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fft.cc
/*************************************************************************/
/* */
/* Centre for Speech Technology Research */
/* University of Edinburgh, UK */
/* Copyright (c) 1994,1995,1996 */
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/* the following conditions: */
/* 1. The code must retain the above copyright notice, this list of */
/* conditions and the following disclaimer. */
/* 2. Any modifications must be clearly marked as such. */
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/* */
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/* SHALL THE UNIVERSITY OF EDINBURGH NOR THE CONTRIBUTORS BE LIABLE */
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/* */
/*************************************************************************/
/* Author : Simon King (taken from Tony Robinson) */
/* Date : July 1994 */
/*-----------------------------------------------------------------------*/
/* FFT functions */
/* */
/*=======================================================================*/
#include <cmath>
//#include <iostream>
//#include <fstream>
#include "sigpr/EST_fft.h"
#include "EST_math.h"
#include "EST_error.h"
#define PI8 0.392699081698724 /* PI / 8.0 */
#define RT2 1.4142135623731 /* sqrt(2.0) */
#define IRT2 0.707106781186548 /* 1.0/sqrt(2.0) */
static void FR2TR(int, float*, float*);
static void FR4TR(int, int, float*, float*, float*, float*);
static void FORD1(int, float*);
static void FORD2(int, float*);
/*
** FAST(b,n)
** This routine replaces the float vector b
** of length n with its finite discrete fourier transform.
** DC term is returned in b[0];
** n/2th harmonic float part in b[1].
** jth harmonic is returned as complex number stored as
** b[2*j] + i b[2*j + 1]
** (i.e., remaining coefficients are as a DPCOMPLEX vector).
**
*/
static int slowFFTsub(EST_FVector &real, EST_FVector &imag, float f)
{
// f = -1 for FFT, 1 for IFFT
// would be nicer if we used a complex number class,
// but we don't, so it isn't
// taken from the FORTRAN old chestnut
// in various sig proc books
// FORTRAN uses 1..n arrays, so subtract 1 all over the place
float u_real,u_imag;
float w_real,w_imag;
float t_real,t_imag;
float tmp_real,tmp_imag;
int M,N;
int i,j,k,l;
M = fastlog2(real.n());
N = (int)pow(float(2.0),(float)M);
if (N != real.n())
{
EST_warning("Illegal FFT order %d", real.n());
return -1;
}
for(l=1;l<=M;l++){
int le = (int)pow(float(2.0),(float)(M+1-l));
int le1=le/2;
u_real = 1.0;
u_imag = 0.0;
w_real=cos(PI/le1);
w_imag=f * sin(PI/le1);
for (j=1;j<=le1;j++)
{
for (i=j;i<=N-le1;i+=le)
{
int ip=i+le1;
t_real = real.a_no_check(i-1) + real.a_no_check(ip-1);
t_imag = imag.a_no_check(i-1) + imag.a_no_check(ip-1);
tmp_real = real.a_no_check(i-1) - real.a_no_check(ip-1);
tmp_imag = imag.a_no_check(i-1) - imag.a_no_check(ip-1);
real.a_no_check(ip-1) = tmp_real*u_real - tmp_imag*u_imag;
imag.a_no_check(ip-1) = tmp_real*u_imag + tmp_imag*u_real;
real.a_no_check(i-1) = t_real;
imag.a_no_check(i-1) = t_imag;
}
tmp_real = u_real*w_real - u_imag*w_imag;
tmp_imag = u_real*w_imag + u_imag*w_real;
u_real=tmp_real;
u_imag=tmp_imag;
}
}
int NV2=N/2;
int NM1=N-1;
j=1;
for (i=1; i<=NM1;i++)
{
if (i < j)
{
t_real=real(j-1);
t_imag=imag(j-1);
real[j-1] = real(i-1);
imag[j-1] = imag(i-1);
real[i-1] = t_real;
imag[i-1] = t_imag;
}
k=NV2;
while(k < j)
{
j=j-k;
k=k/2;
}
j=j+k;
}
return 0;
}
int slowFFT(EST_FVector &real, EST_FVector &imag)
{
return slowFFTsub(real,imag,-1.0);
}
int slowIFFT(EST_FVector &real, EST_FVector &imag)
{
int N=real.n();
if (N <=0 )
return -1;
if (slowFFTsub(real,imag,1.0) != 0)
return -1;
for(int i=1;i<=N;i++){
real[i-1] /= (float)N;
imag[i-1] /= (float)N;
}
return 0;
}
int energy_spectrum(EST_FVector &real, EST_FVector &imag)
{
if (slowFFT(real, imag) != 0)
return -1;
int i;
for(i=0;i<real.n();i++)
real[i] = imag[i] = (real(i)*real(i) + imag(i)*imag(i));
return 0;
}
int power_spectrum_slow(EST_FVector &real, EST_FVector &imag)
{
if (slowFFT(real,imag) != 0)
return -1;
int i;
for(i=0;i<real.n();i++)
real[i] = imag[i] = sqrt((real(i)*real(i) + imag(i)*imag(i)));
return 0;
}
int power_spectrum(EST_FVector &real, EST_FVector &imag)
{
if (fastFFT(real) == 0)
return -1;
int i,j,k;
int n=real.n();
for(i=0,j=0, k=1;i<n;i+=2,j++,k+=2)
real.a_no_check(j)
= imag.a_no_check(j)
= sqrt((real.a_no_check(i)*real.a_no_check(i)
+ real.a_no_check(k)*real.a_no_check(k)));
return 0;
}
// the following code is not by Simon King, as you can see
/*
** Discrete Fourier analysis routine
** from IEEE Programs for Digital Signal Processing
** G. D. Bergland and M. T. Dolan, original authors
** Translated from the FORTRAN with some changes by Paul Kube
**
** Modified to return the power spectrum by Chuck Wooters
**
** Modified again by Tony Robinson (ajr@eng.cam.ac.uk) Dec 92
**
** Modified to use EST_FVector class Simon King (simonk@cstr.ed.ac.uk) Nov 96
**
*/
#define signum(i) (i < 0 ? -1 : i == 0 ? 0 : 1)
int fastFFT(EST_FVector &invec)
{
// Tony Robinsons
int i, in, nn, n2pow, n4pow;
// we could modify all the code to use vector classes ....
