How Do I Upsample and Downsample My Data?
This post covers how to upsample and downsample data and the possible pitfalls of this process. Before we cover the technical details let us first explain what we mean by upsample…
The Effect of the Nyquist Theory on Rotational Order Analysis
Nyquist theory is generally understood, but this understanding usually relates to time sampling and the conversion to the frequency domain. Rotational order analysis and the effect of the Nyquist frequency…
What is the maximum analysis frequency for a waterfall in DATS?
The maximum analysis frequency is always half the sample rate of the input signal.
So if your data is captured at 50kHz the maximum analysis frequency will be 25kHz.
RMS From Time History And FFT Spectrum
The RMS of a time history is a measure of the signal's overall energy and is often used when extracting features from a signal for prognosis and trending of vibration…
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…
Aliasing, Orders and Wagon Wheels
These days most people collecting engineering and scientific data digitally have heard of and know of the implications of the sample rate and the highest observable frequency in order to avoid aliasing. For those people who are perhaps unfamiliar with the phenomenon of aliasing then an Appendix is included below which illustrates the phenomenon.
In saying that most people are aware of the relationship concerning sample rate and aliasing this generally means they are aware of it when dealing with constant time step sampling where digital values are measured at equal increments of time. There is far less familiarity with the relevant relationship when dealing with orders, where an order is a multiple of the rotational rate of the shaft. For example second order is a rate that is exactly twice the current rotational speed of the shaft. What we are considering here then is the relationship between the rate at which we collect data from a rotating shaft and the highest order to avoid aliasing.
The relationship depends on how we do our sampling as we could sample at constant time steps (equi-time step sampling), or at equal angles spaced around the shaft (equi-angular or synchronous sampling). We will consider both of these but first let us recall the relationship for regular equi-time step sampling and the highest frequency permissible to avoid aliasing. This is often known as Shannons Theorem [Learn more about Claude E Shannon].
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10 Educational Mechanical Engineering Videos
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 drop a comment in the box at the bottom of the page.
1. Gas Turbine Animation
Nice animation and explanation of the workings of a gas turbine [Edit: video link changed after first became unavailble]
Interpolation Versus Resampling To Increase The Sample Rate
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.
Evaluating A Closed Loop Control System For High Pressure Pumps
Prosig were recently involved in the validation of a closed loop control system for an automotive pump supplier. The customer has a large number of test cells, each test cell has 8 pumps continually on test. Each pump is instrumented with a revolution or tachometer sensor, giving a once per revolution tachometer pulse. Additionally, there are various analogue transducers on each pump which measure parameters, such as pressure at the pump inlet and outlet.
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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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.
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 so that the signal content at one frequency is delayed a different amount to that at another frequency. Why does this matter?
