-
+
//Title: 1-d mixed radix FFT.
//Version:
//Copyright: Copyright (c) 1998
//
-public class fft1d{
+public class fft1d {
// Maximum numbers of factors allowed.
//private int MaxFactorsNumber = 30;
public int MaxFactorsNumber;
lastRadix = 0;
maxFactor = 20;
factorsWerePrinted = false;
- outputRe = global new double[N];
- outputIm = global new double[N];
+ outputRe = new double[N];
+ outputIm = new double[N];
factorize();
//printFactors();
// Allocate memory for intermediate result of FFT.
- temRe = global new double[maxFactor]; //Check usage of this
- temIm = global new double[maxFactor];
- }
-
- /*
- public void fft(double inputRe[], double inputIm[]) {
- // First make sure inputRe & inputIm are of the same length.
- if (inputRe.length != N || inputIm.length != N) {
- System.printString("Error: the length of real part & imaginary part " +
- "of the input to 1-d FFT are different");
- return;
- } else {
- this.inputRe = inputRe;
- this.inputIm = inputIm;
-
- permute();
- //System.printString("ready to twiddle");
-
- for (int factorIndex = 0; factorIndex < NumofFactors; factorIndex++)
- twiddle(factorIndex);
- //System.printString("ready to copy");
-
- // Copy the output[] data to input[], so the output can be
- // returned in the input array.
- for (int i = 0; i < N; i++) {
- inputRe[i] = outputRe[i];
- inputIm[i] = outputIm[i];
- }
- }
+ temRe = new double[maxFactor]; //Check usage of this
+ temIm = new double[maxFactor];
}
- */
public void printFactors() {
if (factorsWerePrinted) return;
}
public void factorize() {
- int radices[] = global new int[6];
+ int radices[] = new int[6];
radices[0] = 2;
radices[1] = 3;
radices[2] = 4;
radices[3] = 5;
radices[4] = 8;
radices[5] = 10;
- int temFactors[] = global new int[MaxFactorsNumber];
+ int temFactors[] = new int[MaxFactorsNumber];
// 1 - point FFT, no need to factorize N.
if (N == 1) {
while ((n > 1) && (i >= 0)) {
if ((n % radices[i]) == 0) {
- n /= radices[i];
- temFactors[index++] = radices[i];
+ n /= radices[i];
+ temFactors[index++] = radices[i];
} else
- i--;
+ i--;
}
// Substitute 2x8 with 4x4.
if ((index > 0) && (temFactors[index - 1] == 2)) {
int test = 0;
for (i = index - 2; (i >= 0) && (test == 0); i--) {
- if (temFactors[i] == 8) {
- temFactors[index - 1] = temFactors[i] = 4;
- // break out of for loop, because only one '2' will exist in
- // temFactors, so only one substitutation is needed.
- test = 1;
- //break;
- }
+ if (temFactors[i] == 8) {
+ temFactors[index - 1] = temFactors[i] = 4;
+ // break out of for loop, because only one '2' will exist in
+ // temFactors, so only one substitutation is needed.
+ test = 1;
+ }
}
}
if (n > 1) {
for (int k = 2; k < Math.sqrt(n) + 1; k++)
- while ((n % k) == 0) {
- n /= k;
- temFactors[index++] = k;
- }
+ while ((n % k) == 0) {
+ n /= k;
+ temFactors[index++] = k;
+ }
if (n > 1) {
- temFactors[index++] = n;
+ temFactors[index++] = n;
}
}
NumofFactors = index;
- //if(temFactors[NumofFactors-1] > 10)
- // maxFactor = n;
- //else
- // maxFactor = 10;
// Inverse temFactors and store factors into factors[].
- factors = global new int[NumofFactors];
+ factors = new int[NumofFactors];
for (i = 0; i < NumofFactors; i++) {
factors[i] = temFactors[NumofFactors - i - 1];
}
// sofar[] : finished factors before the current stage.
// factors[]: factors of N processed in the current stage.
// remain[] : finished factors after the current stage.