// ... or we could do this:
// TO DO
// use FSimpleVector::copy_section here
// quick fix
int n=invec.n(); // order
#if 0
float *b = new float[n];
for(i=0; i<n; i++)
b[i] = invec(i);
#endif
float *b=invec.memory();
n2pow = fastlog2(n);
if (n2pow <= 0) return 0;
n4pow = n2pow / 2;
/* radix 2 iteration required; do it now */
if (n2pow % 2)
{
nn = 2;
in = n / nn;
FR2TR(in, b, b + in );
}
else nn = 1;
/* perform radix 4 iterations */
for(i = 1; i <= n4pow; i++) {
nn *= 4;
in = n / nn;
FR4TR(in, nn, b, b + in, b + 2 * in, b + 3 * in);
}
/* perform inplace reordering */
FORD1(n2pow, b);
FORD2(n2pow, b);
/* take conjugates */
for(i = 3; i < n; i += 2) b[i] = -b[i];
#if 0
// copy back
for(i=0; i<n; i++)
invec[i] = b[i];
#endif
return 1;
}
/* radix 2 subroutine */
void FR2TR(int in, float *b0, float *b1)
{
int k;
float t;
for (k = 0; k < in; k++)
{
t = b0[k] + b1[k];
b1[k] = b0[k] - b1[k];
b0[k] = t;
}
}
/* radix 4 subroutine */
void FR4TR(int in, int nn, float *b0, float *b1, float *b2, float* b3) {
float arg, piovn, th2;
float *b4 = b0, *b5 = b1, *b6 = b2, *b7 = b3;
float t0, t1, t2, t3, t4, t5, t6, t7;
float r1, r5, pr, pi;
float c1, c2, c3, s1, s2, s3;
int j, k, jj, kk, jthet, jlast, ji, jl, jr, int4;
int L[16], L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15;
int j0, j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
int k0, kl;
L[1] = nn / 4;
for(k = 2; k < 16; k++) { /* set up L's */
switch (signum(L[k-1] - 2)) {
case -1:
L[k-1]=2;
case 0:
L[k]=2;
break;
case 1:
L[k]=L[k-1]/2;
}
}
L15=L[1]; L14=L[2]; L13=L[3]; L12=L[4]; L11=L[5]; L10=L[6]; L9=L[7];
L8=L[8]; L7=L[9]; L6=L[10]; L5=L[11]; L4=L[12]; L3=L[13]; L2=L[14];
L1=L[15];
piovn = PI / nn;
ji=3;
jl=2;
jr=2;
for(j1=2;j1<=L1;j1+=2)
for(j2=j1;j2<=L2;j2+=L1)
for(j3=j2;j3<=L3;j3+=L2)
for(j4=j3;j4<=L4;j4+=L3)
for(j5=j4;j5<=L5;j5+=L4)
for(j6=j5;j6<=L6;j6+=L5)
for(j7=j6;j7<=L7;j7+=L6)
for(j8=j7;j8<=L8;j8+=L7)
for(j9=j8;j9<=L9;j9+=L8)
for(j10=j9;j10<=L10;j10+=L9)
for(j11=j10;j11<=L11;j11+=L10)
for(j12=j11;j12<=L12;j12+=L11)
for(j13=j12;j13<=L13;j13+=L12)
for(j14=j13;j14<=L14;j14+=L13)
for(jthet=j14;jthet<=L15;jthet+=L14)
{
th2 = jthet - 2;
if(th2<=0.0)
{
for(k=0;k<in;k++)
{
t0 = b0[k] + b2[k];
t1 = b1[k] + b3[k];
b2[k] = b0[k] - b2[k];
b3[k] = b1[k] - b3[k];
b0[k] = t0 + t1;
b1[k] = t0 - t1;
}
if(nn-4>0)
{
k0 = in*4 + 1;
kl = k0 + in - 1;
for (k=k0;k<=kl;k++)
{
kk = k-1;
pr = IRT2 * (b1[kk]-b3[kk]);
pi = IRT2 * (b1[kk]+b3[kk]);
b3[kk] = b2[kk] + pi;
b1[kk] = pi - b2[kk];
b2[kk] = b0[kk] - pr;
b0[kk] = b0[kk] + pr;
}
}
}
else
{
arg = th2*piovn;
c1 = cos(arg);
s1 = sin(arg);
c2 = c1*c1 - s1*s1;
