Algorithms Index , Filtering in Triana , Triana Spectral Storage Model


LowPass

Author : Bernard Schutz

Version : 2.0

Input Types : ComplexSpectrumSpectrumTimeFrequency
Output Types : ComplexSpectrumSpectrumTimeFrequency
Date : 04 Mar 2001 

Contents


Description of LowPass

The unit called LowPass performs a low-pass filter in the frequency domain. It takes an input spectrum and ouputs a narrow-band spectrum consisting of just the spectral elements below the upper-frequency cutoff chosen by the user in the parameter window. If the input is two-sided, the output contains both negative and positive frequencies whose absolute value is below the cutoff.

The user can also choose to smooth the edges of the frequency cutoff using a choice of window functions. The functions are those given in WindowFnc. These are useful if the filtered spectrum is 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 the output set to the upper-frequency cutoff. 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.
 

Using LowPass

LowPass's parameter window (double-click on the unit) looks like this.

The first slider chooses the frequency cutoff in Hz. All data at frequencies above this are set to zero.

The second 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.

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

The fourth 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.