Sliding discrete Fourier transform (C++)
This code efficiently computes discrete Fourier transforms (DFTs) from a continuous sequence of input values. It is a recursive algorithm that updates the DFT when each new time-domain measurement arrives, effectively applying a sliding window over the last N samples. This implementation applies the Hanning window in order to minimise spectral leakage.
The update step has computational complexity O(N). If a new DFT is required every M samples, and M < log2(N), then this approach is more efficient that recalculating the DFT from scratch each time.
This is a header-only C++ library. Simply copy sliding_dft.hpp into your project, and use it as follows:
// Use double precision arithmetic and a 512-length DFT
static SlidingDFT<double, 512> dft;
// avoid allocating on the stack because the object is large
// When a new time sample arrives, update the DFT with:
dft.update(x);
// After at least 512 samples have been processed:
std::complex<double> DC_bin = dft.dft[0];
Your application should call update() as each time domain sample arrives. Output
data is an array of std::complex values in the dft field. The length of this
array is the length of the DFT.
The output data is not valid until at least N samples have been processed. You
can detect this using the is_data_valid() method, or by storing the return
value of the update() method.
This is a header-only C++ library. Simply copy sliding_dft.hpp into your project. The included CMakeLists.txt is for building the testbench.
Implementation details
See references [1, 2] for an overview of sliding DFT algorithms. A damping
factor is used to improve stability in the face of numerical rounding errors. If
you experience stability issues, reduce dft.damping_factor. It should be
slightly less than one.
Windowing is done using a Hanning window, computed in the frequency domain [1].
[1] E. Jacobsen and R. Lyons, “The Sliding DFT,” IEEE Signal Process. Mag., vol. 20, no. 2, pp. 74–80, Mar. 2003.
[2] E. Jacobsen and R. Lyons, “An Update to the Sliding DFT,” IEEE Signal Process. Mag., vol. 21, no. 1, pp. 110-111, 2004.
MIT License
Copyright (c) 2016 Bronson Philippa
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
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