Algorithms Index , Filtering in Triana , Triana Spectral Storage Model


MultiBand

Author : Bernard Schutz

Version : 2.0

Input Types : ComplexSpectrum Spectrum TimeFrequency
Output Types :  ComplexSpectrum Spectrum TimeFrequency
Date : 05 Mar 2001 

Contents


Description of MultiBand

The unit called MultiBand filters the input data set into a number of narrow-band output data sets, working in the frequency domain. It takes an input spectrum and ouputs narrow-band spectra consisting of just the spectral elements between the lower- and upper-frequency cutoffs for each band, as chosen by the user in the parameter window. If the input is two-sided, the output sets contain both negative and positive frequencies whose absolute value is between the cutoffs. The output sets contain adjacent bandwidths within a given range. Thus, the user chooses the lowest frequency of this range, the highest frequency, and the number of bands which this range is to be divided into. Each output bandwidth is sent to a separate output node of the unit.

The user can also choose to smooth the edges of the frequency cutoffs using a choice of window functions. The functions are those given in WindowFnc. These are useful if the individual filtered spectra are to be inverted back to the time-domain: a sharp cutoff gives unwanted oscillations in the time-domain that are suppressed if the cutoff is smoothed.

The user can also choose to reduce the Nyquist frequency of each of the output sets to their upper-frequency cutoffs. The Nyquist frequency is the highest frequency that can be held in a spectral data set. When the data set is inverted by FFT,  the time-domain result will have a sampling frequency that is twice the Nyquist frequency. Thus, if the user reduces the Nyquist frequency when filtering, then the time-domain inversion will be sampled at twice the rate of the upper-frequency cutoff. This ensures that the time-domain set contains no more samples than necessary.

Narrow bandwidths created in this way can be re-combined into a single spectrum just by adding them together, using the Unit Adder. This unit will only accept data sets if they are compatible, i.e. of the same length and frequency resolution. Narrow-band data sets should first be converted to full-bandwidth by using the Unit FullSpectrum, which will place zeros in the missing data locations.
 

Using MultiBand

MultiBand's parameter window (double-click on the unit) is shown below.




The first slider chooses the lower-frequency cutoff of the entire output range in Hz. Data at frequencies below this are not included in output sets.

The second slider chooses the upper-frequency cutoff of the entire output range in Hz. Data at frequencies above this are not included in output sets.

The third line is an integer slider that selects the number of ouput bands which this overall range is to be divided into. This is the number of output nodes of the unit. If you change this number, the number of output nodes will automatically change.

The fourth line is a check box. Select this if you want narrow-band output. If it is not selected (the default) then the output spectral data set will have the same length as the input but the filtered data elements will be set to zero. If you choose narrow-band, then these zeros will not be present in the output: this saves storage. The FFT unit will still invert this properly. However, if you want to re-combine narrow-band data sets into a full spectrum later, after some manipulation, then you will have to pass them through FullSpectrum before adding them together.

The fifth choice is the window function that can be used to smooth the edges of the frequency cutoffs.

The sixth choice is a check box. Select this if you want the Nyquist frequency of the output data set to be reduced to the frequency chosen in the slider. The output data set will be a full-bandwidth spectrum with this maximum frequency. See the discussion above for the meaning of the Nyquist frequency.