Add implementation of AudioWindowKaiserBessel

analyze_fft1024.h

@@ -44,6 +44,7 @@ extern const int16_t AudioWindowWelch1024[];
 extern const int16_t AudioWindowHamming1024[];
 extern const int16_t AudioWindowCosine1024[];
 extern const int16_t AudioWindowTukey1024[];
+extern const int16_t AudioWindowKaiserBessel1024[];
 }
 
 class AudioAnalyzeFFT1024 : public AudioStream

analyze_fft256.h

@@ -44,6 +44,7 @@ extern const int16_t AudioWindowWelch256[];
 extern const int16_t AudioWindowHamming256[];
 extern const int16_t AudioWindowCosine256[];
 extern const int16_t AudioWindowTukey256[];
+extern const int16_t AudioWindowKaiserBessel256[];
 }
 
 class AudioAnalyzeFFT256 : public AudioStream

data_windows.c

@@ -1511,6 +1511,141 @@ const int16_t AudioWindowTukey1024[] __attribute__ ((aligned (4))) = {
     11,     5,     1,     0,
 };
 
+const int16_t AudioWindowKaiserBessel256[] __attribute__ ((aligned (4))) = {
+    20,    28,    37,    47,    59,    72,    87,   105,   124,   145,
+   169,   196,   225,   257,   293,   331,   373,   419,   469,   523,
+   581,   643,   710,   782,   860,   942,  1030,  1124,  1224,  1330,
+  1442,  1561,  1687,  1819,  1959,  2106,  2261,  2423,  2594,  2772,
+  2958,  3153,  3357,  3568,  3789,  4018,  4257,  4504,  4760,  5026,
+  5300,  5584,  5877,  6179,  6490,  6810,  7139,  7477,  7824,  8180,
+  8544,  8917,  9298,  9687, 10085, 10489, 10902, 11321, 11748, 12181,
+ 12620, 13065, 13516, 13972, 14433, 14899, 15369, 15842, 16319, 16798,
+ 17279, 17763, 18247, 18733, 19218, 19704, 20188, 20671, 21153, 21631,
+ 22107, 22579, 23047, 23511, 23969, 24421, 24866, 25305, 25736, 26159,
+ 26573, 26978, 27373, 27757, 28131, 28494, 28844, 29183, 29508, 29820,
+ 30119, 30403, 30673, 30928, 31167, 31391, 31599, 31791, 31966, 32125,
+ 32266, 32391, 32497, 32587, 32658, 32712, 32748, 32766, 32766, 32748,
+ 32712, 32658, 32587, 32497, 32391, 32266, 32125, 31966, 31791, 31599,
+ 31391, 31167, 30928, 30673, 30403, 30119, 29820, 29508, 29183, 28844,
+ 28494, 28131, 27757, 27373, 26978, 26573, 26159, 25736, 25305, 24866,
+ 24421, 23969, 23511, 23047, 22579, 22107, 21631, 21153, 20671, 20188,
+ 19704, 19218, 18733, 18247, 17763, 17279, 16798, 16319, 15842, 15369,
+ 14899, 14433, 13972, 13516, 13065, 12620, 12181, 11748, 11321, 10902,
+ 10489, 10085,  9687,  9298,  8917,  8544,  8180,  7824,  7477,  7139,
+  6810,  6490,  6179,  5877,  5584,  5300,  5026,  4760,  4504,  4257,
+  4018,  3789,  3568,  3357,  3153,  2958,  2772,  2594,  2423,  2261,
+  2106,  1959,  1819,  1687,  1561,  1442,  1330,  1224,  1124,  1030,
+   942,   860,   782,   710,   643,   581,   523,   469,   419,   373,
+   331,   293,   257,   225,   196,   169,   145,   124,   105,    87,
+    72,    59,    47,    37,    28,    20
+};
+
+const int16_t AudioWindowKaiserBessel1024[] __attribute__ ((aligned (4))) = {
+    20,    22,    24,    26,    28,    30,    32,    34,    36,    39,
+    41,    44,    47,    49,    52,    55,    58,    62,    65,    68,
+    72,    75,    79,    83,    87,    91,    95,   100,   104,   109,
+   113,   118,   123,   128,   134,   139,   145,   150,   156,   162,
+   169,   175,   181,   188,   195,   202,   209,   217,   224,   232,
+   240,   248,   256,   265,   273,   282,   291,   300,   310,   320,
+   330,   340,   350,   361,   371,   382,   394,   405,   417,   429,
+   441,   453,   466,   479,   492,   506,   520,   534,   548,   562,
+   577,   592,   608,   623,   639,   655,   672,   689,   706,   723,
+   741,   759,   777,   796,   815,   834,   854,   874,   894,   915,
+   936,   957,   979,  1001,  1023,  1046,  1069,  1093,  1117,  1141,
+  1165,  1190,  1216,  1241,  1267,  1294,  1321,  1348,  1376,  1404,
+  1432,  1461,  1490,  1520,  1550,  1581,  1611,  1643,  1675,  1707,
+  1740,  1773,  1806,  1840,  1875,  1910,  1945,  1981,  2017,  2054,
+  2091,  2129,  2167,  2205,  2244,  2284,  2324,  2364,  2405,  2447,
+  2489,  2531,  2574,  2618,  2662,  2706,  2751,  2797,  2843,  2889,
+  2936,  2984,  3032,  3080,  3129,  3179,  3229,  3280,  3331,  3383,
+  3435,  3488,  3541,  3595,  3650,  3705,  3760,  3816,  3873,  3930,
+  3988,  4046,  4105,  4164,  4224,  4285,  4346,  4407,  4469,  4532,
+  4595,  4659,  4724,  4789,  4854,  4920,  4987,  5054,  5122,  5190,
+  5259,  5329,  5399,  5470,  5541,  5613,  5685,  5758,  5831,  5906,
+  5980,  6055,  6131,  6207,  6284,  6362,  6440,  6518,  6598,  6677,
+  6758,  6839,  6920,  7002,  7084,  7168,  7251,  7335,  7420,  7505,
+  7591,  7678,  7765,  7852,  7940,  8029,  8118,  8207,  8298,  8388,
+  8480,  8571,  8664,  8756,  8850,  8944,  9038,  9133,  9228,  9324,
+  9421,  9517,  9615,  9713,  9811,  9910, 10009, 10109, 10210, 10310,
+ 10412, 10513, 10616, 10718, 10821, 10925, 11029, 11133, 11238, 11343,
+ 11449, 11555, 11662, 11769, 11876, 11984, 12092, 12201, 12310, 12419,
+ 12529, 12639, 12750, 12861, 12972, 13084, 13196, 13308, 13420, 13533,
+ 13647, 13760, 13874, 13988, 14103, 14218, 14333, 14448, 14564, 14680,
+ 14796, 14913, 15030, 15146, 15264, 15381, 15499, 15617, 15735, 15853,
