Contents - Index

Composite Channel Processing

Composite channel spectrum analysis provides several very powerful advanced measurements.

Click the <Plots><Select Composite Channel Plots> menu to setup composite channel operations.  Up to 16 composite channels can be defined.  Composite channels indexes use letters A-P instead of numbers.

Definitions
Auto-spectrum - calculated by multiplying a spectrum by its complex conjugate (opposite phase).  The auto-spectrum is real and is identical to the magnitude response.  The auto-spectrum is what is normally displayed in a single channel spectrum plot.

Cross-spectrum - calculated by multiplying one spectrum by the complex conjugate of a second spectrum.   The cross-spectrum is a complex quantity (has both real and imaginary components).  The magnitude of the cross-spectrum represents the amount of power common to both channels, and the phase represents the phase difference between channels.  For example, If two identical signals are 180 degrees out of phase, the magnitude of the cross spectrum is zero.  If two channels are identical, their cross-spectrum is equal to the auto-spectrum of either channel alone.

Transfer Function - is the ratio between two channels and can be computed in one of two ways:
Real - this is the simplest method and is simply the ratio between the auto-spectrum (magnitude) of each channel.  The relative phase of each channel does not contribute to the result.  
Complex - this is the ratio between the cross-spectrum of the two channels and the auto-spectrum of the reference channel.  The relative phase of each channel contributes to the result.  

The transfer function is a very powerful feature.  It allows you to quickly and accurately compute the frequency response of a device under test.  See the topic  "Transfer Function" topic for more setup information

Coherence Function - is the ratio of the squared magnitude of the cross-spectrum and the product of the auto-spectrum of both channels.   It  measures the degree of linearity between the channels and is analogous to the squared correlation coefficient used in statistics.  Two perfectly coherent signals have a coherence value of 1.0

Composite Measurement Type:
  • Add Multiple Channels - sum the selected channels.  This performs a vector sum - if the channels are 180 out of phase the result is zero.
  • Average Multiple Channels - averages the auto-spectrum of two or more source channels.
  • Real Transfer Function - computes and displays the real transfer function between any two source channels (test vs reference)
  • Complex Transfer Function - computes and displays the complex transfer function between any two source channels (test vs reference)
  • Complex Transfer Function and Coherence - computes and displays the complex transfer and the coherence between any two source channels (test vs reference)
  • Cross Spectrum - computes and displays the cross-spectrum of any two source channels.
  • Difference - computes and displays the magnitude and phase differnces by subtracting the source channels spectral data

    Notes:
    - These do not apply to the time series plot.
    - The source channels must have the same sampling rate, format and selected FFT sizes.
    - The scaling used on the composite plots is as follows:
             Average multiple channels: same as scaling selected for the first channel in the average list
             All other types: same as the scaling selected for the "test channel"

    See Also:  Settings, Sampling Format