Hi Folks, I wanna do this median filter to extract harmonic content

page 4 and 5 will tell you about the idea here http://homepages.cae.wisc.edu/~sethares/software/SpectralTools.pdf

you can try spectral tools to see how it works too. I wanna do it in Pd.

And, as you can see, it will separate signal (partials) to noise (transients, attacks).

I know miller's example "Sheep From goats", but I wanna try this and compare the results. I also see that there may be other tools out there that try to do this. Please let me know?

Now, regarding the median filter, we'd need to slice the FFT Amplitude table into small segments, get the median of it, and compare the amplitudes to see if they are above or below this thershold. Doesn't seem too crazy and hard.

Maybe something you can design just using a [fexpr~] object?

I was thinking that maybe throwing the amplitudes in a table and then using the [median] objects could work too, but I'm just concerned that all the math should be done in the audio blocks, otherwise it will be out of sync.

I figure if I first throw it into a table and then do the math on the table, by the time I throw it back into the audio chain, the analysis input will be another.

what do you say?

thanks

Hello Porres,

From the article I understand the median filter could be done with a FIR filter. Like [iemlib/FIR~]. You want a median point for each index and not one point per spectrum segment. The filter is causal so if you want to use results to operate on the signal itself (spectrum coefficients in this case) you have to delay the signal by the amount N of filter points, or N/2 if you want to consider it a zero-phase filter. Problems arise at the FFT frame boundaries, the convolution gets circular so it takes input from the old or next FFT frame for computing the current FFT frame's results and vice versa. If not at signal rate you could make exceptions for the boundary regions (folding the index numbers back into range is allowed for a zero-phase convolution of the spectrum, because the spectrum is considered periodic) but with the signal objects you can't. But if you use complex FFT, it won't be so much of a problem because the spectrum is symmetric then, and the harmonic components are not supposed to fluctuate much from frame to frame.

Katja

hi there, thanks a lot,

unfortunately, a bit over my head.

how do I attach files to the forum? I wanted to show what I had, I'm gonna put the code in the body of the message.

I guess one way would be to write an external that would give me back this block of audio with the median of each section. I'd replace it in the [avg~] object. Cheers.

noise-floor_filter.pd

#N canvas 1374 303 359 446 12;
#X obj 52 128 readsf~;
#X obj 52 46 openpanel;
#X obj 52 73 symbol;
#X msg 52 101 open \$1 \, start;
#X obj 52 26 bng 15 250 50 0 empty empty empty 17 7 0 10 -262144 -1
-1;
#X obj 142 288 tgl 15 0 empty empty empty 17 7 0 10 -262144 -1 -1 0
1;
#X obj 70 286 tgl 15 1 empty empty empty 17 7 0 10 -262144 -1 -1 0
1;
#X obj 86 347 +~;
#X obj 78 387 dac~;
#X obj 179 112 noise~;
#X floatatom 117 142 5 0 0 0 - - -;
#X obj 52 166 *~ 1;
#X text 187 178 floor level;
#X floatatom 196 262 5 0 0 0 - - -;
#X text 239 264 floor (average);
#X text 74 24 open sample;
#X obj 179 142 *~ 0.01;
#X text 60 264 dirty;
#X text 133 263 clean;
#N canvas 222 138 574 729 noise-floor_filter 0;
#X obj -38 635 *~;
#X obj -98 78 *~;
#X obj 3 503 *~;
#X obj -98 50 inlet~;
#X obj -38 504 *~;
#X obj -99 107 rfft~;
#X obj -38 534 rifft~;
#X obj -38 665 outlet~;
#X obj -263 221 block~ 1024 4;
#X obj -57 78 tabreceive~ \$0-hann;
#X obj -20 597 tabreceive~ \$0-hann;
#X text -42 104 real Fourier transform;
#X obj -151 638 *~;
#X obj -110 506 *~;
#X obj -151 507 *~;
#X obj -151 537 rifft~;
#X obj -151 665 outlet~;
#X obj -151 566 /~ 1536;
#X obj 1 194 expr~ ($v1*$v1+$v2*$v2);
#X obj 118 258 avg~;
#X obj 118 226 bang~;
#X obj -251 255 loadbang;
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#X obj -38 564 /~ 1536;
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stupid bug; dsp $1 instead of dsp 1 on loadbang

Hey porres,

To attach files to the forum, you have to click on the "Post reply" link under the last comment instead of using the "Quick post" box.

ok then, let me show the patch I have, the idea is just switch~ [avg~] for a so called "median~" object, I have a "median~" subpatch that behaves as this object should, but over lists instead of actual audio blocks.

I'm gonna get some help to make this object, hope it works, if anyone is interested in doing this, let me know.

cheers

http://www.pdpatchrepo.info/hurleur/noise-floorII.pd

Hey Porres,

This is an interesting topic. I've tried to separate noise from harmonics once, using a very different method, and what I found was: it worked well, until the harmonics came from my voice and not from a synthesizer. My voice turned out to be so unstable that it could not be distinguished from noise, hah! But then, I'm a bad singer.

