C++ Constant-Q

h1. Synthetic test material

{{>toc}}

h2. Sinusoid at fs/4

In Yeti terms:

<pre>
testStream = manipulate.withDuration 64 (syn.sinusoid 8 2);
cq = cqt { maxFreq = testStream.sampleRate/2, minFreq = 1, binsPerOctave = 4 } testStream;
</pre>

Or to put it another way (in MATLAB this time):

<pre>
test = [0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1 ];
out = cqt(test,1,4,4,8)
</pre>

That is, a 64-sample input of 8Hz sample rate containing a sinusoid at fs/4, transformed using CQ parameters fmin = 1, fmax = 4 (or fs/2), and bpo = 4.



h3. Data from MATLAB implementation

!/attachments/download/868/Screenshot%20-%20181113%20-%2016_05_56.png!

<pre>
actual fmin = 1.1892
octaves = 2
weight = 16.3452
drop = 3
kernel size = 32x20
output size = 8x59
</pre>

and the output (magnitudes only):

<pre>
Columns 1 through 8

0.0001 0 0.0002 0 0.0001 0 0.0002 0
0.0001 0 0.0001 0 0.0002 0 0.0004 0
0.0001 0 0.0001 0 0.0003 0 0.0011 0
0.0002 0 0.0000 0 0.0003 0 0.0013 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

Columns 9 through 16

0.0011 0 0.0044 0 0.0980 0 0.3084 0
0.0018 0 0.0082 0 0.0468 0 0.3858 0
0.0050 0 0.0243 0 0.1211 0 0.6447 0
0.0065 0 0.0309 0 0.1543 0 0.8114 0
0 0 0 0 0.0002 0.0086 0.2742 1.1185
0 0 0 0 0.0011 0.0010 0.0711 0.7025
0 0 0 0 0.0001 0.0002 0.0099 0.5388
0 0 0 0 0.0001 0.0019 0.0006 0.4688

Columns 17 through 24

0.3962 0 0.2374 0 0.0484 0 0.0032 0
0.6804 0 0.3858 0 0.0468 0 0.0082 0
1.1968 0 0.6447 0 0.1211 0 0.0243 0
1.6297 0 0.8114 0 0.1544 0 0.0309 0
2.1085 2.4893 2.4383 2.4312 2.4314 2.4307 2.4311 2.4311
1.3506 0.9697 0.7693 0.7692 0.7688 0.7693 0.7691 0.7691
0.8193 0.0813 0.0491 0.0649 0.0499 0.0643 0.0493 0.0646
0.7188 0.0108 0.0492 0.0010 0.0493 0.0001 0.0488 0.0000

Columns 25 through 32

0.0007 0 0.0003 0 0.0006 0 0.0019 0
0.0019 0 0.0005 0 0.0004 0 0.0032 0
0.0051 0 0.0012 0 0.0019 0 0.0086 0
0.0062 0 0.0008 0 0.0021 0 0.0111 0
2.4311 2.4311 2.4311 2.4311 2.4311 2.4311 2.4311 2.4311
0.7691 0.7691 0.7691 0.7691 0.7691 0.7691 0.7691 0.7691
0.0493 0.0646 0.0493 0.0646 0.0493 0.0646 0.0493 0.0646
0.0488 0.0000 0.0488 0.0000 0.0488 0.0000 0.0488 0.0000

Columns 33 through 40

0.0168 0 0.1633 0 0.3646 0 0.3646 0
0.0143 0 0.1184 0 0.5325 0 0.6406 0
0.0414 0 0.2181 0 0.9118 0 1.1190 0
0.0532 0 0.2679 0 1.1926 0 1.5069 0
2.4311 2.4309 2.4305 2.4835 2.3188 1.4767 0.4927 0.0454
0.7692 0.7695 0.7692 0.7707 1.1679 1.2359 0.4175 0.0087
0.0494 0.0639 0.0494 0.0651 0.3139 0.8970 0.2914 0.0008
0.0490 0.0000 0.0490 0.0024 0.2044 0.8567 0.1557 0.0024

Columns 41 through 48

0.1633 0 0.0168 0 0.0019 0 0.0003 0
0.2373 0 0.0229 0 0.0052 0 0.0012 0
0.3956 0 0.0706 0 0.0144 0 0.0029 0
0.4838 0 0.0905 0 0.0184 0 0.0037 0
0.0000 0.0002 0 0 0 0 0 0
0.0012 0.0004 0 0 0 0 0 0
0.0002 0.0007 0 0 0 0 0 0
0.0002 0.0000 0 0 0 0 0 0

