Utilities

The options  from  the Utilitities menu combine a collection of tools for manipulating data traces such as integration, differentiation, filtering, spectral analysis as well as simulation of sampling and analog-to digital conversion. 'Input traces' can be actual digital seismograms loaded from the Web Server or from CD  or synthetic signals created using options from the the Test Signals menu. 'Output traces'  from any of the tools from the Utilitites menu can in turn become 'input
traces' for the other tools.
 

Discretization

Simulate discretization in time
In computer memory all traces reside as sequences of numbers, that is all traces are already existing as discrete sets of numbers. Nevertheless, the effects of discretization can be simulated on such a trace  if its internal sampling frequency is high enough (very much higher than the signal frequency).  Then the trace can be  treated as a pseudo-continuous trace from which discrete samples are taken every 1 / FDIS samples. Here FDIS is the discretization frequency for which the user is prompted. The resulting trace keeps the original sampling rate, but trace values are set to zero at points between the "resampled" points. This option does not  work  if the  specified discretization frequency is larger than the internal sampling  frequency. Vertical bars in the resulting trace represent the discrete samples taken. Using the Apply button instead of the Ok button the resulting sampled trace is superimposed on the input trace.

Reconstruction of discretized signal
A trace that has been obtained by using the Simulating discretization in time as described above can subsequently be used to simulate the process of discrete to analog conversion. DST will prompt for the discretization  frequency which has been used to obtain the discretized trace.

Integration

This option results in numerical  integration of the input trace. It  is used e.g.  to convert an acceleration-proportional record to a velocity-proportional record, or a velocity-proportional record to a displacement-proportional record. There are no input options for this utility.

Differentiate

This option results in numerical differentiation  of the input trace. It  is used e.g. to convert a velocity-proportional record to an acceleration-proportional record, or a displacement-proportional record to a velocity-proportional record. There are no input options for this utility.

Decimation filtering

This option applies a FIR lowpass filter to the input trace which restricts the frequency range to 0.8 x FDIG/DECFAC with FDIG being the sampling frequency of the data and DECFAC being the intended decimation ratio. If Resampling is turned on,  filtering is accompanied by decimation by a factor of DECFAC. If Resampling is turned off, only the lowpass filtering is done.

Decimate

Integer decimation allows the selection of every n-th value in the input trace (starting with the first one). The user has to provide the decimation ratio as an integer value. E.g. giving an input value of 2 will result in an output trace containing the first, third, fifth, and so forth values of the input trace.

Spectrum

The spectral analysis tool uses the FFT to calculate the discrete Fourier spectrum  of the input  trace. The spectrum is calculated using a Fast Fourier Transform (FFT) algorithm. The frequency range for which the frequency response is evaluated  ranges from  DELTAF = FDIG/NFFT to  FDIG/2. Here FDIG is  the internal sampling frequency and NFFT is the number of points used for calculating the FFT. Both values can be entered or modified  in the Setup menu to obtain a particular frequency range. In the context of using the FFT algorithm the window length has to be a power of 2.  If  this is not the case the user will be prompted for a proper value.

The spectral values shown have been multiplied by the sampling rate in order to approximate the values of the Fourier transform within the given frequency band. The type of spectral information displayed may be chosen between:
Amplitude
Phase
Real part
Imaginary part

For all quantities the axis type can be switched between various combinations of linear and logarithmic scale. The selected spectrum is displayed in a separate window.

Delta Modulation

This tool allows the simulation of the Delta modulation technique as described in 'Of poles and Zeros'. The user is prompted for the value of the modulator quantum (least significant bit). If the Apply button is used, the input trace is superimposed by the predicted input trace (integrated modulator output signal). Only after  the Ok button has been pressed, the modulator output signal replaces the input signal trace.

Moving Average

The moving average value of a data trace contains the slowly varying (low frequency) components of a trace. In this utility the 'baseline' is calculated from the original trace by sliding an averaging window over the data serie. The length of the time window has to be assigned by the user. For each window position, the baseline is calculated as the average value in the data window.

Sigma Delta Modulation

This tool allows the simulation of the Sigma Delta Modulation technique as described in 'Of Poles and Zeros'. The user is prompted for the value of the modulator quantum (least significant bit). If the Apply button is used, the input trace is superimposed by the predicted input trace (integrated modulator output signal). Only after  the Ok button has been pressed, the modulator output signal replaces the input signal trace.

Interpolate

This tool implements a time domain interpolation of the input trace by an interpolation factor given by the user. E. g. if an interpolation factor of 2 is used, the resulting output trace conatains twice as many samples as the input trace. It is based on an interpolation routine provided by E. Wielandt (pers. comm.).

