PHP FFT module error - php

Question

I wrote a FFT (Fast Fourier Transform) module for PHP recently. When I tried to test it, It always throws an error that the array $this->reverseTable has some index not defined. I got no clue of how to solve this problem.
Here's the PHP code:
<?php
class FourierTransform {
public $bufferSize;
public $sampleRate;
public $bandwidth;
public $spectrum = array();
public $real = array();
public $imag = array();
public $peakBand = 0;
public $peak = 0;
public function __construct($bufferSize,$sampleRate){
$this->bufferSize = $bufferSize;
$this->sampleRate = $sampleRate;
$this->bandwidth = 2 / $bufferSize * $sampleRate / 2;
}
public function getBandFrequency($index){
return $this->bandwidth * $index + $this->bandwidth / 2;
}
public function calculateSpectrum(){
$bSi = 2 / $this->bufferSize;
for($i = 0,$N = $this->bufferSize/2; $i < $N; $i++){
$rval = $this->real[$i];
$ival = $this->imag[$i];
$mag = $bSi * sqrt($rval * $rval + $ival * $ival);
if($mag > $this->peak){
$this->peakBand = $i;
$this->peak = $mag;
}
$this->spectrum[$i] = $mag;
}
}
}
class FFT extends FourierTransform {
public $reverseTable = array();
public $sinTable = array();
public $cosTable = array();
public function __construct($bufferSize,$sampleRate){
parent::__construct($bufferSize,$sampleRate);
$limit = 1;
$bit = $bufferSize >> 1;
while($limit < $bufferSize){
for($i = 0; $i < $limit; $i++){
$this->reverseTable[$i + $limit] = $this->reverseTable[$i] + $bit;
}
$limit = $limit << 1;
$bit = $bit >> 1;
}
for($i = 0; $i < $bufferSize; $i++){
$this->sinTable[$i] = sin(-M_PI / $i);
$this->cosTable[$i] = cos(-M_PI / $i);
}
}
public function foward($buffer){
$k = floor(log($this->bufferSize,2));
if(pow(2,$k) !== $this->bufferSize) throw new Exception('Invalid buffer size, must be a power of 2.');
if($this->bufferSize !== count($buffer)) throw new Exception('Supplied buffer is not the same size as defined FFT.');
$halfSize = 1;
for($i = 0; $i < $this->bufferSize; $i++){
$this->real[$i] = $buffer[$this->reverseTable[$i]];
$this->imag[$i] = 0;
}
while($halfSize < $this->bufferSize){
$phaseShiftReal = $this->cosTable[$halfSize];
$phaseShiftImag = $this->sinTable[$halfSize];
$currentPhaseShiftReal = 1;
$currentPhaseShiftImag = 0;
for($fftStep = 0; $fftStep < $halfSize; $fftStep++){
while($fftStep < $this->bufferSize){
$off = $fftStep + $halfSize;
$tr = ($currentPhaseShiftReal * $this->real[$off]) - ($currentPhaseShiftImag * $this->imag[$off]);
$ti = ($currentPhaseShiftReal * $this->imag[$off]) + ($currentPhaseShiftImag * $this->real[$off]);
$this->real[$off] = $this->real[$fftStep] - $tr;
$this->imag[$off] = $this->imag[$fftStep] - $ti;
$this->real[$fftStep] += $tr;
$this->imag[$fftStep] += $ti;
$fftStep += $halfSize << 1;
}
$tmpReal = $currentPhaseShiftReal;
$currentPhaseShiftReal = ($tmpReal * $phaseShiftReal) - ($currentPhaseShiftImag * $phaseShiftImag);
$currentPhaseShiftImag = ($tmpReal * $phaseShiftImag) + ($currentPhaseShiftImag * $phaseShiftReal);
}
$halfSize = $halfSize << 1;
}
$this->calculateSpectrum();
}
}
?>
The test sample is a sine wave at 440Hz.
When I tried to run the code, it throws this error
Notice: Undefined offset: 0 in C:\Program Files
(x86)\EasyPHP-12.1\www\fft.php on line 48
continuously.
The array that has problem has data like this:
Array
(
[1] => 512
[2] => 256
[3] => 768
[4] => 128
[5] => 640
[6] => 384
[7] => 896
[8] => 64
[9] => 576
[10] => 320
[11] => 832
[12] => 192
[13] => 704
[14] => 448
[15] => 960
[16] => 32
[17] => 544
[18] => 288
[19] => 800
[20] => 160
[21] => 672
[22] => 416
[23] => 928
[24] => 96
[25] => 608
[26] => 352
[27] => 864
[28] => 224
[29] => 736
[30] => 480
[31] => 992
[32] => 16
[33] => 528
[34] => 272
[35] => 784
[36] => 144
[37] => 656
[38] => 400
[39] => 912
[40] => 80
[41] => 592
[42] => 336
[43] => 848
[44] => 208
[45] => 720
...
[978] => 303
[979] => 815
[980] => 175
[981] => 687
[982] => 431
[983] => 943
[984] => 111
[985] => 623
[986] => 367
[987] => 879
[988] => 239
[989] => 751
[990] => 495
[991] => 1007
[992] => 31
[993] => 543
[994] => 287
[995] => 799
[996] => 159
[997] => 671
[998] => 415
[999] => 927
[1000] => 95
[1001] => 607
[1002] => 351
[1003] => 863
[1004] => 223
[1005] => 735
[1006] => 479
[1007] => 991
[1008] => 63
[1009] => 575
[1010] => 319
[1011] => 831
[1012] => 191
[1013] => 703
[1014] => 447
[1015] => 959
[1016] => 127
[1017] => 639
[1018] => 383
[1019] => 895
[1020] => 255
[1021] => 767
[1022] => 511
[1023] => 1023
)
Edit: The previous problem is solved but now another problem is raised. At function forward() it throws an uncaught exception Invalid buffer size, must be a power of 2. Even if the buffer size is right.
Any help will be appreciated.

Answer 1

Assuming that this is the whole class, I presume that the issue lies on this line inside your FFT constructor:
$this->reverseTable[$i + $limit] = $this->reverseTable[$i] + $bit;
From what I can tell you declare reverseTable as an array, but this line is the only place in the class where any elements are added to that array, so the fact that you're setting the reverseTable[$i+$limit] element using a never-defined reverseTable[$i] value is going to give you problems in the first first iteration of that while loop when it tries to use the undefined index $i (reverseTable[$i]). You'll have to give reverseTable[0] a value before you enter that loop.

Answer 2

Although you didn't provide where the line was, my guess is it has something to do with this line:
$this->reverseTable[$i + $limit] = $this->reverseTable[$i] + $bit;
This is in your constructor, and this bit especially looks wrong $this->reverseTable[$i] + $bit;. You are asking for the value from the reverseTable array, but this key is not initialized anywhere in the constructor.
I am not sure how to fix this, as it is a logic error on your part.