- sofar = global new int[NumofFactors];
- remain = global new int[NumofFactors];
+
+ sofar = new int[NumofFactors];
+ remain = new int[NumofFactors];
remain[0] = N / factors[0];
sofar[0] = 1;
remain[i] = remain[i - 1] / factors[i];
}
} // End of function factorize().
-/*
- private void permute() {
- int count[] = new int[MaxFactorsNumber];
- int j;
- int k = 0;
-
- for (int i = 0; i < N - 1; i++) {
- outputRe[i] = inputRe[k];
- outputIm[i] = inputIm[k];
- j = 0;
- k = k + remain[j];
- count[0] = count[0] + 1;
- while (count[j] >= factors[j]) {
- count[j] = 0;
- k = k - (j == 0?N:remain[j - 1]) + remain[j + 1];
- j++;
- count[j] = count[j] + 1;
- }
- }
- outputRe[N - 1] = inputRe[N - 1];
- outputIm[N - 1] = inputIm[N - 1];
- } // End of function permute().
- */
-/*
- private void twiddle(int factorIndex) {
- // Get factor data.
- int sofarRadix = sofar[factorIndex];
- int radix = factors[factorIndex];
- int remainRadix = remain[factorIndex];
-
- double tem; // Temporary variable to do data exchange.
-
- double W = 2 * (double) Math.PI / (sofarRadix * radix);
- double cosW = (double) Math.cos(W);
- double sinW = -(double) Math.sin(W);
-
- double twiddleRe[] = new double[radix];
- double twiddleIm[] = new double[radix];
- double twRe = 1.0f, twIm = 0f;
-
- //Initialize twiddle addBk.address variables.
- int dataOffset = 0, groupOffset = 0, address = 0;
-
- for (int dataNo = 0; dataNo < sofarRadix; dataNo++) {
- //System.printString("datano="+dataNo);
- if (sofarRadix > 1) {
- twiddleRe[0] = 1.0f;
- twiddleIm[0] = 0.0f;
- twiddleRe[1] = twRe;
- twiddleIm[1] = twIm;
- for (int i = 2; i < radix; i++) {
-
-
- twiddleRe[i] = twRe * twiddleRe[i - 1] - twIm * twiddleIm[i - 1];
- twiddleIm[i] = twIm * twiddleRe[i - 1] + twRe * twiddleIm[i - 1];
- }
- tem = cosW * twRe - sinW * twIm;
- twIm = sinW * twRe + cosW * twIm;
- twRe = tem;
- }
- for (int groupNo = 0; groupNo < remainRadix; groupNo++) {
- //System.printString("groupNo="+groupNo);
- if ((sofarRadix > 1) && (dataNo > 0)) {
- temRe[0] = outputRe[address];
- temIm[0] = outputIm[address];
- int blockIndex = 1;
- do {
- address = address + sofarRadix;
- temRe[blockIndex] = twiddleRe[blockIndex] * outputRe[address] -
- twiddleIm[blockIndex] * outputIm[address];
- temIm[blockIndex] = twiddleRe[blockIndex] * outputIm[address] +
- twiddleIm[blockIndex] * outputRe[address];
- blockIndex++;
- } while (blockIndex < radix);
- } else
- for (int i = 0; i < radix; i++) {
- //System.printString("temRe.length="+temRe.length);
- //System.printString("i = "+i);
- temRe[i] = outputRe[address];
- temIm[i] = outputIm[address];
- address += sofarRadix;
- }
- //System.printString("radix="+radix);
- if(radix == 2) {
- case 2:
- tem = temRe[0] + temRe[1];
- temRe[1] = temRe[0] - temRe[1];
- temRe[0] = tem;
- tem = temIm[0] + temIm[1];
- temIm[1] = temIm[0] - temIm[1];
- temIm[0] = tem;
- break;
- case 3:
- double t1Re = temRe[1] + temRe[2];
- double t1Im = temIm[1] + temIm[2];
- temRe[0] = temRe[0] + t1Re;
- temIm[0] = temIm[0] + t1Im;
-
- double m1Re = cos2to3PI * t1Re;
- double m1Im = cos2to3PI * t1Im;
- double m2Re = sin2to3PI * (temIm[1] - temIm[2]);
- double m2Im = sin2to3PI * (temRe[2] - temRe[1]);
- double s1Re = temRe[0] + m1Re;
- double s1Im = temIm[0] + m1Im;
-
- temRe[1] = s1Re + m2Re;
- temIm[1] = s1Im + m2Im;
- temRe[2] = s1Re - m2Re;
- temIm[2] = s1Im - m2Im;
- break;
- case 4:
- fft4(temRe, temIm);
- break;
- case 5:
- fft5(temRe, temIm);
- break;
- case 8:
- fft8();
- break;
- case 10:
- fft10();
- break;
- default :
- fftPrime(radix);
- break;
- }
- address = groupOffset;
- for (int i = 0; i < radix; i++) {
- outputRe[address] = temRe[i];
- outputIm[address] = temIm[i];
- address += sofarRadix;
- }
- groupOffset += sofarRadix * radix;
- address = groupOffset;
- }
- groupOffset = ++dataOffset;
- address = groupOffset;
- }
- } // End of function twiddle().