FIR2CAUS

This tool demonstrates the performance of  the FIR filter correction technique described in detail in 'Of Poles and Zeros'. Input traces for this tool have to be loaded into DST using the Open File with Data Trace option of the File menu. The FIR20HZ folder of this option contains some example files which can be used for this purpose (e. g. the file  example20HZ).

To correct for unwanted acausal effects on seismic onsets stemming from the two-sidedness of the  impulse response of  a  digital anti-alias FIR filter, the trace has first to be interpolated back to the sampling frequency before FIR-filtering. This can be done using the Interpolate tool. In case of the file example20HZ this would be 40Hz. Hence an interpolation factor of 2 would have to be used.

The resulting interpolated trace can subsequently be post-filtered by a 'correction filter' which replaces the maximum phase portion of the FIR filter by its minimum phase equivalent. This is done using the FIR2CAUS option. The user will be asked to select the name of the  'correction filter file' to be used on the interpolated data trace. Depending on your mode of operation either the Web server or the CD will provide correction files  for a number of 'standard' data acquisition systems. For the interpolated example20HZ file  the proper correction filter would be quant40Hz.prt.

FIR filter correction causes the linear phase FIR filter response to be modified to a minimum phase response. This  results in a trace  in which an impulsive onset will appear too early by an amount corresponding to half of length of the FIR filter impulse response (the linear phase component of the FIR filter). This time shift can be corrected for if the 'Correct for linear phase' option is turned on.

Notes for advanced users:
- The input trace can also be extended in length by pre/appending zeros which is helpful if one wants to work with sequences of FIR filter coefficients directly as input trace.

- The input panel also allows the user to overwrite the digitization frequency read from the correction filter file. This option might come in handy if the same filter coefficients have been used with different sampling frequencies.

Additional hint: If the FIR2CAUS option is used with the 'Correct for linear phase' option turned on and started using the Apply button  instead of the Ok button, the corrected and the uncorrected traces are  plotted in two different windows. Using  the mouse to Zoom in on the onset allows an easy comparison of uncorrected and corrected traces.  E. g. for the example20HZ trace this nicely shows how the acausal precursory oscillations can be removed.
 

Plain A/D Converter

This utility simulates the behavior of a gain-ranging A/D converter (ADC)on a pseudo-conttinuous trace.

For the ADC simulation, the user has the choice of four output signals:
Quanized Value (mant * 2**exp): Actual output signal from the gain-ranging ADC.
Mantissa: Output of the plain ADC.
Exponent (PGA deamplification): Gain setting of the PGA
Error Signal: Difference between the quantized value and the input trace.

After selecting the output signal type, you will be prompted for the following parameters:

  • the digitization frequency for resampling
  • the pre-amplifier gain, a scaling factor which simulates a fixed gain pre-amplifier
  • the resolution, this is the number of bit
  • the LSB value, the value of least significant bit
  • the number of bits for exponent, that is how many times the PGA can decrease the amplitude of the input signal
  • Difference Equation

    An important way of describing linear time invariant (LTI) systems is by means of linear difference equations with constant coefficients. The Difference equation is described by autoregressive (AR) coefficients and moving average (MA) coefficients. Enter the autoregressive coefficients in the top panel and the moving average coeffcients in the bottom panel. You also have to assign a gain factor and to decide if the filtering should be done "forwards" or  "backwards", that is on the time inverted trace.
     

    Filter with Response from Poles/Zeros

    Once pole and/or  zero locations have been entered into DST either from file (Choose from file option from the Poles/Zero menu or Open File with GSE Calibration from the File menu) or by entering them manually (Modify and Enter option from the Poles/Zeros menu), DST allows to apply  the corresponding filter response to existing data traces. This is done  in the frequency domain by multiplication of  the complex frequency response with the discrete Fourier spectrum of the input trace.

    The user is asked for the number of points for the FFT. DST will provide a default value which is large enough to avoid wrap-around effects. You may always increase the number, as long as it is a power of 2, but using a smaller number will lead to spurious results.

    Buterworth Filter

    The trace will be filtered by a  Butterworth filter. Butterworth filters are recursive time-domain filters using the bilinear z-transform design of Stearns (1984). Applied in sections of 40 dB/decade or 12 dB/octave for the slope of the transition band. They may be given zero phase characteristic by bilateral filtering.

    You have to chosse the kind of filter:
    Bandpass
    Lowpass
    Highpass

    and provide input parameters:

  • low and high cut-off frequencies for a bandpass, for lowpass and highpass only single cut-off frequencies
  • decide, whether or not to filter "forwards" or  "backwards"
  • the number of filter sections. Each filter section corresponds to an increase of the slope of the transition band by 20 dB per decade.