sdft 0.1

Forward and inverse Sliding Discrete Fourier Transform (SDFT)

Sliding Discrete Fourier Transform (SDFT)

Forward and inverse SDFT according to [1] and [2] with following goodies:

• Arbitrary number of DFT bins
• Hann window at analysis
• Single or multiple sample processing at once
• Continuous data processing without resets
• Optional synthesis latency control parameter

Usage

C

#define SDFT_TD_FLOAT  // time domain data type (float by default)
#define SDFT_FD_DOUBLE // frequency domain data type (double by default)

#include <sdft/sdft.h> // see also src/c folder

size_t n = ...; // number of samples
size_t m = ...; // number of dft bins

float* x = ...; // analysis samples of shape (n)
float* y = ...; // synthesis samples of shape (n)

double complex* dft = ...; // dft matrix of shape (n, m)

sdft_t* sdft = sdft_alloc(m); // create sdft plan

sdft_sdft_n(sdft, n, x, dft); // extract dft matrix from input samples
sdft_isdft_n(sdft, n, dft, y); // synthesize output samples from dft matrix

sdft_free(sdft); // destroy sdft plan

C++

#include <sdft/sdft.h> // see also src/cpp folder

size_t n = ...; // number of samples
size_t m = ...; // number of dft bins

float* x = ...; // analysis samples of shape (n)
float* y = ...; // synthesis samples of shape (n)

std::complex<double>* dft = ...; // dft matrix of shape (n, m)

SDFT<float, double> sdft(m); // create sdft plan with time/frequency domain data type

sdft.sdft(n, x, dft); // extract dft matrix from input samples
sdft.isdft(n, dft, y); // synthesize output samples from dft matrix

Python

from sdft import SDFT # see also src/python folder

n = ... # number of samples
m = ... # number of dft bins

x = ... # analysis samples of shape (n)

sdft = SDFT(m) # create sdft plan

dft = sdft.sdft(x) # extract dft matrix from input samples
y = sdft.isdft(dft) # synthesize output samples from dft matrix

References

1. Krzysztof Duda (2010). Accurate, Guaranteed Stable, Sliding Discrete Fourier Transform. IEEE Signal Processing Magazine. https://ieeexplore.ieee.org/document/5563098

2. Russell Bradford et al. (2005). Sliding is Smoother Than Jumping. International Computer Music Conference Proceedings. http://hdl.handle.net/2027/spo.bbp2372.2005.086