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window.h
Go to the documentation of this file.
/* -*- c++ -*- */
/*
* Copyright 2002,2007,2008,2012,2013 Free Software Foundation, Inc.
*
* This file is part of GNU Radio
*
* SPDX-License-Identifier: GPL-3.0-or-later
*
*/
#ifndef INCLUDED_FFT_WINDOW_H
#define INCLUDED_FFT_WINDOW_H
#include <gnuradio/fft/api.h>
#include <gnuradio/gr_complex.h>
#include <cmath>
#include <vector>
namespace gr {
namespace fft {
class FFT_API window
{
public:
// illegal value for any window that requires a parameter
static constexpr double INVALID_WIN_PARAM = -1;
enum win_type {
WIN_NONE = -1, //!< don't use a window
WIN_HAMMING = 0, //!< Hamming window; max attenuation 53 dB
WIN_HANN = 1, //!< Hann window; max attenuation 44 dB
WIN_HANNING = 1, //!< alias to WIN_HANN
WIN_BLACKMAN = 2, //!< Blackman window; max attenuation 74 dB
WIN_RECTANGULAR = 3, //!< Basic rectangular window; max attenuation 21 dB
WIN_KAISER = 4, //!< Kaiser window; max attenuation see window::max_attenuation
WIN_BLACKMAN_hARRIS = 5, //!< Blackman-harris window; max attenuation 92 dB
WIN_BLACKMAN_HARRIS =
5, //!< alias to WIN_BLACKMAN_hARRIS for capitalization consistency
WIN_BARTLETT = 6, //!< Barlett (triangular) window; max attenuation 26 dB
WIN_FLATTOP = 7, //!< flat top window; useful in FFTs; max attenuation 93 dB
WIN_NUTTALL = 8, //!< Nuttall window; max attenuation 114 dB
WIN_BLACKMAN_NUTTALL = 8, //!< Nuttall window; max attenuation 114 dB
WIN_NUTTALL_CFD =
9, //!< Nuttall continuous-first-derivative window; max attenuation 112 dB
WIN_WELCH = 10, //!< Welch window; max attenuation 31 dB
WIN_PARZEN = 11, //!< Parzen window; max attenuation 56 dB
WIN_EXPONENTIAL =
12, //!< Exponential window; max attenuation see window::max_attenuation
WIN_RIEMANN = 13, //!< Riemann window; max attenuation 39 dB
WIN_GAUSSIAN =
14, //!< Gaussian window; max attenuation see window::max_attenuation
WIN_TUKEY = 15, //!< Tukey window; max attenuation see window::max_attenuation
};
/*!
* \brief Given a window::win_type, this tells you the maximum
* attenuation (really the maximum approximation error) you can expect.
*
* \details
* For most windows, this is a set value. For the Kaiser, Exponential, Gaussian, and
* Tukey windows, the attenuation is based on the value of a provided parameter.
*
* For the Kaiser window the actual relationship is a piece-wise exponential
* relationship to calculate beta from the desired attenuation and can be found on
* page 542 of Oppenheim and Schafer (Discrete-Time Signal Processing, 3rd edition).
* To simplify this function to solve for A given beta, we use a linear form that is
* exact for attenuation >= 50 dB. For an attenuation of 50 dB, beta = 4.55; for an
* attenuation of 70 dB, beta = 6.76.
*
* Exponential attenuation is complicated to measure due to the irregular error ripple
* structure, but it ranges between 23 and 26 dB depending on the decay factor; 26 dB
* is a good bound.
*
* The Gaussian window should not be used for window based filter construction;
* instead there is a dedicated gaussian filter construction function. There is no
* meaningful way to measure approximation error 'delta' as shown in Fig 7.23 of
* Oppenheim and Schafer (Discrete-Time Signal Processing, 3rd edition).
*
* Tukey windows provide attenuation that varies non-linearily between Rectangular (21
* dB) and Hann (44 dB) windows.
