Help with resampling/upsampling

Question

I have an array of 240 data points sampled at 600hz, representing 400ms. I need to resample this data to 512 data points sampled at 1024hz, representing 500ms. I assume since I'm starting with 400ms of data, the last 100ms will just need to be padded with 0s.

Is there a best approach to take to accomplish this?

Answer 1

If you want to avoid interpolation then you need to upsample to a 76.8 kHz sample rate (i.e. insert 127 0s after every input sample), low pass filter, then decimate (drop 74 out of every 75 samples).

Answer 2

You can use windowed Sinc interpolation, which will give you the same result as upsampling and downsampling using a linear phase FIR low-pass filter with a windowed Sinc impulse response. When using a FIR filter, one normally has to pad a signal with zeros the length of the FIR filter kernel on both sides.

Added:

Another possibility is to zero pad 240 samples with 60 zeros, apply a non-power-of-2 FFT of length 300, "center" zero pad the FFT result with 212 complex zeros to make it 512 long, but with the identical spectrum, and do an IFFT of length 512 to get the resampled result.

Answer 3

Yes to endolith's response, if you want to interpolate x[n] by simply computing the FFT, zero-stuff, and then IFFT, you'll get errors if x[n] is not periodic. See this reference: http://www.embedded.com/design/other/4212939/Time-domain-interpolation-using-the-Fast-Fourier-Transform-

Answer 4

FFT based resampling/upsampling is pretty easy...

If you can use python, scipy.signal.resample should work.

For C/C++, there is a simple fftw trick to upsample if you have real (as opposed to complex) data.

nfft = the original data length
upnfft = the new data length
double * data = the original data

// allocate 
fftw_complex * tmp_fd = (fftw_complex*)fftw_malloc((upnfft/2+1)*sizeof(fftw_complex));
double * result = (double*)fftw_malloc(upnfft*sizeof(double));

// create fftw plans
fftw_plan fft_plan = fftw_plan_dft_r2c_1d(nfft, data, tmp_fd, FFTW_ESTIMATE);
fftw_plan ifft_plan = fftw_plan_dft_c2r_1d(upnfft, tmp_fd, result, FFTW_ESTIMATE);

// zero out tmp_fd
memset(tmp_fd, 0, (upnfft/2+1)*sizeof(fftw_complex));

// execute the plans (forward then reverse)
fftw_execute_dft_r2c(fft_plan, data, tmp_fd);
fftw_execute_dft_c2r(ifft_plan, tmp_fd, result);

// cleanup
fftw_free(tmp_fd);