Frequency Shifting with FFT - signal-processing

Question

I've been experimenting with a few different techniques that I can find for a freq shifting (specifically I want to shift high freq signals to a lower freq). At the moment I'm trying to use this technique -
take the original signal, x(t), multiply it by: cos(2 PI dF t), sin(2
PI dF t)
R(t) = x(t) cos(2 PI dF t)
I(t) = x(t) sin(2 PI dF t)
where dF is the delta frequency to be shifted.
Now you have two time series signals: R(t) and I(t).
Conduct complex Fourier transform using R(t) as real and I(t) as
imaginary parts. The results will be frequency shifted spectrum.
I have interpreted this into the following code -
for(j=0;j<(BUFFERSIZE/2);j++)
{
Partfunc = (((double)j)/2048);
PreFFTShift[j+x] = PingData[j]*(cos(2*M_PI*Shift*(Partfunc)));
PreFFTShift[j+1+x] = PingData[j]*(sin(2*M_PI*Shift*(Partfunc)));
x++;
}
//INITIALIZE FFT
status = arm_cfft_radix4_init_f32(&S, fftSize, ifftFlag, doBitReverse);
//FFT on FFTData
arm_cfft_radix4_f32(&S, PreFFTShift);
This builds me an array with interleaved real and imag data and then FFT. I then inverse the FFT, but the output im getting is pretty garbled. Results seem huge in comparison to what I think they should be, and although there are a few traces of a freq shifted signal, its hard to tell as the result seems mostly pretty noisy.
I've also attempted simply revolving the array values of a standard FFT of my original signal to get a freq shift, but to no avail. Is there a better method for doing this?

Answer 1

have you tried something like:
Use a Hanning window for each framed data
Once you have your windowed frame of audio data, you do an FFT on it
Do some kind of transformation in the frequency domain (you can use
Flanagan - phase vocoder)
Now you need to go back to the time domain with an IFFT
Apply Hanning window in the IFFT data
Use overlap-add at each new frame of time-domain data into the output
stream
My results:
I created two concatenated sinusoids (250Hz and 400Hz) and move one octave UP!
Blue waveform is the original and red was changed, you can see one fadeIN-fadeOut caused by overlap add and hann window !

Answer 2

If you want the frequency shift to sound more "natural", you will have to maintain the ratios between all the initial frequency bins, where the amount of shift will depend on the FFT bin, thus requiring lots of interpolation. The Phase Vocoder algorithm will use multiple FFTs to reduce phase distortion in the result.