+ 15972, 16090, 16209, 16328, 16448, 16567, 16687, 16806, 16926, 17046,
+ 17166, 17286, 17407, 17527, 17648, 17768, 17889, 18010, 18131, 18251,
+ 18372, 18493, 18614, 18735, 18856, 18978, 19099, 19220, 19341, 19462,
+ 19583, 19704, 19824, 19945, 20066, 20187, 20307, 20428, 20548, 20668,
+ 20789, 20909, 21029, 21148, 21268, 21387, 21507, 21626, 21745, 21863,
+ 21982, 22100, 22218, 22336, 22454, 22571, 22688, 22805, 22922, 23038,
+ 23154, 23269, 23385, 23500, 23615, 23729, 23843, 23957, 24070, 24183,
+ 24295, 24408, 24519, 24631, 24742, 24852, 24962, 25072, 25181, 25290,
+ 25398, 25506, 25613, 25720, 25826, 25932, 26037, 26142, 26246, 26349,
+ 26452, 26555, 26657, 26758, 26859, 26959, 27058, 27157, 27256, 27353,
+ 27450, 27547, 27642, 27737, 27832, 27925, 28018, 28111, 28202, 28293,
+ 28383, 28473, 28562, 28650, 28737, 28823, 28909, 28994, 29078, 29161,
+ 29244, 29326, 29407, 29487, 29566, 29644, 29722, 29799, 29875, 29950,
+ 30024, 30097, 30170, 30242, 30312, 30382, 30451, 30519, 30586, 30652,
+ 30717, 30782, 30845, 30908, 30969, 31030, 31089, 31148, 31205, 31262,
+ 31318, 31372, 31426, 31479, 31531, 31581, 31631, 31680, 31727, 31774,
+ 31820, 31864, 31908, 31950, 31992, 32032, 32072, 32110, 32147, 32183,
+ 32219, 32253, 32286, 32318, 32348, 32378, 32407, 32435, 32461, 32487,
+ 32511, 32534, 32556, 32578, 32598, 32616, 32634, 32651, 32666, 32681,
+ 32694, 32707, 32718, 32728, 32737, 32744, 32751, 32757, 32761, 32765,
+ 32767, 32767, 32767, 32767, 32765, 32761, 32757, 32751, 32744, 32737,
+ 32728, 32718, 32707, 32694, 32681, 32666, 32651, 32634, 32616, 32598,
+ 32578, 32556, 32534, 32511, 32487, 32461, 32435, 32407, 32378, 32348,
+ 32318, 32286, 32253, 32219, 32183, 32147, 32110, 32072, 32032, 31992,
+ 31950, 31908, 31864, 31820, 31774, 31727, 31680, 31631, 31581, 31531,
+ 31479, 31426, 31372, 31318, 31262, 31205, 31148, 31089, 31030, 30969,
+ 30908, 30845, 30782, 30717, 30652, 30586, 30519, 30451, 30382, 30312,
+ 30242, 30170, 30097, 30024, 29950, 29875, 29799, 29722, 29644, 29566,
+ 29487, 29407, 29326, 29244, 29161, 29078, 28994, 28909, 28823, 28737,
+ 28650, 28562, 28473, 28383, 28293, 28202, 28111, 28018, 27925, 27832,
+ 27737, 27642, 27547, 27450, 27353, 27256, 27157, 27058, 26959, 26859,
+ 26758, 26657, 26555, 26452, 26349, 26246, 26142, 26037, 25932, 25826,
+ 25720, 25613, 25506, 25398, 25290, 25181, 25072, 24962, 24852, 24742,
+ 24631, 24519, 24408, 24295, 24183, 24070, 23957, 23843, 23729, 23615,
+ 23500, 23385, 23269, 23154, 23038, 22922, 22805, 22688, 22571, 22454,
+ 22336, 22218, 22100, 21982, 21863, 21745, 21626, 21507, 21387, 21268,
+ 21148, 21029, 20909, 20789, 20668, 20548, 20428, 20307, 20187, 20066,
+ 19945, 19824, 19704, 19583, 19462, 19341, 19220, 19099, 18978, 18856,
+ 18735, 18614, 18493, 18372, 18251, 18131, 18010, 17889, 17768, 17648,
+ 17527, 17407, 17286, 17166, 17046, 16926, 16806, 16687, 16567, 16448,
+ 16328, 16209, 16090, 15972, 15853, 15735, 15617, 15499, 15381, 15264,
+ 15146, 15030, 14913, 14796, 14680, 14564, 14448, 14333, 14218, 14103,
+ 13988, 13874, 13760, 13647, 13533, 13420, 13308, 13196, 13084, 12972,
+ 12861, 12750, 12639, 12529, 12419, 12310, 12201, 12092, 11984, 11876,
+ 11769, 11662, 11555, 11449, 11343, 11238, 11133, 11029, 10925, 10821,
+ 10718, 10616, 10513, 10412, 10310, 10210, 10109, 10009,  9910,  9811,
+  9713,  9615,  9517,  9421,  9324,  9228,  9133,  9038,  8944,  8850,
+  8756,  8664,  8571,  8480,  8388,  8298,  8207,  8118,  8029,  7940,
+  7852,  7765,  7678,  7591,  7505,  7420,  7335,  7251,  7168,  7084,
+  7002,  6920,  6839,  6758,  6677,  6598,  6518,  6440,  6362,  6284,
+  6207,  6131,  6055,  5980,  5906,  5831,  5758,  5685,  5613,  5541,
+  5470,  5399,  5329,  5259,  5190,  5122,  5054,  4987,  4920,  4854,
+  4789,  4724,  4659,  4595,  4532,  4469,  4407,  4346,  4285,  4224,
+  4164,  4105,  4046,  3988,  3930,  3873,  3816,  3760,  3705,  3650,
+  3595,  3541,  3488,  3435,  3383,  3331,  3280,  3229,  3179,  3129,
+  3080,  3032,  2984,  2936,  2889,  2843,  2797,  2751,  2706,  2662,
+  2618,  2574,  2531,  2489,  2447,  2405,  2364,  2324,  2284,  2244,
+  2205,  2167,  2129,  2091,  2054,  2017,  1981,  1945,  1910,  1875,
+  1840,  1806,  1773,  1740,  1707,  1675,  1643,  1611,  1581,  1550,
+  1520,  1490,  1461,  1432,  1404,  1376,  1348,  1321,  1294,  1267,
+  1241,  1216,  1190,  1165,  1141,  1117,  1093,  1069,  1046,  1023,
+  1001,   979,   957,   936,   915,   894,   874,   854,   834,   815,
+   796,   777,   759,   741,   723,   706,   689,   672,   655,   639,
+   623,   608,   592,   577,   562,   548,   534,   520,   506,   492,
+   479,   466,   453,   441,   429,   417,   405,   394,   382,   371,
+   361,   350,   340,   330,   320,   310,   300,   291,   282,   273,
+   265,   256,   248,   240,   232,   224,   217,   209,   202,   195,
+   188,   181,   175,   169,   162,   156,   150,   145,   139,   134,
+   128,   123,   118,   113,   109,   104,   100,    95,    91,    87,
+    83,    79,    75,    72,    68,    65,    62,    58,    55,    52,
+    49,    47,    44,    41,    39,    36,    34,    32,    30,    28,
+    26,    24,    22,    20
+};
+
 