I really think you want a 'noise floor value' for each bin in the spectrum, and with this, separate bin values above it and below it. My previous post was cryptic, yes, and even worse, it was speculative. Bad habit. If I have time I'll try to put it to objects instead of words.

Katja

Ok so I've put my earlier suggestion in a patch (attached). A FIR filter computes the average over the last 40 FFT bins and gives an average output for each bin (instead of [avg~] computing the average over the full frame). So it's a kind of envelope follower for the spectrum.

This still doesn't match the concept. I overlooked the crucial difference between mean and median. I think the underlying idea to use median is, that energy in noise is spread over a lot of bins, so energy per bin is low even when total noise energy is high. For a sinusoidal component it is the other way round, the energy is concentrated in a four adjacent FFT bins if a Hann window was used on the input. So if you take an average of bins, the sinusoidal components still have a relatively large weight and pull the average upwards too much. With median it is more like 'one man one vote'.

By the way, some time ago Toxonic has posted a method to convert signals to message domain temporarily, and convert it back to signal after processing. It's here:

http://puredata.hurleur.com/sujet-5257-audio-floatstream-message-domain

Katja

http://www.pdpatchrepo.info/hurleur/noise-floorII-FIR.pd

Wow, I had no idea there was such a thing as the [pack~] & [unpack~] objects. I was about to ask about something like this, or propose it, because it is very cool the idea of acting on audio blocks as if they were lists, and do all sorts of operations we cant with audio objects.

Anyway, now that I there is such a thing, and since I already had programmed the median filter I needed with control objetcs... voilá! I have the thing working well.

But then, I need to delay the signal, since [pack~]/[unpack~] delays a block of audio.

My question is, is it possible to have it done without the delays?

thanks a lot, here's my patch for you people to check this out.

http://www.pdpatchrepo.info/hurleur/noise-floorIII.pd

i'll check you're FIR filter, but I know this stuff is a bit over me head, so nevermind if I dont follow it or reply, thanks a lot

Hi Porres,

What do you think of results with the median filter? I checked it with voice and found the separation much better than with the average filter. But the sound sucks. If you look at the median output, it goes in blocks of 32 identical values. I think it should be smooth, one unique value per bin. So the median of 32 bins should be computed 1024 times per spectrum, if a spectrum is 1024 points. Might be CPU intensive, and hard to code with existing Pd objects. Anyway you made a clever patch.

Katja

Attached is a patch with median values computed for each individual bin in a spectrum. It is only a demo working on one single spectrum recorded from [adc~]. I don't know how to synch it with the dsp chain yet. It needs to read the same data multiple times with overlap.

The median filter stretches beyond the spectrum boundaries by folding indexes within the spectrum range. Like so: -1 becomes 1, Nyquist+1 becomes Nyquist-1 etc. As long as a filter does not change phases, this is allowed because an FFT spectrum is considered to be periodical.

Remarkably, neighbor median values are often identical, like 3 or 4 or 5 identical values on a row.

Hopefully the routine can somehow be plugged in the FFT patch. Otherwise, a specialized external could do the work much more efficiently.

Katja

http://www.pdpatchrepo.info/hurleur/median-of-spectrum.pd

A median filter is indeed much more CPU intensive than a FIR average filter, because all the values in overlapping sections have to be sorted. Small example:

4 7 2 3 1 5 6 0 > 0 1 2 3 4 5 6 7
7 2 3 1 5 6 0 8 > 0 1 2 3 5 6 7 8
2 3 1 5 6 0 8 4 > 0 1 2 4 3 5 6 8

With the [median] object, each list is sorted from scratch. But if it could start from the previous sorted list with only the oldest value replaced by the newest value, sorting would be much faster. The only point is then, how to remember the original spectrum indexes belonging to the values in the sorted section, so you could replace the right one. In C, this can be done with a struct, like so:

typedef struct
{
t_float value;
t_int index;
}t_spectrumpoint;

Then make an array of the filter length M, to hold the bin indexes and values of the section being sorted:

t_spectrumpoint spectrumsection[M];

To sort values, you iterate over the value fields, and to find the spectrumpoint to replace, you iterate over the index fields. Only the first loop has to be sorted with a normal sorting routine like the shell sort in [median]. All subsequent loops can be reduced to finding and replacing the oldest bin value with the newest, and performing the simplified sort where only one known value is out of place. On average, this need not be more CPU intensive than a FIR filter.

A [median~] object written this way would be very useful. But for spectra, the folding at the spectrum boundaries should be taken into account as well. So, the object should have separate methods for 'signal' and 'spectrum'. All taken together, it is not a trivial object to write. Porres, do you think it's worth the effort, shall we collaborate on this?

Katja