Algorithms Index , Filtering in Triana , Triana Spectral Storage Model


WinFT

Author : Bernard Schutz

Version : 1.0

Input Types : SampleSet
Output Types : TimeFrequency

Date : 5 January 2001 

Contents


Description of WinFT

The unit called WinFT performs a windowed Fourier transform on an input data set. A window function, normally shorter in length than the input data set, is multiplied into the data set and a Fourier transform is taken of the resulting data. The window is then stepped along the data set, re-applied, and a new transform performed. The resulting set of transforms is arranged as a matrix and output as a TimeFrequency data type.

This can in turn be mapped to a color map, for example by ImageMapper, and displayed.

The user can choose the kind of window function, or input a window function at the second (optional) input node of the unit. The user can also choose the length of the window, and the size of the step as the window moves along the whole data set. The first transform places the start of the window at the first data point of the input. The last transform is the last one that can be done without wrapping the window around to the front of the input data set.

The built-in windows are defined by the following names 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 the rectangular one 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 chosen by the user, and it is then normalized, so that the sum of the squares of the values of its elements equals 1. If a window width is chosen to have 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 chosen to have an even number of elements, then they are sampled symmetrically about the maximum, so that the maximum is not actually a sampled value.

If the user inputs a window, it is also normalized before being used.

The window is multiplied into the data set in the appropriate domain, and a Fourier transform is performed with a length equal to the size of the window. Then the window is stepped along and the process is repeated.
 

Using WinFT

WinFT has has the following parameter window:

The first choice box offers the user the choice of the windows described above. If the user inputs a window function at the second input node (see below) then this choice is ignored. The second parameter is an integer which is the width in data points of the chosen window. The user should choose this in the light of the size of the input data set. If the width is longer than the input, only one Fourier transform will be performed. The third parameter is the step between successive windows. The difference between the two integer parameters is the overlap between successive Fourier transforms.

If the user uses the node dialog box to choose two input nodes, then a VectorType data set may be routed to the second input node and this will be used as the window, after normalizing it. The window type and width parameters will be ignored, but the step will be used as selected in the parameter window. The input window could be constructed, for example, using MathCalc.