What is waterfall frequency spacing? And how does the DATS parameter ‘Requested Frequency Spacing’ work?

Let us try to understand what waterfall frequency spacing is. Waterfall frequency spacing is the gap between spectral lines in an FFT plot.

For example, if you had an analysis frequency of 0Hz to 100Hz and 100 spectral lines, then Frequency Spacing is 1Hz.

So why is there a ‘Requested Frequency Spacing’ and an ‘Actual Frequency Spacing’? (more…)

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What is “waterfall smearing”?

When analysing a waterfall or performing order analysis it is important to consider the frequency resolution or the frequency spacing.

There is often a desire to increase the resolution to finer and finer detail. But that is a process of diminishing returns, and actually fraught with danger. And that danger is waterfall smearing. (more…)

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What is Synchronous (Angular) Sampling?

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 of rotary mechanical device. Typically these items are subjected to out-of-balance forces that cause them to vibrate at frequencies that are multiples of the fundamental (once per revolution) rotation speed frequency. (more…)

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Read more about the article Amplitude And Energy Correction – A Brief Summary
Figure 4: Energy corrected spectrum

Amplitude And Energy Correction – A Brief Summary

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 numbers calculated.

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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 signal.
  • Second, an FFT converts the signal representation between time and frequency domains. The time domain representation shows when something happens and the frequency domain representation shows how often something happens.
  • And finally, an FFT assumes that the signal is repetitive and continuous.

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10 Great Fourier Transform Links

Joseph Fourier

Following a discussion in the office about Fourier Transforms we did a little searching on the web. As always, we discovered that the Internet is packed with some great resources on Fourier and his work. So rather than keep all of the information to ourselves we thought we should share it with our readers. We have whittled our list down to 10 links that we think represent the whole range of information from beginners guides to reference pages. So there should be something for everyone whether you’re a grizzled signal processing veteran or a student looking to learn something new. If you have your own favourite Fourier links then please add them to the comments. Maybe we could use them for a future blog post. Or if you have other comments please feel free to add them below.

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Sound Steering

The requirement was to develop a ‘standard’ test for assessing power steering pump noise (and sound quality) in vehicles. Measurements needed to be objective so that the method would be suitable for evaluating dissimilar vehicles and different types of pump.

Noise is an important consideration when a consumer is selecting a new vehicle. It is therefore imperative that every aspect of the vehicle’s acoustic profile is thoroughly understood and refined.

From an end user point of view the assessment criterion is simply how much will the driver or passengers hear the pump noise in relation to the vehicle background noise. That is, will the pump produce, what may be called, audible tones with the vehicle in different operating conditions.

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Order Cuts And Overall Level

Order cuts are taken from a set of FFTs, each one at a different rpm. The rms level is then found as the Square root of the Sum of the squares of each of the FFT values. Mathematically, if x_{ks} is the modulus (magnitude) of the k^{th} value of the FFT at speed s for k = 1,\dots,N-1 then the rms value at that speed is given by

rms_s = \sqrt{\sum_{k=0}^{N-1}{x_{ks} ^2}}

This takes into account the entire energy at that speed both the order and the non order components, including any noise.

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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

In this article, we look at the relationships between frequency, the unit Hertz and order tracking. The most common form of digitising data is to use a regular time-based method. 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.

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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 transfer function like approach were used to determine the location. (more…)

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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, except in pathological conditions where you know that there is no frequency content above the new Nyquist frequency.

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