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/*
* Copyright (c) 2020-2021 Vasile Vilvoiu <vasi@vilvoiu.ro>
*
* specgram is free software; you can redistribute it and/or modify
* it under the terms of the MIT license. See LICENSE for details.
*/
#ifndef _FFT_HPP_
#define _FFT_HPP_
#include "window-function.hpp"
#include <fftw3.h>
/**
* Computes the fast Fourier transform of an input window.
*/
class FFT {
private:
/* FFT window width */
const std::size_t window_width_;
/* fftw buffers */
fftw_complex *in_;
fftw_complex *out_;
/* fftw plan */
fftw_plan plan_;
/* window function */
std::unique_ptr<WindowFunction> window_function_;
public:
/* plan and buffers are not copiable */
FFT() = delete;
FFT(const FFT &c) = delete;
FFT(FFT &&) = delete;
FFT & operator=(const FFT&) = delete;
/**
* @param win_width Width of window this object must support.
* NOTE: Only supports this window size!
*/
explicit FFT(std::size_t win_width);
/**
* @param win_width Width of window this object must support.
* @param win_func Window function to apply before FFT computations.
* NOTE: Only supports this window size!
*/
FFT(std::size_t win_width, std::unique_ptr<WindowFunction>& win_func);
virtual ~FFT();
/**
* Compute the fast Fourier transform.
* @param input Array of complex input values.
* @return Complex values corresponding to the FFT terms, equal in size to input.
*
* NOTE: This functions normalizes the output by 1/N.
* NOTE: This function provides the negative frequencies in the first half
* and the positive frequencies in the second half.
* NOTE: For even-sized inputs, the Nyquist frequency term is the last in
* the output vector.
*/
ComplexWindow Compute(const ComplexWindow& input);
/**
* Retrieve the (real) magnitudes of a complex input vector (window).
* @param input Array of complex values.
* @param alias If true, will alias negative and positive frequencies.
* @return Array of real values, containing amplitudes.
*
* NOTE: When aliasing, each output value will be the sum of that term's
* magnitude as well as the corresponding negative or positive
* frequency term's magnitude.
*/
static RealWindow GetMagnitude(const ComplexWindow& input, bool alias);
/**
* Compute the frequency bounds of a specific FFT window.
* @param rate Sampling rate of the input signal.
* @param width Width of the FFT window.
* @return Lower and upper bounds, in Hz.
*/
static std::tuple<double, double> GetFrequencyLimits(double rate, std::size_t width);
/**
* Compute the index in the FFT window of a given frequency.
* @param rate Sampling rate of input.
* @param width Width of the FFT window.
* @param f Frequency, in Hz.
* @return Index (computed exactly) of the frequency.
*/
static double GetFrequencyIndex(double rate, std::size_t width, double f);
/**
* Resample a real, scaled output of the FFT.
* @param input Real window, values between [0..1].
* @param rate Sampling rate of input.
* @param width Desired output width.
* @param fmin Frequency lower bound (from input).
* @param fmax Frequency upper bound (from input).
* @return Resampled values, clamped to [0..1].
*
* NOTE: Uses Lanczos resampling algorithm.
* NOTE: Will resize the [fmin..fmax] band from input (computed as if
* input is a FFT output) to a width-sized output window.
*/
static RealWindow Resample(const RealWindow& input, double rate, std::size_t width, double fmin, double fmax);
/**
* Crop a real, scaled output of the FFT.
* @param input Real window, values between [0..1].
* @param rate Sampling rate of input.
* @param fmin fmin Frequency lower bound (from input).
* @param fmax fmax Frequency upper bound (from input).
* @return Cropped window.
*
* NOTE: The [fmin..fmax] band from input is computed as if input is a FFT
* output, which under normal circumstances it should be.
*/
static RealWindow Crop(const RealWindow& input, double rate, double fmin, double fmax);
};
#endif
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