Algorithms Index , Frequency-Domain Filtering in Triana , Time-Domain Filtering in TrianaTriana Spectral Storage Model


WindowFnc

Author : Ian Taylor, Bernard Schutz

Version: 2.0

Input Types : VectorType, TimeFrequency
Output Types : VectorType, TimeFrequency
Date : 3 March 2001

Contents


Description of WindowFnc

WindowFnc allows the user to apply one of six window functions to the input data set. A window function is a function which is multiplied into a data set in order to taper it at its edges. Such functions begin at a small value, rise smoothly to a peak, and then fall again in a symmetrical way. The choices offered here defined below.

The unit can accept any VectorType input, and works intelligently on special types. By default, it scales the chosen window to the width of the input data set, multiplies the data (real or complex is allowed) by the window, and outputs a data set of the same type as the input but with the shaped data. However, if the input is a Spectrum or ComplexSpectrum, then the function is applied in a way that matches the meaning of the data. If the input spectrum contains zero-frequency, then the shaping is applied only to the upper-frequency limit of the data. If the data is narrow-band and does not include zero-frequency, then the shaping is applied to the frequency band, rounding it off at its lower and upper limits.

The unit can also accept TImeFrequency input data. It windows the frequency dimension of this two-dimensional data set, using the same principles as described in the previous paragraph, and outputs a TimeFrequency data set containing the shaped data.

Windowing can be used with Fourier transforms to make the result of a transform seem more reasonable. If a time-series has sharp edges, then its Fourier transform will show oscillations or peaks. Rounding the shoulders of the time-series makes the Fourier transform smoother. Conversely, if the window function is applied to a spectrum before it is inverted to the time domain, then the inversion will be smoother and not show the oscillations that sharp edges in the spectrum would generate. The FFT unit contains the option to apply these windows to the input time-series data. Other units offer rounding of spectral data sets using these as well: WinFT, LowPass, HighPass, BandPass, MultiBand, and HetdyneF. Windowing is also available for time-domain filtering in the units FIR_LowPass, FIR_HighPass, FIR_BandPass.
 

Using WindowFnc


The parameter window for WindowFnc is shown below:

Just select the appropriate window from the choice box.
 
 

Description of the Windows

The built-in windows are defined by the following names (see below for a reference) and associated functions, all of which are given here on the domain (-0.5, 0.5): All windows defined here are symmetrical about their center (x=0), and (except for Rectangle) they taper monotonically to a very small value from a maximum of 1. When a window function is used, its domain is scaled to the width of the input data set. If a window width has an odd number of elements, then the central value is 1 and values are sampled from the continuous functions defined here on either side of the maximum. If the window width is even, then the values are sampled symmetrically about the maximum, so that the maximum is not actually a sampled value. Note that the Rectangle window is not really a window at all: it does not modify the input data.

The reference used for constructing these windows, and for naming them, is: G Heinzel, A Rudiger, R Schilling, "Spectrum and spectral density estimation by the discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows", preprint (2002). Contact: ghh@mpq.mpg.de