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.
When one thinks of noise in a signal, it is generally associated with having been added in some way to the amplitude of a signal. This is not always the…
Recently when discussing with an engineering student the characteristics of filters, it became clear that some confusion exists around this subject area. This note attempts to explain the differences between types of filter and the effects of the parameters of those filters. (more…)
When using vibration data, especially in conjunction with modelling systems, the measured data is often needed as an acceleration, as a velocity and as a displacement. Sometimes different analysis groups require the measured signals in a different form. Clearly, it is impractical to measure all three at once even if we could. Physically it is nigh on impossible to put three different types of transducer in the same place.
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.
It is quite straightforward to apply “classical” integration techniques to calculate either a velocity time history from an acceleration time history or the corresponding displacement time history from a velocity time history. The standard method is to calculate the area under the curve of the appropriate trace. If the curve follows a known deterministic function then a numerically exact solution can be found; if it follows a non-deterministic function then an approximate solution can be found by using numerical integration techniques such as rectangular or trapezoidal integration. Measured or digitized data falls in to the latter category. However, if the data contains even a small amount of low frequency or DC offset components then these can often lead to misleading (although numerically correct) results. The problem is not caused by loss of information inherent in the digitisation process; neither is it due to the effects of amplitude or time quantisation; it is in fact a characteristic of integrated trigonometric functions that their amplitudes increase with decreasing frequency.
The following article was written in response to a question from a visitor to the website. The gentleman in question had been reading some of the Prosig signal processing articles and had the following question.
Dear Sir, It was interesting reading the articles in your mail.I would like to know the options available in hardware and/or software for measurement/calculation of phase angle of first harmonic of a vibration signal which is sinosoidal. The phase angle is the relative phase angle difference between the signal and the tacho - one into rpm signal. Regards. etc.
[latexpage]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.