 /*
 #! /usr/bin/perl
@@ -1616,3 +1751,46 @@ for ($i=0; $i < $len; $i++) {
 print "\n" unless ($len % 10) == 9;
 print "};\n";
 */
+
+/*
+#! /usr/bin/python
+
+import numpy
+import scipy.special
+
+"https://en.wikipedia.org/wiki/Window_function"
+
+N=255
+
+scale = 32767.4 / 0.999931
+
+def transform(x):
+    x *= 32768
+    x[x>32767] = 32767
+    return (x+0.5).astype(numpy.int16)
+
+def kaiser(x, len, a=3):
+    a = a * numpy.pi
+    x = 2*x/(len-1)-1
+    return scipy.special.i0(a * numpy.sqrt(1-x*x)) / scipy.special.i0(a)
+
+if __name__ == "__main__":
+    len = 1024
+    cols = 10
+    name = "KaiserBessel"
+    func = kaiser
+    kwargs = {'a': 3}
+
+    y = func(numpy.arange(0,len), len, **kwargs)
+    y = transform(y)
+
+    print(f"const int16_t AudioWindow{name}{len}[] __attribute__ ((aligned (4))) = {{")
+
+    tail = ","
+    for  i in range(0, len, cols):
+        if i+cols >= len:
+            tail = ""
+        print(",".join(map("{:6d}".format,y[i:i+cols])) + tail)
+
+    print("};")
+*/

