Vibration signals can be filtered using various filter types to isolate different frequency bands. Active filters use op-amps and transistors while passive filters use inductors, capacitors, and resistors. Filter types include low-pass, high-pass, band-pass, and band-stop filters based on the frequencies allowed. Filter designs like Butterworth, Chebyshev, and elliptic provide different frequency responses. Spectrum analysis separates a signal into its frequency components using filters. Fast Fourier transforms allow real-time analysis by rapidly converting time signals to frequency spectra.

1. Vibration Signal Filtering
Rahman Wijaya 13/349752/TK/41177
Safira P. Larasati 14/363219/TK/41401
Saraf Iftin Atsani 14/363263/TK/41428
Muhammad Iqbal S. 14/363228/TK/41408

2. Introduction
• Filter is a circuit designed to flow a certain frequency band and
eliminate the different frequencies with this band. Another
terminology of a filter is a circuit that can select a frequency to flow
the desired frequency and hold, or discard other frequencies.
• Filters are used for 2 general purposes. That is the separation of
signals that have been fused and repair / restoration of signals that
have been distorted / deviated in various ways. Separation of signals
is used when the signal is interrupted and has been intermingled with
interference, noise, or other signals.

3. Type Of Filters
• Active Filter
Active Filter is a filter circuit using active electronic components. The
components consist of op-amps, transistors, and other components.
Therefore, filters can be made with good performance with relatively
simple components. An inductor that will become expensive at audio
frequency, is not needed because its active element, the operating
amplifier, can be used to simulate the inductive reactance of the inductor.
The advantages of this active filter circuit are its smaller size, lighter,
cheaper, and more flexible in its design. While the disadvantage is the
heat generated component, there is a frequency limitation of the
components used so that the application for high frequency is limited.
Based on its strengthening properties

4. Type Of Filters
• Passive Filter
Passive Filter is a filter circuit that uses passive electronic components
only. Where the passive components are inductors, capacitors, and
resistors. The advantages of this passive filter circuit are that there is not
so much noise as there is no reinforcement, and is used for high
frequencies. While the disadvantage is that it can not amplify the signal, it
is difficult to design a filter of good quality / response.

5. Type Of Filters
• Low Pass Filter (LPF)
• High Pass Filter (HPF)
• Band Pass Filter (BPF)
• Band Stop Filter (BSF)
• A highpass filter is a filter which allows the high-frequency energy to pass
through. It is thus used to remove low-frequency energy from a signal.
• A lowpass filter is a filter which allows the low-frequency energy to pass
through. It is thus used to remove high-frequency energy from a signal.
• A bandpass filter may be constructed by using a highpass filter and lowpass
filter in series.
Based on the Area of Frequency

6. Type Of Filters
Different filters influence on a noise signal’s frequency spectrum when the signal passes through
them Low pass filter.
(i) Low pass filter (ii) High pass filter (iii) Band pass filter (iv) Band stop filter (Source: Brüel & Kjær, course material.)

7. Type Of Filters
• Butterworth filter – no gain ripple in pass band and stop band, slow cutoff
• Chebyshev filter (Type I) – no gain ripple in stop band, moderate cutoff
• Chebyshev filter (Type II) – no gain ripple in pass band, moderate cutoff
• Bessel filter – no group delay ripple, no gain ripple in both bands, slow gain
cutoff
• Elliptic filter – gain ripple in pass and stop band, fast cutoff
• Optimum "L" filter
• Gaussian filter – no ripple in response to step function
• Hourglass filter
• Raised-cosine filter
Based on Frequency Response to Gain

8. Type Of Filters
• Here is an image comparing Butterworth, Chebyshev, and elliptic filters. The filters in this
illustration are all fifth-order low-pass filters. The particular implementation – analog or digital,
passive or active – makes no difference; their output would be the same.

9. Characteristics and causes
The characteristics of the filter are determined by the window shape.
In the case of the Hanning :

10. Characteristics and causes
The filter shape has sloping sides and does not have a flat top. Thus,
some errors are introduced (up to 16% error in amplitude). This is
leakage. See Figure 15.

11. Characteristics and causes
Flat Top :
The flat top window has a very wide filter which covers several bins. It shows
a signal appearing at several frequencies, but has the advantage of giving
very accurate amplitude. Its primary use is for calibration.
Rectangular :
This is actually no window at all. The advantage of using this comes in run-up
or coast-down where if the windows are triggered by a signal in phase with
rotation, where very good order tracking can be achieved. This window is
also used for transients.

12. Characteristics and causes
Hamming
The Hamming window provides better frequency resolution at the expense
of amplitude. Less of the signal leaks into adjacent bins than with the
Hanning window. This can be used to separate close frequency components.
Kaiser-Bessel
This window is even better than the Hamming technique for separating close
frequencies because the filter has even less leakage into side bins. The initial
main envelope however covers several bins so resolution is less than with
Hamming.