- */
-/*
- // The two arguments dataRe[], dataIm[] are mainly for using in fft8();
- private void fft4(double dataRe[], double dataIm[]) {
- double t1Re,t1Im, t2Re,t2Im;
- double m2Re,m2Im, m3Re,m3Im;
-
- t1Re = dataRe[0] + dataRe[2];
- t1Im = dataIm[0] + dataIm[2];
- t2Re = dataRe[1] + dataRe[3];
- t2Im = dataIm[1] + dataIm[3];
-
- m2Re = dataRe[0] - dataRe[2];
- m2Im = dataIm[0] - dataIm[2];
- m3Re = dataIm[1] - dataIm[3];
- m3Im = dataRe[3] - dataRe[1];
-
- dataRe[0] = t1Re + t2Re;
- dataIm[0] = t1Im + t2Im;
- dataRe[2] = t1Re - t2Re;
- dataIm[2] = t1Im - t2Im;
- dataRe[1] = m2Re + m3Re;
- dataIm[1] = m2Im + m3Im;
- dataRe[3] = m2Re - m3Re;
- dataIm[3] = m2Im - m3Im;
- } // End of function fft4().
- */
-/*
- // The two arguments dataRe[], dataIm[] are mainly for using in fft10();
- private void fft5(double dataRe[], double dataIm[]) {
- double t1Re,t1Im, t2Re,t2Im, t3Re,t3Im, t4Re,t4Im, t5Re,t5Im;
- double m1Re,m1Im, m2Re,m2Im, m3Re,m3Im, m4Re,m4Im, m5Re,m5Im;
- double s1Re,s1Im, s2Re,s2Im, s3Re,s3Im, s4Re,s4Im, s5Re,s5Im;
-
- t1Re = dataRe[1] + dataRe[4];
- t1Im = dataIm[1] + dataIm[4];
- t2Re = dataRe[2] + dataRe[3];
- t2Im = dataIm[2] + dataIm[3];
- t3Re = dataRe[1] - dataRe[4];
- t3Im = dataIm[1] - dataIm[4];
- t4Re = dataRe[3] - dataRe[2];
- t4Im = dataIm[3] - dataIm[2];
- t5Re = t1Re + t2Re;
- t5Im = t1Im + t2Im;
-
- dataRe[0] = dataRe[0] + t5Re;
- dataIm[0] = dataIm[0] + t5Im;
-
- m1Re = c51 * t5Re;
- m1Im = c51 * t5Im;
- m2Re = c52 * (t1Re - t2Re);
- m2Im = c52 * (t1Im - t2Im);
- m3Re = -c53 * (t3Im + t4Im);
- m3Im = c53 * (t3Re + t4Re);
- m4Re = -c54 * t4Im;
- m4Im = c54 * t4Re;
- m5Re = -c55 * t3Im;
- m5Im = c55 * t3Re;
-
- s3Re = m3Re - m4Re;
- s3Im = m3Im - m4Im;
- s5Re = m3Re + m5Re;
- s5Im = m3Im + m5Im;
- s1Re = dataRe[0] + m1Re;
- s1Im = dataIm[0] + m1Im;
- s2Re = s1Re + m2Re;
- s2Im = s1Im + m2Im;
- s4Re = s1Re - m2Re;
- s4Im = s1Im - m2Im;
-
- dataRe[1] = s2Re + s3Re;
- dataIm[1] = s2Im + s3Im;
- dataRe[2] = s4Re + s5Re;
- dataIm[2] = s4Im + s5Im;
- dataRe[3] = s4Re - s5Re;
- dataIm[3] = s4Im - s5Im;
- dataRe[4] = s2Re - s3Re;
- dataIm[4] = s2Im - s3Im;
- } // End of function fft5().