*
* \param type The window::win_type enumeration of the window type.
* \param param Parameter value used for Kaiser (beta), Exponential (d), Gaussian
* (sigma) and Tukey (alpha) window creation.
*/
static double max_attenuation(win_type type, double param = INVALID_WIN_PARAM);
/*!
* \brief Helper function to build cosine-based windows. 3-coefficient version.
*/
static std::vector<float> coswindow(int ntaps, float c0, float c1, float c2);
/*!
* \brief Helper function to build cosine-based windows. 4-coefficient version.
*/
static std::vector<float>
coswindow(int ntaps, float c0, float c1, float c2, float c3);
/*!
* \brief Helper function to build cosine-based windows. 5-coefficient version.
*/
static std::vector<float>
coswindow(int ntaps, float c0, float c1, float c2, float c3, float c4);
/*!
* \brief Build a rectangular window.
*
* Taps are flat across the window.
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> rectangular(int ntaps);
/*!
* \brief Build a Hamming window.
*
* See:
* <pre>
* A. V. Oppenheim and R. W. Schafer, "Discrete-Time
* Signal Processing," Upper Saddle River, N.J.: Prentice
* Hall, 2010, pp. 535-538.
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> hamming(int ntaps);
/*!
* \brief Build a Hann window (sometimes known as Hanning).
*
* See:
* <pre>
* A. V. Oppenheim and R. W. Schafer, "Discrete-Time
* Signal Processing," Upper Saddle River, N.J.: Prentice
* Hall, 2010, pp. 535-538.
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> hann(int ntaps);
/*!
* \brief Alias to build a Hann window.
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> hanning(int ntaps);
/*!
* \brief Build an exact Blackman window.
*
* See:
* <pre>
* A. V. Oppenheim and R. W. Schafer, "Discrete-Time
* Signal Processing," Upper Saddle River, N.J.: Prentice
* Hall, 2010, pp. 535-538.
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> blackman(int ntaps);
/*!
* \brief Build Blackman window, variation 1.
*/
static std::vector<float> blackman2(int ntaps);
/*!
* \brief Build Blackman window, variation 2.
*/
static std::vector<float> blackman3(int ntaps);
/*!
* \brief Build Blackman window, variation 3.
*/
static std::vector<float> blackman4(int ntaps);
/*!
* \brief Build a Blackman-harris window with a given attenuation.
*
* <pre>
* f. j. harris, "On the use of windows for harmonic analysis
* with the discrete Fourier transforms," Proc. IEEE, Vol. 66,
* ppg. 51-83, Jan. 1978.
* </pre>
*
* \param ntaps Number of coefficients in the window.
* \param atten Attenuation factor. Must be [61, 67, 74, 92].
* See the above paper for details.
*/
static std::vector<float> blackman_harris(int ntaps, int atten = 92);
/*!
* Alias to gr::fft::window::blackman_harris.
*/
static std::vector<float> blackmanharris(int ntaps, int atten = 92);
/*!
* \brief Build a minimum 4-term Nuttall (or Blackman-Nuttall) window, referred to by
* Heinzel G. et al. as a Nuttall4c window.
*
* See: A.H. Nuttall: 'Some windows with very good sidelobe behaviour', IEEE Trans. on
* Acoustics, Speech and Signal Processing, Vol ASSP-29, figure 15
*
* See: 'Spectrum and spectral density estimation by the Discrete Fourier transform
* (DFT), including a comprehensive list of window functions and some new flat-top
* windows', February 15, 2002 https://holometer.fnal.gov/GH_FFT.pdf
*
* Also: http://en.wikipedia.org/wiki/Window_function#Blackman.E2.80.93Nuttall_window
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> nuttall(int ntaps);
/*!
* \brief Alias to the Nuttall window.
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> blackman_nuttall(int ntaps);
/*!
