Wide Band Integrators – What Are They?

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 approach and is particularly useful if the data is already in the frequency domain, which was its prime purpose.

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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]

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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).

Figure1

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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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.

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