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.

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.

Copyright (c) 2016 Bronson Philippa

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