* \brief Build a Nuttall 4-term continuous first derivative window, referred to by
* Heinzel G. et al. as a Nuttall4b window
*
* See: A.H. Nuttall: 'Some windows with very good sidelobe behaviour', IEEE Trans. on
* Acoustics, Speech and Signal Processing, Vol ASSP-29, figure 12
*
* See: 'Spectrum and spectral density estimation by the Discrete Fourier transform
* (DFT), including a comprehensive list of window functions and some new flat-top
* windows', February 15, 2002 https://holometer.fnal.gov/GH_FFT.pdf
*
* Also:
* http://en.wikipedia.org/wiki/Window_function#Nuttall_window.2C_continuous_first_derivative
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> nuttall_cfd(int ntaps);
/*!
* \brief Build a flat top window per the SRS specification
*
* See:
* <pre>
* Stanford Research Systems, "Model SR785 Dynamic Signal
* Analyzer: Operating Manual and Programming Reference,"
* 2017, pp 2-13
* </pre>
*
* Note: there are many flat top windows, and this implementation is different from
* SciPY and Matlab which use the coefficients from D’Antona et al. "Digital Signal
* Processing for Measurement Systems" with the following cosine coefficients: <pre>
* [0.21557895, 0.41663158, 0.277263158, 0.083578947, 0.006947368]
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> flattop(int ntaps);
/*!
* \brief Build a Kaiser window with a given beta.
*
* See:
* <pre>
* A. V. Oppenheim and R. W. Schafer, "Discrete-Time
* Signal Processing," Upper Saddle River, N.J.: Prentice
* Hall, 2010, pp. 541-545.
* </pre>
*
* \param ntaps Number of coefficients in the window.
* \param beta Shaping parameter of the window. See the
* discussion in Oppenheim and Schafer.
*/
static std::vector<float> kaiser(int ntaps, double beta);
/*!
* \brief Build a Barlett (triangular) window.
*
* See:
* <pre>
* A. V. Oppenheim and R. W. Schafer, "Discrete-Time
* Signal Processing," Upper Saddle River, N.J.: Prentice
* Hall, 2010, pp. 535-538.
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> bartlett(int ntaps);
static std::vector<float> welch(int ntaps);
/*!
* \brief Build a Parzen (or de la Valle-Poussin) window.
*
* See:
* <pre>
* A. D. Poularikas, "Handbook of Formulas and Tables for
* Signal Processing," Springer, Oct 28, 1998
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> parzen(int ntaps);
/*!
* \brief Build an exponential window with a given decay.
*
* See: http://en.wikipedia.org/wiki/Window_function#Exponential_or_Poisson_window
*
* \param ntaps Number of coefficients in the window.
* \param d Decay of \p d dB over half the window length.
*/
static std::vector<float> exponential(int ntaps, double d);
/*!
* \brief Build a Riemann window.
*
* See:
* <pre>
* A. D. Poularikas, "Handbook of Formulas and Tables for
* Signal Processing," Springer, Oct 28, 1998
* </pre>
*
* \param ntaps Number of coefficients in the window.
*/
static std::vector<float> riemann(int ntaps);
/*!
* \brief Build a Tukey window.
* <pre>
* Bloomfield, P. Fourier Analysis of Time Series: An Introduction. New York:
* Wiley-Interscience, 2000, pp 69 (eqn 6.9)
* </pre>
*
* \param ntaps Number of coefficients in the window.
* \param alpha Shaping parameter for the Tukey window, an
* alpha of zero is equivalent to a rectangular
* window, an alpha of 1 is equivalent to Hann.
*/
static std::vector<float> tukey(int ntaps, float alpha);
/*!
* \brief Build a Gaussian window using the equation
* <pre>
* exp(-(1/2) * (n/sigma)^2)
* </pre>
*
* \param ntaps Number of coefficients in the window.
* \param sigma Standard deviation of gaussian distribution.
*/
static std::vector<float> gaussian(int ntaps, float sigma);
/*!
* \brief Build a window using gr::fft::win_type to index the
* type of window desired.
*
* \param type a gr::fft::win_type index for the type of window.
