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

Due to incomplete C complex math support in MSVC, optionally use following universal typedefs:

• sdft_float_t instead of float
• sdft_double_complex_t instead of double complex

or even better the corresponding generic typedefs:

• sdft_td_t
• sdft_fdx_t

In both cases, the underlying data type results from the SDFT_TD_* and SDFT_FD_* definitions.

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> 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

Optionally specify a different frequency domain data type like so SDFT<float, double>.

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

Feel free to obtain the current version from the PyPI pip install sdft.

Test spectrogram

Below you can see two spectrograms of the same file test.wav computed by SDFT and STFT with identical spectral resolution, window function and hop size. Do you see any difference between them?

SDFT	STFT

Well, the results are very similar, which is the proof of concept...

Implementation details

• The C/C++ implementation corresponds to figure 4 in [1].
• The Python implementation corresponds to figure 3b in [1].

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

License

This sdft implementation is licensed under the terms of the MIT license. For details please refer to the accompanying LICENSE file distributed with it.