- */
-
- /*
- private void fft8() {
- double data1Re[] = new double[4];
- double data1Im[] = new double[4];
- double data2Re[] = new double[4];
- double data2Im[] = new double[4];
- double tem;
-
- // To improve the speed, use direct assaignment instead for loop here.
- data1Re[0] = temRe[0];
- data2Re[0] = temRe[1];
- data1Re[1] = temRe[2];
- data2Re[1] = temRe[3];
- data1Re[2] = temRe[4];
- data2Re[2] = temRe[5];
- data1Re[3] = temRe[6];
- data2Re[3] = temRe[7];
-
- data1Im[0] = temIm[0];
- data2Im[0] = temIm[1];
- data1Im[1] = temIm[2];
- data2Im[1] = temIm[3];
- data1Im[2] = temIm[4];
- data2Im[2] = temIm[5];
- data1Im[3] = temIm[6];
- data2Im[3] = temIm[7];
-
- fft4(data1Re, data1Im);
- fft4(data2Re, data2Im);
-
- tem = OnetoSqrt2 * (data2Re[1] + data2Im[1]);
- data2Im[1] = OnetoSqrt2 * (data2Im[1] - data2Re[1]);
- data2Re[1] = tem;
- tem = data2Im[2];
- data2Im[2] = -data2Re[2];
- data2Re[2] = tem;
- tem = OnetoSqrt2 * (data2Im[3] - data2Re[3]);
- data2Im[3] = -OnetoSqrt2 * (data2Re[3] + data2Im[3]);
- data2Re[3] = tem;
-
- temRe[0] = data1Re[0] + data2Re[0];
- temRe[4] = data1Re[0] - data2Re[0];
- temRe[1] = data1Re[1] + data2Re[1];
- temRe[5] = data1Re[1] - data2Re[1];
- temRe[2] = data1Re[2] + data2Re[2];
- temRe[6] = data1Re[2] - data2Re[2];
- temRe[3] = data1Re[3] + data2Re[3];
- temRe[7] = data1Re[3] - data2Re[3];
-
- temIm[0] = data1Im[0] + data2Im[0];
- temIm[4] = data1Im[0] - data2Im[0];
- temIm[1] = data1Im[1] + data2Im[1];
- temIm[5] = data1Im[1] - data2Im[1];
- temIm[2] = data1Im[2] + data2Im[2];
- temIm[6] = data1Im[2] - data2Im[2];
- temIm[3] = data1Im[3] + data2Im[3];
- temIm[7] = data1Im[3] - data2Im[3];
- } // End of function fft8().
- */
-
- /*
- private void fft10() {
- double data1Re[] = new double[5];
- double data1Im[] = new double[5];
- double data2Re[] = new double[5];
- double data2Im[] = new double[5];
-
- // To improve the speed, use direct assaignment instead for loop here.
