A Fourier Transform takes a signal and represents it either as a series of cosines (real part) and sines (imaginary part) or as a cosine with phase (modulus and phase form). As an illustration we will look at Fourier analysing…

## Data Smoothing : RC Filtering And Exponential Averaging

[Updated 12th March 2013] What are RC Filtering and Exponential Averaging and how do they differ? The answer to the second part of the question is that they are the same process! If one comes from an electronics background then…

## Spectrum Smoothing : Why and How?

Sometimes data has spikes which are clearly artefacts of the processing or are due to some other external source. One is used to seeing these on time series but in some cases there are unrepresentative “spikes” in the frequency analysed…

## Measuring Torsional Twist & Vibration Along a Shaft or Through a Geartrain

The measurement of torsional twist, or the twist angle, between two points along a shaft or through a gear train may be derived from a pair of tacho signals, one at each end of the shaft. Typically the tacho signals…

## Order Tracking, Frequency and Hertz

The most common form of digitising data is to use a regular time based method. That is data is sampled at a constant rate specified as a number of samples/second. The Nyquist frequency, fN, is defined such that fN =…

## Dynamic Range And Overall Level : What Are They ?

Accurate measurement of a signal depends on the dynamic range and the overall level of the data acquisition system. The overall level setting may be thought of as determining the largest signal that can be measured. This clearly depends on…

## High Pass Filtering And Tacho Signals

It is sometimes necessary to perform high pass filtering to eliminate low frequency signals. These may arise for instance from whole body vibrations when perhaps our interest is in higher frequency components from a substructure such as an engine or…

## Don’t Let Spikes Spoil Your Data

In many real-world applications it is impossible to avoid “spikes” or “dropouts” in data that we record. Many people assume that these only cause problems with their data if they become obvious. This is not always the case. Consider the…

## Non Linear Calibration Curve And Polynomial

Not all systems vary linearly. One very well known case is, of course, thermocouples. International standard curves are available for these so they present little difficulty. The issue discussed here is determining a non linear calibration curve and if appropriate…

## A Weighting. And B. And C.

Some devices, particularly digital tape recorders, apply A-weighting to all their data in order to achieve acceptable data compression. This is fine unless you want to analyse the unweighted data or apply a different weighting factor. Using Prosig’s DATS software…

## Understanding The Cross Correlation Function

To illustrate the use of the cross correlation function, a source location example is shown below. For this, it is assumed that there is a noise source at some unknown position between 2 microphones. A cross correlation technique and a…

## How Do I Downsample Data?

Sometimes we have digitised data at a much higher rate than we need. How can we downsample data? If I wanted to say halve the sample rate can I just throw away every other data point? The answer is NO,…

## Does The Signal Have A Gaussian Probability Density?

The PROB module in DATS for Windows provides, amongst other options, a probability density analysis. Also, the signal generation suite has a module, GENPRB, which generates a classical gaussian probability density curve (and others). How then may these be used…

## Removing Phase Delay Using A Phaseless Filter

In many instances we need to filter a signal to remove unwanted frequencies. If we use classical filters such as Butterworth, Chebyshev or even Bessel then a phase delay is introduced. This phase delay is itself a function of frequency…

## Methods To Remove Spikes From Data

For various reasons data captured in the real world often contains spikes that will give erroneous results when analysed. The DATS software package provides various ways of editing and to remove spikes from data. Let us consider a real life…

## Time Varying Overall Level Vibration (or Noise)

A common requirement to measure overall level vibration (or noise) as a function of time. Now, the overall level is a measure of the total dynamic energy in the signal. That is it does not contain the energy due to the…

## Interpretation of the Articulation Index

The Articulation Index or AI gives a measure of the intelligibility of hearing speech in a given noise environment. The metric was originally developed in 1949 in order to give a single value that categorised the speech intelligibility of a…