Columns 49 through 56

0.0003 0 0.0000 0 0.0000 0 0.0000 0
0.0003 0 0.0000 0 0.0000 0 0.0000 0
0.0006 0 0.0001 0 0.0000 0 0.0000 0
0.0009 0 0.0002 0 0.0000 0 0.0000 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

Columns 57 through 59

0.0000 0 0.0000
0.0000 0 0.0000
0.0000 0 0.0000
0.0000 0 0.0000
0 0 0
0 0 0
0 0 0
0 0 0
</pre>



h3. Data from Yeti implementation



h4. Process data

<pre>
sampleRate = 8
maxFreq = 4
minFreq = 1
actualMinFreq = 1.189207115002721
octaves = 2
binsPerOctave = 4

overall output size = {columns=40, rows=8}
</pre>



h4. Kernel data

That is,

<pre>
> (load cqtkernel).makeKernel { binsPerOctave = 4, maxFreq = 4, sampleRate = 8 }
</pre>

gives

<pre>
minFreq = 2.378414230005442, bigQ = 5.285213507883246, maxNK = 18, minNK = 11, atomHop = 3, firstCentre = 9, fftSize = 32
winNr = 5, lastCentre = 21, fftHop = 15
density = 0.6953125 (445 of 640)
weight = 16.34515230237943
{
atomSpacing = 3,
atomsPerFrame = 5,
bigQ = 5.285213507883246,
binsPerOctave = 4,
fftHop = 15,
fftSize = 32,
firstCentre = 9,
kernel = { ... , size = { columns = 32, rows = 20 } },
maxFreq = 4,
minFreq = 2.378414230005442
}
</pre>

h4. Output

<pre>
Columns 1 to 8

0.0062 0 0.1939 0 0.5393 0 0.6454 0
2.0E-4 0 0.0579 0 0.5993 0 1.0286 0
1.0E-4 0 0.0075 0 0.6026 0 1.757 0
6.0E-4 0 1.0E-4 0 0.4464 0 2.2625 0
8.0E-4 0.1289 0.7799 1.8196 2.4423 2.4596 2.4313 2.4312
4.0E-4 0.0086 0.4173 1.2368 1.1677 0.7713 0.7694 0.7692
0 3.0E-4 0.2913 0.8965 0.314 0.0646 0.0491 0.0646
0 0.0023 0.1558 0.8546 0.2042 3.0E-4 0.0487 0

Columns 9 to 16

0.357 0 0.0622 0 0.005 0 0.0036 0
0.5072 0 0.0268 0 0.035 0 0.0297 0
1.4134 0 0.7419 0 0.4654 0 0.2754 0
2.2998 0 1.3286 0 0.8006 0 0.422 0
2.4311 2.4304 2.4311 2.4311 2.4311 2.4311 2.4311 2.4311
0.7688 0.7692 0.7691 0.7691 0.7691 0.7691 0.7691 0.7691
0.0494 0.0646 0.0493 0.0645 0.0493 0.0645 0.0493 0.0645
0.0492 0 0.0487 0 0.0487 0 0.0487 0

Columns 17 to 24

0.0028 0 0.0032 0 0.0042 0 0.0356 0
0.0276 0 0.0281 0 0.0311 0 0.0364 0
0.1564 0 0.1849 0 0.3315 0 0.5455 0
0.1018 0 0.2055 0 0.5387 0 0.9529 0
2.4311 2.4311 2.4311 2.4311 2.4311 2.4311 2.459 2.442
0.7691 0.7691 0.7691 0.7691 0.7691 0.7694 0.7691 0.969
0.0493 0.0645 0.0493 0.0645 0.0497 0.0642 0.0492 0.0816
0.0487 0 0.0487 0 0.049 9.0E-4 0.0494 0.0087

Columns 25 to 32

0.2089 0 0.3834 0 0.3231 0 0.1176 0
0.1912 0 0.6183 0 0.5288 0 0.1079 0
0.9105 0 1.3187 0 0.6723 0 0.0493 0
1.572 0 1.856 0 0.6379 0 0.0053 0
1.8192 0.7802 0.1289 8.0E-4 3.0E-4 3.0E-4 0 0
1.3506 0.7023 0.0712 0.001 1.0E-4 2.0E-4 0 0
0.819 0.5381 0.0101 6.0E-4 2.0E-4 7.0E-4 0 0
0.7186 0.4668 4.0E-4 0.002 1.0E-4 0 0 0

Columns 33 to 40

0.0037 0 3.0E-4 0 4.0E-4 0 4.0E-4 0
5.0E-4 0 2.0E-4 0 1.0E-4 0 2.0E-4 0
0 0 1.0E-4 0 0 0 1.0E-4 0
0 0 2.0E-4 0 0 0 2.0E-4 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
</pre>