13. SPECTRUM
• Spectrum or frequency analyzers can be used for signal analysis. These devices analyze a signal in the
frequency domain by separating the energy of the signal into various frequency bands. The separation
of signal energy into frequency bands is accomplished through a set of filters. The analyzers are usually
classified according to the type of filter employed.
• In recent years, digital analyzers have become quite popular for real-time signal analysis. In a real-time
frequency analysis, the signal is continuously analyzed over all the frequency bands. Thus the
calculation process must not take more time than the time taken to collect the signal data. Real-time
analyzers are especially useful for machinery health monitoring, since a change in the noise or
vibration spectrum can be observed at the same time that change in the machine occurs. There are
two types of real-time analysis procedures: the digital filtering method and the fast Fourier transform
(FFT) method.
• The digital filtering method is best suited for constant-percent bandwidth analysis, the FFT method for
constant-bandwidth analysis. Before we consider the difference between those two approachers, we
first discuss the basic component of a spectrum analyzer namely, the bandpass filter.

14. SPECTRUM
• A vibration FFT (Fast Fourier Transform) spectrum is an incredibly useful tool for
machinery vibration analysis. If a machinery problem exists, FFT spectra provide
information to help determine the source and cause of the problem and, with trending,
how long until the problem becomes critical.
• FFT spectra allow us to analyze vibration amplitudes at various component frequencies
on the FFT spectrum. In this way, we can identify and track vibration occurring at specific
frequencies. Since we know that particular machinery problems generate vibration at
specific frequencies, we can use this information to diagnose the cause of excessive
vibration.
• The key focus of this article hinges on the proper techniques regarding data collection
and common types of problems diagnosable with vibration analysis techniques. This
article can be used as a reference source when diagnosing vibration signatures.

15. SPECTRUM
Theory
• Non-sinusoidal periodic signals are made up of many discrete sinusoidal frequency
components (see applet Fourier Synthesis of Periodic Waveforms). The process of
obtaining the spectrum of frequencies H(f) comprising a time-dependent signal h(t) is
called Fourier Analysis and it is realized by the so-called Fourier Transform (FT). Typical
examples of frequency spectra of some simple periodic signals composed of finite or
infinite number of discrete sinusoidal components are shown in the figure below.

16. SPECTRUM
• However, most electronic signals are not periodic and also have a finite duration. A single
square pulse or an exponentially decaying sinusoidal signal are typical examples of non-
periodic signals, of finite duration. Even these signals are composed of sinusoidal
components but not discrete in nature, i.e. the corresponding H(f) is a continuous
function of frequency rather than a series of discrete sinusoidal components, as shown in
the figure below.

17. SPECTRUM
• H(f) can be derived from h(t) by employing the Fourier Integral:
• This conversion is known as (forward) Fourier Transform (FT). The inverse Fourier Transform (FT-1) can
also be carried out. The relevant expression is:
• These conversions (for discretely sampled data) are normally done on a digital computer and involve a
great number of complex multiplications (N2, for N data points). Special fast algorithms have been
developed for accelerating the overall calculation, the most famous of them being the Cooley-Tukey
algorithm, known as Fast Fourier Transform (FFT). With FFT the number of complex multiplications is
reduced to Nlog2N. The difference between Nlog2N and N2 is immense, i.e. with N=106 , it is the
difference between 0.1 s and 1.4 hours of CPU time for a 300 MHz processor.
• All FT algorithms manipulate and convert data in both directions, i.e. H(f) can be calculated from h(t)
and vice versa, or schematically:

18. SPECTRUM
Signal Smoothing Using Fourier Transforms
• Selected parts of the frequency spectrum H(f) can easily be subjected to piecewise mathematical
manipulations (attenuated or completely removed). These manipulations result into a modified or
"filtered" spectrum HΜ(f). By applying FT-1 to HΜ(f) the modified signal or "filtered" signal hΜ(t) can be
obtained. Therefore, signal smoothing can be easily performed with removing completely the
frequency components from a certain frequency and up, while the useful (information bearing) low
frequency components are retained. The process is depicted schematically below (the pink area
represents the range of removed frequencies):

19. References
1. Rao, Singiresu S., Mechanical Vibrations-5th Ed, Pearson Educations, 2004.
2. http://www.skf.com/binary/tcm:12-113997/CM5118%20EN%20Spectrum%20Analysis.pdf accessed
on December 3rd 2017.
3. https://en.wikipedia.org/wiki/Filter_(signal_processing) accessed on December 3rd 2017.
4. http://195.134.76.37/applets/AppletFourAnal/Appl_FourAnal2.html accessed on December 4th
2017.