* \param ntaps Number of coefficients in the window.
* \param param Parameter value used for Kaiser (beta), Exponential (d), Gaussian
* (sigma) and Tukey (alpha) window creation. \param normalize If true, return a
* window with unit power
*/
static std::vector<float> build(win_type type,
int ntaps,
double param = INVALID_WIN_PARAM,
const bool normalize = false);
};
} /* namespace fft */
} /* namespace gr */
#endif /* INCLUDED_FFT_WINDOW_H */
gr::fft::window
Definition window.h:23
gr::fft::window::gaussian
static std::vector< float > gaussian(int ntaps, float sigma)
Build a Gaussian window using the equation.
gr::fft::window::blackman_harris
static std::vector< float > blackman_harris(int ntaps, int atten=92)
Build a Blackman-harris window with a given attenuation.
gr::fft::window::coswindow
static std::vector< float > coswindow(int ntaps, float c0, float c1, float c2, float c3, float c4)
Helper function to build cosine-based windows. 5-coefficient version.
gr::fft::window::blackman3
static std::vector< float > blackman3(int ntaps)
Build Blackman window, variation 2.
gr::fft::window::blackman
static std::vector< float > blackman(int ntaps)
Build an exact Blackman window.
gr::fft::window::blackman2
static std::vector< float > blackman2(int ntaps)
Build Blackman window, variation 1.
gr::fft::window::INVALID_WIN_PARAM
static constexpr double INVALID_WIN_PARAM
Definition window.h:26
gr::fft::window::welch
static std::vector< float > welch(int ntaps)
gr::fft::window::rectangular
static std::vector< float > rectangular(int ntaps)
Build a rectangular window.
gr::fft::window::flattop
static std::vector< float > flattop(int ntaps)
Build a flat top window per the SRS specification.
gr::fft::window::build
static std::vector< float > build(win_type type, int ntaps, double param=INVALID_WIN_PARAM, const bool normalize=false)
Build a window using gr::fft::win_type to index the type of window desired.
gr::fft::window::blackmanharris
static std::vector< float > blackmanharris(int ntaps, int atten=92)
gr::fft::window::blackman_nuttall
static std::vector< float > blackman_nuttall(int ntaps)
Alias to the Nuttall window.
gr::fft::window::hann
static std::vector< float > hann(int ntaps)
Build a Hann window (sometimes known as Hanning).
gr::fft::window::win_type
win_type
Definition window.h:28
gr::fft::window::WIN_HANN
@ WIN_HANN
Hann window; max attenuation 44 dB.
Definition window.h:31
gr::fft::window::WIN_RECTANGULAR
@ WIN_RECTANGULAR
Basic rectangular window; max attenuation 21 dB.
Definition window.h:34
gr::fft::window::WIN_BARTLETT
@ WIN_BARTLETT
Barlett (triangular) window; max attenuation 26 dB.
Definition window.h:39
gr::fft::window::WIN_BLACKMAN_hARRIS
@ WIN_BLACKMAN_hARRIS
Blackman-harris window; max attenuation 92 dB.
Definition window.h:36
gr::fft::window::WIN_BLACKMAN_HARRIS
@ WIN_BLACKMAN_HARRIS
alias to WIN_BLACKMAN_hARRIS for capitalization consistency
Definition window.h:37
gr::fft::window::WIN_GAUSSIAN
@ WIN_GAUSSIAN
Gaussian window; max attenuation see window::max_attenuation.
Definition window.h:50
gr::fft::window::WIN_NUTTALL
@ WIN_NUTTALL
Nuttall window; max attenuation 114 dB.
Definition window.h:41
gr::fft::window::WIN_KAISER
@ WIN_KAISER
Kaiser window; max attenuation see window::max_attenuation.
