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title:Naive FFT implementation in C
keywords:c,linux,fir,dsp,octave,fft
# Naive FFT implementation in C
## Intro
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']]
}
};
</script>
<script type="text/javascript" id="MathJax-script" async
src="/js/tex-chtml.js">
</script>
Time to implement DFT/FFT by myself. Just followed Ifeachor book on theory part and
IOWA FFT source on implementation side.
## Implementation
### DFT
$$X(k) = F_{D}[x(nT)] = $$
$$ \sum_{n=0}^{N-1} x(nT) e^{-jk\omega nT} , k=0,1,...,N-1 $$
```c
void dft(double *x_i, double *x_q, int n, int inv) {
double Wn,Wk;
//static array
//double Xi[DATA_SIZE],Xq[DATA_SIZE];
//dynamic array
double *Xi, *Xq;
double c,s;
int i,j;
Xi = malloc(n*sizeof(double));
Xq = malloc(n*sizeof(double));
Wn = 2*M_PI/n;
if (inv==1) {
Wn=-Wn;
}
for (i=0;i<n;i++) {
Xi[i] = 0.0f;
Xq[i] = 0.0f;
Wk = i*Wn;
for (j=0;j<n;j++) {
c = cos(j*Wk);
s = sin(j*Wk);
//i - real, q - imaginary
Xi[i] = Xi[i] + x_i[j]*c + x_q[j]*s;
Xq[i] = Xq[i] - x_i[j]*s + x_q[j]*c;
}
if (inv==1) {
Xi[i] = Xi[i]/n;
Xq[i] = Xq[i]/n;
}
}
for (i=0;i<n;i++) {
x_i[i] = Xi[i];
x_q[i] = Xq[i];
}
}
```
### FFT
#### Shuffling arrays
```c
void ffti_shuffle_1(double *x_i, double *x_q, uint64_t n) {
int Nd2 = n>>1;
int Nm1 = n-1;
int i,j;
for (i = 0, j = 0; i < n; i++) {
if (j > i) {
double tmp_r = x_i[i];
double tmp_i = x_q[i];
//data[i] = data[j];
x_i[i] = x_q[j];
x_q[i] = x_q[j];
//data[j] = tmp;
x_i[j] = tmp_r;
x_q[j] = tmp_i;
}
/*
* Find least significant zero bit
*/
unsigned lszb = ~i & (i + 1);
/*
* Use division to bit-reverse the single bit so that we now have
* the most significant zero bit
*
* N = 2^r = 2^(m+1)
* Nd2 = N/2 = 2^m
* if lszb = 2^k, where k is within the range of 0...m, then
* mszb = Nd2 / lszb
* = 2^m / 2^k
* = 2^(m-k)
* = bit-reversed value of lszb
*/
unsigned mszb = Nd2 / lszb;
/*
* Toggle bits with bit-reverse mask
*/
unsigned bits = Nm1 & ~(mszb - 1);
j ^= bits;
}
}
```
#### Implementation
```c
void fft_1(double *x_i, double *x_q, uint64_t n, uint64_t inv) {
uint64_t n_log2;
uint64_t r;
uint64_t m, md2;
uint64_t i,j,k;
uint64_t i_e, i_o;
double theta_2pi;
double theta;
double Wm_r, Wm_i, Wmk_r, Wmk_i;
double u_r, u_i, t_r, t_i;
//find log of n
i=n;
n_log2 = 0;
while (i>1) {
i=i/2;
n_log2+=1;
}
if (inv==1) {
theta_2pi = -2*M_PI;
} else {
theta_2pi = 2*M_PI;
}
for (i=1; i<= n_log2; i++) {
m = 1 << i;
md2 = m >> 1;
theta = theta_2pi / m;
Wm_r = cos(theta);
Wm_i = sin(theta);
for (j=0; j<n; j+=m) {
Wmk_r = 1.0f;
Wmk_i = 0.0f;
for (k=0; k<md2; k++) {
i_e = j+k;
i_o = i_e + md2;
u_r = x_i[i_e];
u_i = x_q[i_e];
t_r = complex_mul_re(Wmk_r, Wmk_i, x_i[i_o], x_q[i_o]);
t_i = complex_mul_im(Wmk_r, Wmk_i, x_i[i_o], x_q[i_o]);
x_i[i_e] = u_r + t_r;
x_q[i_e] = u_i + t_i;
x_i[i_o] = u_r - t_r;
x_q[i_o] = u_i - t_i;
t_r = complex_mul_re(Wmk_r, Wmk_i, Wm_r, Wm_i);
t_i = complex_mul_im(Wmk_r, Wmk_i, Wm_r, Wm_i);
Wmk_r = t_r;
Wmk_i = t_i;
}
}
}
```
## Octave verification code
```matlab
data1 = [1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]
res1 = fft(data1)
data2 = [1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0]
res2 = fft(data2)
data3 = [1.0 1.0 i i 0.0 0.0 0.0 0.0]
res3 = fft(data3)
data4 = [1.0+i 1.0+i 1.0+i 1.0+i 0.0 0.0 0.0 0.0]
res4 = fft(data4)
```
### Source
Source located in main branch of git repo
```
git clone http://git.main.lv/cgit.cgi/NaiveFFT.git
git checkout main
```
### Build
#### Linux
```
cd NaiveFFT/Build
make
```
#### Macos
Open with Xcode and build
## Links
[01] https://rosettacode.org/wiki/Fast_Fourier_transform#C
[02] https://www.math.wustl.edu/~victor/mfmm/fourier/fft.c
[03] https://www.strauss-engineering.ch/libdsp.html
[04] http://www.iowahills.com/FFTCode.html
[05] https://github.com/rshuston/FFT-C/blob/master/libfft/fft.c
[06] http://www.guitarscience.net/papers/fftalg.pdf
[07] https://root.cern/doc/master/FFT_8C_source.html
[08] https://lloydrochester.com/post/c/example-fft/
[09] https://github.com/mborgerding/kissfft/blob/master/kiss_fft.c
[10] https://community.vcvrack.com/t/complete-list-of-c-c-fft-libraries/9153
[11] https://octave.org/doc/v4.2.1/Signal-Processing.html
[12] https://en.wikipedia.org/wiki/Fast_Fourier_transform
[13] http://www.iowahills.com/FFTCode.html
[14] Digital Signal Processing: A Practical Approach by (Emmanuel Ifeachor, Barrie Jervis)
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