C source code for IIR Bilinear Transform, Parks McClellan FIR and Windowed FIR filters, Fast Fourier Transform, and code for implementing IIR and FIR filters. Newest algorithm Questions Stack Overflow. FFT, PSD, and Spectrogram Basics Free DownloadFFT, PSD and spectrograms dont need to be so complicated. Once you understand the basics they can really help with your vibration analysis. In this post Ill try to provide the right mix of theory and practical information, with examples, so that you can hopefully take your vibration analysis to the next level In order to effectively do your job of vibration analysis, you may be more interested in some practical information but it is important to understand a bit of the theory behind FFTs, PSDs and spectrograms. Ill provide an overview of the math behind the FFT, PSD and spectrogram for more detail, check out our blog on Fourier Transforms but Ill use plots to make my point instead of only equations and text. Lets go through the important differences between an FFT, PSD, and spectrogram and Ill try to illustrate when it is appropriate to use each type of vibration analysis tool. Automatically generates platformtuned implementations in C or Fortran of signal processing transform such as the discrete Fourier transform, and discrete cosine. Chapter 10 Fourier Transform Properties. The time and frequency domains are alternative ways of representing signals. The Fourier transform is the mathematical. The amorphous FFT bucket SYLTFFT by Davey Taylor GitHub link Fixedpoint 32bit, radix2, FFT and inverse FFT. FFTs using fixed point arthmetic in C. Youll be doing your vibration analysis in the real world so well look at realworld examples, and analyze data captured from an actual accelerometer. All data presented and the MATLAB scripts used to perform the vibration analysis are available to download so you can do your own vibration analysis. Simple Vibration Analysis in the Time Domain. When analyzing vibration data in the time domain accelerationvibration amplitude plotted against time were limited to a few parameters in quantifying the strength of a vibration profile amplitude, peak to peak value, and RMS. A simple sine wave is shown below with these parameters identified. The peak or amplitude is valuable for shock events but it doesnt take into account the time duration and thus the energy in the event. The same is true for peak to peak with the added benefit of providing the maximum excursion of the wave, useful when looking at displacement information, specifically clearances. The RMS root mean square value is generally the most useful because it is directly related to the energy content of the vibration profile and thus the destructive capability of the vibration. RMS also takes into account the time history of the wave form. Vibration is an oscillating motion about an equilibrium so most vibration analysis looks to determine the rate of that oscillation, or the frequency. The number of times a complete motion cycle occurs during a period of one second is the vibrations frequency and is measured in hertz Hz. For simple sine waves the vibration frequency could be determined from looking at the waveform in the time domain but as we add different frequency components and noise, we need to perform spectrum analysis to get a clearer picture of the vibration frequency. LabVIEW-and-Arduino.jpg' alt='C Program Fft Algorithm' title='C Program Fft Algorithm' />Fast Fourier Transform FFTFFT Background. Any waveform is actually just the sum of a series of simple sinusoids of different frequencies, amplitudes, and phases. A Fourier series is that series of sine waves and we use Fourier analysis or spectrum analysis to deconstruct a signal into its individual sine wave components. The result is accelerationvibration amplitude as a function of frequency, which lets us perform analysis in the frequency domain or spectrum to gain a deeper understanding of our vibration profile. Most vibration analysis will typically be done in the frequency domain. Fourier analysis works by testing for the presence of each frequency component. A discrete Fourier transform DFT multiplies the raw waveform by sine waves of discrete frequencies to determine if they match and what their corresponding amplitude and phase are. A fast Fourier transform FFT is just a DFT using a more efficient algorithm that takes advantage of the symmetry in sine waves. The FFT requires a signal length of some power of two for the transform and splits the process into cascading groups of 2 to exploit these symmetries. This dramatically improves processing speed if N is the length of the signal, a DFT needs N2 operations while a FFT needs Nlog. N operations.   So for example, lets take a signal length of 1. DFT needs 1,0. 48,5. FFT and its 1. 0,2. Although the execution time of an FFT will be fastest when the signal length is some power of 2, todays computing power and modern FFT algorithms make this time difference insignificant. Baksultanov.files/image010.jpg' alt='C Program Fft Algorithm' title='C Program Fft Algorithm' />The number of discrete frequencies that are tested as part of a Fourier transform is directly proportional to the number of samples in the original waveform. With N being the length of the signal, the number of frequency lines or bins is equal to N2. These frequency bins occur at intervals f equal to the sample rate of the raw waveform Fs divided by the number of samples N, which is another way of saying that the frequency resolution is equal to the inverse of the total acquisition time T. To improve the frequency resolution, you must extend the recording time. The lowest frequency tested is 0 Hz, the DC component and the highest frequency is the Nyquist frequency Fs2. Windowing can be used to scale the frequency range of interest and manipulate the frequency bin width. Theres a lot that goes into understanding how windowing works and how to choose the right function for your application. If this overview on the math only whets your appetite, read this post on Fourier Transforms. Enough math though Lets dive into some examples to understand how spectrum analysis can be used for your vibration testing application Constructed Sine Wave and FFT Example. To illustrate how an FFT can be used, lets build a simple waveform with and use an FFT for vibration analysis. This constructed waveform will consist of three different frequency components 2. Hz, 6. 0 Hz, and 1. Hz.  These frequencies will have an amplitude of 1g, 2g, and 1. The following figure shows how this waveform looks a little confusing in the time domain and also illustrates how the signal length affects the frequency resolution of the FFT. The function used to generate this waveform is available to download. If we sample this wave at a 5. Hz rate 5. 00 samples per second and take an FFT of the first 5. FFT due to our bin width being 1. Hz Fs of 5. 00 divided by N of 5. The amplitude of these frequency components are also a bit low. But if the range is extended to the first 2. FFT is able to accurately calculate both the frequency and amplitude of the individual sine wave components. Not that the pure waveform didnt look confusing enough in the time domain but if broadband noise is added as shown in the bottom plots then the waveform becomes even less distinguishable. This is the power of an FFT, it is able to clearly identify the major frequencies that exist to help the analyzer determine the cause of any vibration signal. Real World FFT and Spectrogram Examples. Vibration Analysis of a Car Engine. In real world applications there will typically be many different frequency components of a vibration profile as well as mechanical and electrical noise. Lets look at some data taken on a passenger car engine while it was idling and do some vibration analysis. Autoit All Files In Dir. This data was generated with a Slam Stick vibration data logger as part of a how to video series if youre interested in some more details about the test setup. We can use spectrum analysis of the vibration profile to indicate what the engines crank shaft rotation speed was. This is a 4 cylinder 4 cycle engine.