add max-rE and modified Tukey window

[fietew]

max-rE weighting has been widely used in the (NFC-HO)Ambisonics community. I added it for comparison. The Tukey window is a second adjustable window, which might have some benefits compared to the Kaiser windows as its inner part (m < alpha*M) is always one.

[fietew]

@fs446: Many window functions (number of samples denoted as N) are defined such that its first (n=0) and last (n=N-1) value are zero, e.g. many windows with a cosine shaped fade out involved. Is it in general sensible to modify the cosine fade out such that it yields non-zero values for n=0 and n=N-1, but would yield zero for n=-1 and n=N?

[fs446]

That’s indeed an issue, but not often suffiently discussed in literature. So, it’s good to open this up here. I remember that Ifeachor, Digital Signal Processing: A Practical Approach has short comments on this. And the script of Michael Möser’s course on signal processing is brilliant regarding this issue https://www.akustik.tu-berlin.de/fileadmin/fg23/Lehre/Digitale_Signalverarbeitung_gesamt.pdf, from ch. 2.4 signal model. See also his habilitation script 'Analyse und Synthese akustischer Spektren' at Springer 1988. Unfortunately all in german.

The essence is: How many of the available zeros of the weighting polynomial are to be used and where they should be located within the unit circle?

Is it in general sensible to modify the cosine fade out such that it yields non-zero values for n=0 and n=N-1, but would yield zero for n=-1 and n=N? I would precisely do this for FIR filters or gain shading windows for acoustic array (which is an FIR filter :-) ), since it is useless to have weights/taps with zero gain. Then you'd use all potential zeros for shaping the spectrum.

For DFT-windowing I’d rather use a window that starts with zero at n=0 and gets to zero at n=N, thus having non-zero value at n=N-1. That’s the ‘periodic’ flag in Matlab.

On 12 May 2017, at 2:33 PM, Fiete Winter notifications@github.com wrote:

@fs446: Many window functions (number of samples denoted as N) are defined such that its first (n=0) and last (n=N-1) value are zero, e.g. many windows with a cosine shaped fade out involved. Is it in general sensible to modify the cosine fade out such that it yields non-zero values for n=0 and n=N-1, but would yield zero for n=-1 and n=N?

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[hagenw]

As max-rE is indeed widely used we might also considering adding an example to the documentation?

[fietew]

I tried to add a plot to generate_plots.m, but getting the error:

Undefined function or variable 'xticks'.

Error in generate_plots (line 24)
xticks(-2:1:2); yticks(-2:1:2);

I don't think, that this is related to the changes.

[hagenw]

That's true, the xticks() was introduced only in MatlabR2016b. So maybe we should replace it with a version that also works on older versions. Do you know how to achieve the same in older versions?

[fietew]

I hope, that d9a4014 does the trick.

[hagenw]

Yes, this works for me. But know I'm getting the following error:

> In sound_field_mono_localwfs (line 36)
  In generate_plots (line 175) 
Variable output array "varargout" must be a cell array.

Error in sound_field_mono_localwfs

Error in generate_plots (line 175)
sound_field_mono_localwfs([-1 1],[-1 1],0,[1.0 -1.0 0],'pw',7000,conf);

[fietew]

I don't know, where to include such example because the modal window function has no effect on the monochromatic NFC-HOA driving functions.

[hagenw]

I would say we have two options. Wait until we have a monochromatic implementation of it or go with an example in the time domain. As far as I understand it, this example should use a low number of loudspeakers as those are the systems that are normally used with max-rE, correct? And if we do an example with and without weighting I guess you should be able to see that with weighting not all loudspeakers are active any longer.

[fietew]

I added a new subsection for the modal windows in NFC-HOA. This could be further extended, when adding documentation about LWFS-SBL. Latter should however not be handled in this pull request.