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 // Copyright ©2020 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // Package window provides a set of functions to perform the transformation // of sequence by different window functions. // // Window functions can be used to control spectral leakage parameters // when performing a Fourier transform on a signal of limited length. // See https://en.wikipedia.org/wiki/Window_function for more details. // // Spectral leakage parameters // // Application of window functions to an input will result in changes // to the frequency content of the signal in an effect called spectral // leakage. See https://en.wikipedia.org/wiki/Spectral_leakage. // // The characteristic changes associated with each window function may // be described using a set of spectral leakage parameters; β, ΔF_0, ΔF_0.5, // K and ɣ_max. // // The β, attenuation, coefficient of a window is the ratio of the // constant component of the spectrum resulting from use of the window // compared to that produced using the rectangular window, expressed in // a logarithmic scale. // β_w = 20 log10(A_w / A_rect) dB // // The ΔF_0 parameter describes the normalized width of the main lobe of // the frequency spectrum at zero amplitude. // // The ΔF_0.5 parameter describes the normalized width of the main lobe of // the frequency spectrum at -3 dB (half maximum amplitude). // // The K parameter describes the relative width of the main lobe of the // frequency spectrum produced by the window compared with the rectangular // window. The rectangular window has the lowest ΔF_0 at a value of 2. // K_w = ΔF_0_w/ΔF_0_rect. // The value of K divides windows into high resolution windows (K≤3) and // low resolution windows (K>3). // // The ɣ_max parameter is the maximum level of the side lobes of the // normalized spectrum, in decibels. package window // import "gonum.org/v1/gonum/dsp/window" // The article at http://www.dsplib.ru/content/win/win.html is the origin // of much of the information used in this package. It is in Russian, but // Google translate does a pretty good job with it.