For some time now it has been conventional ‘wisdom’ that using time based digital integration may cause amplitude errors in the result and that these get worse as the frequency increases. As a result of this, integration using Omega arithmetic has been prevalent by using Fourier Transforms of the signal. This, of course, remains a valid appro [...]
Posts tagged Fourier
Wide Band Integrators – What Ar...
For some time now it has been conventional ‘wisdom’ that using time based digital integration may cause amplitude errors in the result and that these get worse as the frequency increases. As a result of this, integration using Omega arithmetic has been prevalent by using Fourier Transforms of the signal. This, of course, remains a valid appro [...]
Noise & Vibration Analysis: Back...
Sometimes it doesn’t hurt to revisit some of the basic building blocks that form the foundation of what we do. And so we have gathered together a few of our most popular past articles that deal with the fundamental aspects of measuring and analysing noise and vibration data. Please leave a comment if you have a favourite. Or, if you thi [...]
Negative Frequencies – What Are...
Normally when we are analysing a signal it is a purely real signal, that is it has no imaginary part. A classic example is of course a sine wave. When we analyse a signal with a Fourier transform, typically using an FFT algorithm, most people are aware that we will obtain a result from 0 Hz(dc) to (Sample rate/2)Hz. It is also generally un [...]
What is Synchronous (Angular) Samplin...
The term synchronous data is usually applied to vibration or acoustic data that is captured from an item of rotating equipment at regularly spaced angle intervals as distinct from regularly spaced time intervals. The rotating part could be an engine, a gear wheel, a drive shaft, a turbine rotor, a propeller, a turbocharger or any other type o [...]
10 Educational Mechanical Engineering...
We’ve had a good look around YouTube and dug up a great collection of educational mechanical engineering videos. There’s a wide range of information here from simple maths tutorial to explanations of the inner workings of the internal combustion engine. We hope you enjoy watching and if you have any favorites of your own please dr [...]
Amplitude And Energy Correction – A B...
Amplitude and energy correction has been and is a continuing point of confusion for many people calculating spectra from time domain signals using Fourier transform methods. The first thing to say, the information contained in data presented as amplitude and energy corrected spectra is equivalent. The only difference is the scaling of the num [...]
Data Windows : What, why and when?
Before we discuss the use of data windows, we should first remind ourselves of three basic properties of the FFT (Fast Fourier Transform) process.
First, energy information in signal must be preserved during transformation. That is, the energy measured on time signal must equal the energy measured on the frequency representation of that sign [...]
Interpolation Versus Resampling To In...
These are two different techniques aimed at different objectives. First consider a simple sinewave that has been sampled close to the Nyquist frequency (sample rate/2).
Visually this looks very pointy. We will examine it using a filter based interpolation and a classical curve fitting procedure to obtain a better representation.
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Vibration Monitoring Phase Measuremen...
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, [...]
Average Waterfalls Or Average Orders?
One would expect that averaging waterfalls and then extracting orders would give the same result as extracting orders from individual waterfalls and then averaging them. This is not the case.
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Notes On Fourier Analysis
Fourier analysis 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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