gui/index.html

@@ -4933,6 +4933,7 @@ <h3>Notes</h3>
 		<li><span class=literal>AudioWindowHamming256</span></li>
 		<li><span class=literal>AudioWindowCosine256</span></li>
 		<li><span class=literal>AudioWindowTukey256</span></li>
+		<li><span class=literal>AudioWindowKaiserBessel256</span></li>
 		</ul>
 	</p>
 </script>
@@ -5000,6 +5001,7 @@ <h3>Notes</h3>
 		<li><span class=literal>AudioWindowHamming1024</span></li>
 		<li><span class=literal>AudioWindowCosine1024</span></li>
 		<li><span class=literal>AudioWindowTukey1024</span></li>
+		<li><span class=literal>AudioWindowKaiserBessel1024</span></li>
 		</ul>
 	</p>
 	<p>1024 point FFT has a peak CPU usage of approx 52% on Teensy 3.1.

keywords.txt

@@ -234,6 +234,7 @@ AudioWindowWelch256	LITERAL1
 AudioWindowHamming256	LITERAL1
 AudioWindowCosine256	LITERAL1
 AudioWindowTukey256	LITERAL1
+AudioWindowKaiserBessel256	LITERAL1
 
 FILTER_LOPASS	LITERAL1
 FILTER_HIPASS	LITERAL1

library.json

@@ -5,7 +5,7 @@
   "keywords": "sound, audio, FFT, filter, effect",
   "description": "Teensy Audio Library",
   "url": "http://www.pjrc.com/teensy/td_libs_Audio.html",
-  "version": "1.3",
+  "version": "1.4",
   "export": {
     "exclude": [
       "gui",

library.properties

@@ -1,5 +1,5 @@
 name=Audio
-version=1.3
+version=1.4
 author=Paul Stoffregen
 maintainer=Paul Stoffregen
 sentence=Teensy Audio Library - Flexible, High Quality Audio Processing