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A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function [1]) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are ...
L is the window duration, and; α is a non-negative real number that determines the shape of the window. In the frequency domain, it determines the trade-off between main-lobe width and side lobe level, which is a central decision in window design. Sometimes the Kaiser window is parametrized by β, where β = πα.
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [6] [2] However, the term Hanning function is also conventionally used, [7] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.
English: Two different ways to generate Gaussian window functions (σ=0.4) for spectral analysis applications. MATLAB calls them "symmetric" and "periodic". The latter is also called "DFT Even" in the classic Frederic Harris paper.
The design of an N-dimensional window particularly a 2-D window finds applications in various fields such as spectral estimation of multidimensional signals, design of circularly symmetric and quadrantally symmetric non-recursive 2D filters, [1] design of optimal convolution functions, image enhancement so as to reduce the effects of data ...
Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a one-dimensional function) of the resulting signal is taken, then the window is slid along the time axis until the end resulting in a two-dimensional representation of the signal.
Two power spectra (magnitude-squared) (rectangular and Hamming window functions plus background noise), calculated by the periodogram method. For sufficiently small values of parameter T, an arbitrarily-accurate approximation for X(f) can be observed in the region < < of the function:
Lag windowing is a technique that consists of windowing the autocorrelation coefficients prior to estimating linear prediction coefficients (LPC). The windowing in the autocorrelation domain has the same effect as a convolution (smoothing) in the power spectral domain and helps in stabilizing the result of the Levinson-Durbin algorithm.