8.5. RECONSTRUCTION 125
8.5 RECONSTRUCTION
Reconstruction or synthesis is the process by which a time-domain signal is recovered from
a frequency domain signal. It involves performing inverse Fourier transform and overlap-add
reconstruction when overlap processing is performed.
8.5.1 INVERSE FOURIER TRANSFORM
e inverse Fourier transform is operationally very similar to the forward Fourier transform.
From Eq. (8.3), one can see that to recover the time domain signal, the complex conjugate of the
twiddle factor W
N
can be used while scaling the resulting value by the inverse of the transform
size. e code is easily implemented by modifying the code stated earlier for DFT/FFT. An
inverse transform C code is shown below:
void iDFT(Complex* data){
int i, j;
int N = data->N;
float arg, wI, wR;
float sumXr[N];
float sumXi[N];
for (i=0; i<N; i++) {
sumXr[i] = 0.0f;
sumXi[i] = 0.0f;
for(j=0; j<N; j++) {
arg = 2*PI*i*j/N;
wI = cos(arg);
wR = -sin(arg);
sumXr[i] += data->real[j] * wR + data->imaginary[j] * wI;
sumXi[i] += data->imaginary[j] * wR - data->real[j] * wI;
}
}
for(i=0; i<N; i++) {
out->real[i] = sumXr[i]/N;
out->imaginary[i] = sumXi[i]/N;
}
}
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.