Definition window.h:35
gr::fft::window::WIN_HANNING
@ WIN_HANNING
alias to WIN_HANN
Definition window.h:32
gr::fft::window::WIN_NONE
@ WIN_NONE
don't use a window
Definition window.h:29
gr::fft::window::WIN_TUKEY
@ WIN_TUKEY
Tukey window; max attenuation see window::max_attenuation.
Definition window.h:52
gr::fft::window::WIN_BLACKMAN
@ WIN_BLACKMAN
Blackman window; max attenuation 74 dB.
Definition window.h:33
gr::fft::window::WIN_PARZEN
@ WIN_PARZEN
Parzen window; max attenuation 56 dB.
Definition window.h:46
gr::fft::window::WIN_FLATTOP
@ WIN_FLATTOP
flat top window; useful in FFTs; max attenuation 93 dB
Definition window.h:40
gr::fft::window::WIN_WELCH
@ WIN_WELCH
Welch window; max attenuation 31 dB.
Definition window.h:45
gr::fft::window::WIN_BLACKMAN_NUTTALL
@ WIN_BLACKMAN_NUTTALL
Nuttall window; max attenuation 114 dB.
Definition window.h:42
gr::fft::window::WIN_HAMMING
@ WIN_HAMMING
Hamming window; max attenuation 53 dB.
Definition window.h:30
gr::fft::window::WIN_NUTTALL_CFD
@ WIN_NUTTALL_CFD
Nuttall continuous-first-derivative window; max attenuation 112 dB.
Definition window.h:43
gr::fft::window::WIN_EXPONENTIAL
@ WIN_EXPONENTIAL
Exponential window; max attenuation see window::max_attenuation.
Definition window.h:47
gr::fft::window::WIN_RIEMANN
@ WIN_RIEMANN
Riemann window; max attenuation 39 dB.
Definition window.h:49
gr::fft::window::hamming
static std::vector< float > hamming(int ntaps)
Build a Hamming window.
gr::fft::window::nuttall
static std::vector< float > nuttall(int ntaps)
Build a minimum 4-term Nuttall (or Blackman-Nuttall) window, referred to by Heinzel G....
gr::fft::window::nuttall_cfd
static std::vector< float > nuttall_cfd(int ntaps)
Build a Nuttall 4-term continuous first derivative window, referred to by Heinzel G....
gr::fft::window::coswindow
static std::vector< float > coswindow(int ntaps, float c0, float c1, float c2, float c3)
Helper function to build cosine-based windows. 4-coefficient version.
gr::fft::window::hanning
static std::vector< float > hanning(int ntaps)
Alias to build a Hann window.
gr::fft::window::riemann
static std::vector< float > riemann(int ntaps)
Build a Riemann window.
gr::fft::window::blackman4
static std::vector< float > blackman4(int ntaps)
Build Blackman window, variation 3.
gr::fft::window::max_attenuation
static double max_attenuation(win_type type, double param=INVALID_WIN_PARAM)
Given a window::win_type, this tells you the maximum attenuation (really the maximum approximation er...
gr::fft::window::kaiser
static std::vector< float > kaiser(int ntaps, double beta)
Build a Kaiser window with a given beta.
gr::fft::window::coswindow
static std::vector< float > coswindow(int ntaps, float c0, float c1, float c2)
Helper function to build cosine-based windows. 3-coefficient version.
gr::fft::window::tukey
static std::vector< float > tukey(int ntaps, float alpha)
Build a Tukey window.
gr::fft::window::parzen
static std::vector< float > parzen(int ntaps)
Build a Parzen (or de la Valle-Poussin) window.
gr::fft::window::exponential
static std::vector< float > exponential(int ntaps, double d)
Build an exponential window with a given decay.
gr::fft::window::bartlett
static std::vector< float > bartlett(int ntaps)
Build a Barlett (triangular) window.
api.h
FFT_API
#define FFT_API
Definition gr-fft/include/gnuradio/fft/api.h:18
gr_complex.h
gr::fft
Definition ctrlport_probe_psd.h:18
gr
GNU Radio logging wrapper.
Definition basic_block.h:29