# tsadifference

Difference signal of a time-synchronous averaged signal

## Syntax

## Description

computes the difference signal `Y`

= tsadifference(`X`

,`fs`

,`rpm`

,`orderList`

)`Y`

of the time-synchronous averaged
(TSA) signal vector `X`

using sampling rate `fs`

,
the rotational speed `rpm`

, and the orders to be filtered
`orderList`

. `Y`

is computed by removing the
regular signal, the value of '`NumSidebands`

', and their respective
harmonics from `X`

. For more information on regular signal, see
`tsaregular`

.

You can use `Y`

to further extract condition indicators of rotating
machinery for predictive maintenance. For example, extracting the
*FM4* indicator from `Y`

is useful to detect
faults isolated to only a limited number of teeth in a gear mesh.

`___ = tsadifference(___)`

allows you to
specify additional parameters using one or more name-value pair arguments. You can use
this syntax with any of the previous input and output arguments.

`tsadifference(___)`

with no output arguments plots the
time-domain and frequency-domain plots of the raw and difference TSA signals.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

**Difference Signal**

The difference signal is computed from the TSA signal by filtering the following from the signal spectrum:

Shaft frequency and its harmonics

Gear meshing frequencies and their harmonics

First-order sidebands at the gear meshing frequencies and their harmonics

Optionally, the sidebands specified in '

`NumSidebands`

' at the gear meshing frequencies and their harmonics

`tsadifference`

uses a bandwidth equal to three times the shaft speed and the
value of '`NumSidebands`

', around the frequencies of interest, to compute
`Y`

from the TSA signal.

**Amplitude Spectrum**

The amplitude spectrum of the difference signal is computed as follows,

$$\text{S=}\frac{\text{fft}(Y)}{\text{length}(Y)*2}$$

Here, `Y`

is the difference signal.

## References

[1] McFadden, P.D. "Examination of a
Technique for the Early Detection of Failure in Gears by Signal Processing of the Time
Domain Average of the Meshing Vibration." *Aero Propulsion Technical Memorandum
434*. Melbourne, Australia: Aeronautical Research Laboratories, Apr.
1986.

[2] Večeř, P., Marcel Kreidl, and R. Šmíd.
"Condition Indicators for Gearbox Monitoring Systems." *Acta
Polytechnica* 45.6 (2005), pages 35-43.

[3] Zakrajsek, J. J., Townsend, D. P.,
and Decker, H. J. "An Analysis of Gear Fault Detection Methods as Applied to Pitting Fatigue
Failure Data." *Technical Memorandum 105950*. NASA, Apr.
1993.

[4] Zakrajsek, James J. "An investigation of gear mesh failure prediction techniques." National Aeronautics and Space Administration Cleveland OH Lewis Research Center, 1989. No. NASA-E-5049.

## See Also

**Introduced in R2018b**