- data1Re[0] = temRe[0];
- data2Re[0] = temRe[5];
- data1Re[1] = temRe[2];
- data2Re[1] = temRe[7];
- data1Re[2] = temRe[4];
- data2Re[2] = temRe[9];
- data1Re[3] = temRe[6];
- data2Re[3] = temRe[1];
- data1Re[4] = temRe[8];
- data2Re[4] = temRe[3];
-
- data1Im[0] = temIm[0];
- data2Im[0] = temIm[5];
- data1Im[1] = temIm[2];
- data2Im[1] = temIm[7];
- data1Im[2] = temIm[4];
- data2Im[2] = temIm[9];
- data1Im[3] = temIm[6];
- data2Im[3] = temIm[1];
- data1Im[4] = temIm[8];
- data2Im[4] = temIm[3];
-
- fft5(data1Re, data1Im);
- fft5(data2Re, data2Im);
-
- temRe[0] = data1Re[0] + data2Re[0];
- temRe[5] = data1Re[0] - data2Re[0];
- temRe[6] = data1Re[1] + data2Re[1];
- temRe[1] = data1Re[1] - data2Re[1];
- temRe[2] = data1Re[2] + data2Re[2];
- temRe[7] = data1Re[2] - data2Re[2];
- temRe[8] = data1Re[3] + data2Re[3];
- temRe[3] = data1Re[3] - data2Re[3];
- temRe[4] = data1Re[4] + data2Re[4];
- temRe[9] = data1Re[4] - data2Re[4];
-
- temIm[0] = data1Im[0] + data2Im[0];
- temIm[5] = data1Im[0] - data2Im[0];
- temIm[6] = data1Im[1] + data2Im[1];
- temIm[1] = data1Im[1] - data2Im[1];
- temIm[2] = data1Im[2] + data2Im[2];
- temIm[7] = data1Im[2] - data2Im[2];
- temIm[8] = data1Im[3] + data2Im[3];
- temIm[3] = data1Im[3] - data2Im[3];
- temIm[4] = data1Im[4] + data2Im[4];
- temIm[9] = data1Im[4] - data2Im[4];
- } // End of function fft10().
- */
-
- /*
- public double sqrt(double d) {
- return Math.sqrt(d);
- }
- */
-
- /*
- private void fftPrime(int radix) {
- // Initial WRe, WIm.
- double W = 2 * (double) Math.PI / radix;
- double cosW = (double) Math.cos(W);
- double sinW = -(double) Math.sin(W);
- double WRe[] = new double[radix];
- double WIm[] = new double[radix];
-
- WRe[0] = 1;
- WIm[0] = 0;
- WRe[1] = cosW;
- WIm[1] = sinW;
-
- for (int i = 2; i < radix; i++) {
- WRe[i] = cosW * WRe[i - 1] - sinW * WIm[i - 1];
- WIm[i] = sinW * WRe[i - 1] + cosW * WIm[i - 1];
- }
-
- // FFT of prime length data, using DFT, can be improved in the future.
- double rere, reim, imre, imim;
- int j, k;
- int max = (radix + 1) / 2;
-
- double tem1Re[] = new double[max];
- double tem1Im[] = new double[max];
- double tem2Re[] = new double[max];
- double tem2Im[] = new double[max];
-
- for (j = 1; j < max; j++) {
- tem1Re[j] = temRe[j] + temRe[radix - j];
- tem1Im[j] = temIm[j] - temIm[radix - j];
- tem2Re[j] = temRe[j] - temRe[radix - j];
- tem2Im[j] = temIm[j] + temIm[radix - j];
- }
-
- for (j = 1; j < max; j++) {
- temRe[j] = temRe[0];
- temIm[j] = temIm[0];
- temRe[radix - j] = temRe[0];
- temIm[radix - j] = temIm[0];
- k = j;
- for (int i = 1; i < max; i++) {
- rere = WRe[k] * tem1Re[i];
- imim = WIm[k] * tem1Im[i];
- reim = WRe[k] * tem2Im[i];
- imre = WIm[k] * tem2Re[i];
-
- temRe[radix - j] += rere + imim;
- temIm[radix - j] += reim - imre;
- temRe[j] += rere - imim;
- temIm[j] += reim + imre;
-
- k = k + j;
- if (k >= radix)
- k = k - radix;
- }
- }
- for (j = 1; j < max; j++) {
- temRe[0] = temRe[0] + tem1Re[j];
- temIm[0] = temIm[0] + tem2Im[j];
- }
- } // End of function fftPrime().
- */
-
-} // End of class FFT2d
+} // End of class FFT1d
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