FFTs from corresponding time windowing of the PIR. The number of Merge Per Octave, will determine the frequency resolution. The wavelet scalogram is made of a number of time slices. These time slices are made in the same way as a Sliding CSD, by sliding the whole multiple window packages stepwise. Note: Wavelets are very computing intensive. Even with the lowest frequency resolution with 20 merging bands, it’s 2000 of 32k points FFTs to calculate. With Ultra high quality and 320 frequency bands there will be 256 000 FFTs to make!

Bävholm