In this article we will look at why we need to consider energy correction when producing frequency spectra and how we go about it. We will use a perfect, ’special case’ signal to keep the explanation as simple as possible. The signal we will use is periodic within the time record used to calculate the [...]
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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. Share:
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 [...] Share:
The requirement was to develop a ‘standard’ test for assessing the sound quality of power steering pumps 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 [...] Share:
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 Xks is the modulus (magnitude) of the kth value of the FFT at speed s for [...] Share:
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 [...] Share:
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 Share:
The most common form of digitising data is to use a regular time based method. That is 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 Shannons Sampling [...] Share:
To illustrate the use of the cross correlation function, a source location example is shown below. For this it is assumed 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. Share:
Sometimes we have digitised data at a much higher rate than we need. How can we reduce the sampling rate? 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 [...] |
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