## How To Calculate A Resultant Vector

When we are dealing with multiple measurements we often need to calculate a resultant vector to understand their combined effect. What do we mean by this? And how do we…

## Which Should I Use? Real & imaginary? Or magnitude & phase?

In one of our recent articles a question was asked regarding the practical use of real & imaginary type plots compared with modulus & phase type plots. In general, noise…

## Vibration Monitoring Phase Measurement And The Tacho Signal

Any vibration signal may be analyzed into amplitude and phase as a function of frequency. The phase represents fifty percent of the information so it is most important to measure phase for vibration monitoring. Most vibrations on a rotating machine are related to the rotational speed so it is clearly important to have a measure of the speed, either directly or as a once per revolution tacho pulse. A question sometimes arises as to whether a once per revolution tacho reference signal is needed to measure phase. Is it possible to get phase if we only have a speed signal? This note gives some insight into those questions.

Actually the question that should be asked is – “Can we measure a meaningful phase, for use in vibration monitoring, if we only have a speed signal as well as the vibration signals?”

## What Is A Fourier Transform?

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 the sum of the two sine waves shown below. The resultant summed signal is shown in the third graph.

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## 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 = SampleRate/2. As discussed elsewhere Shannon’s Sampling Theorem tells us that if the signal we are sampling is band limited so that all the information is at frequencies less than fN then we are alias free and have a valid digitised signal. Furthermore the theorem assures us that we have all the available information on the signal. (more…)