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>