s2 = c1*s1 + c1*s1;
c3 = c1*c2 - s1*s2;
s3 = c2*s1 + s2*c1;
int4 = in*4;
j0=jr*int4 + 1;
k0=ji*int4 + 1;
jlast = j0+in-1;
for(j=j0;j<=jlast;j++)
{
k = k0 + j - j0;
kk = k-1; jj = j-1;
r1 = b1[jj]*c1 - b5[kk]*s1;
r5 = b1[jj]*s1 + b5[kk]*c1;
t2 = b2[jj]*c2 - b6[kk]*s2;
t6 = b2[jj]*s2 + b6[kk]*c2;
t3 = b3[jj]*c3 - b7[kk]*s3;
t7 = b3[jj]*s3 + b7[kk]*c3;
t0 = b0[jj] + t2;
t4 = b4[kk] + t6;
t2 = b0[jj] - t2;
t6 = b4[kk] - t6;
t1 = r1 + t3;
t5 = r5 + t7;
t3 = r1 - t3;
t7 = r5 - t7;
b0[jj] = t0 + t1;
b7[kk] = t4 + t5;
b6[kk] = t0 - t1;
b1[jj] = t5 - t4;
b2[jj] = t2 - t7;
b5[kk] = t6 + t3;
b4[kk] = t2 + t7;
b3[jj] = t3 - t6;
}
jr += 2;
ji -= 2;
if(ji-jl <= 0) {
ji = 2*jr - 1;
jl = jr;
}
}
}
}
/* an inplace reordering subroutine */
void FORD1(int m, float *b) {
int j, k = 4, kl = 2, n = 0x1 << m;
float t;
for(j = 4; j <= n; j += 2) {
if (k - j>0) {
t = b[j-1];
b[j - 1] = b[k - 1];
b[k - 1] = t;
}
k -= 2;
if (k - kl <= 0) {
k = 2*j;
kl = j;
}
}
}
/* the other inplace reordering subroutine */
void FORD2(int m, float *b)
{
float t;
int n = 0x1<<m, k, ij, ji, ij1, ji1;
int l[16], l1, l2, l3, l4, l5, l6, l7, l8, l9, l10, l11, l12, l13, l14, l15;
int j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
l[1] = n;
for(k=2;k<=m;k++) l[k]=l[k-1]/2;
for(k=m;k<=14;k++) l[k+1]=2;
l15=l[1];l14=l[2];l13=l[3];l12=l[4];l11=l[5];l10=l[6];l9=l[7];
l8=l[8];l7=l[9];l6=l[10];l5=l[11];l4=l[12];l3=l[13];l2=l[14];l1=l[15];
ij = 2;
for(j1=2;j1<=l1;j1+=2)
for(j2=j1;j2<=l2;j2+=l1)
for(j3=j2;j3<=l3;j3+=l2)
for(j4=j3;j4<=l4;j4+=l3)
for(j5=j4;j5<=l5;j5+=l4)
for(j6=j5;j6<=l6;j6+=l5)
for(j7=j6;j7<=l7;j7+=l6)
for(j8=j7;j8<=l8;j8+=l7)
for(j9=j8;j9<=l9;j9+=l8)
for(j10=j9;j10<=l10;j10+=l9)
for(j11=j10;j11<=l11;j11+=l10)
for(j12=j11;j12<=l12;j12+=l11)
for(j13=j12;j13<=l13;j13+=l12)
for(j14=j13;j14<=l14;j14+=l13)
for(ji=j14;ji<=l15;ji+=l14) {
ij1 = ij-1; ji1 = ji - 1;
if(ij-ji<0) {
t = b[ij1-1];
b[ij1-1]=b[ji1-1];
b[ji1-1] = t;
t = b[ij1];
b[ij1]=b[ji1];
b[ji1] = t;
}
ij += 2;
}
}
int fastlog2(int n) {
int num_bits, power = 0;
if ((n < 2) || (n % 2 != 0)) return(0);
num_bits = sizeof(int) * 8; /* How big are ints on this machine? */
while(power <= num_bits) {
n >>= 1;
power += 1;
if (n & 0x01) {
if (n > 1) return(0);
else return(power);
}
}
return(0);
}
EST_FVector
Definition EST_FMatrix.h:114
EST_TVector::memory
const T * memory() const
Definition EST_TVector.h:241
EST_TVector::n
INLINE int n() const
number of items in vector.
Definition EST_TVector.h:254
EST_TVector::a_no_check
INLINE const T & a_no_check(int n) const
read-only const access operator: without bounds checking
Definition EST_TVector.h:257