FFT Analysis

The program FFT (Fast Fourier Transform) Analysis is used for narrow-band spectral processing of signals coming from the input channels of ADC modules and FFT spectrum analyzers (in real-time or recorded time realization view mode), as well as for viewing various spectral characteristics of signals.

Spectral analysis is used for dividing signals into basic constituents in the frequency area. This analysis is based on signal time realization decomposition into the frequency spectrum with an even frequency increment by means of Fourier transform.

Using the Narrowband spectrum program, based on the spectrum shape, the user can determine the presence of any signal tones (discrete constituents) and noise components in the measuring channel. Additional options of spectrogram building (in a 2- and 3-dimensional view) enable tracking of the non-stationary processes dynamics. A spectrogram is a spectral time representation of a signal, calculated for even time intervals. Building spectrogram sections based on time and frequency enables control of the non-stationary processes parameters.

Narrow-band-spectrum-Metallica-1-Spectrogram

The possibility to obtain the maximum and averaged spectra values and to compare them with their pre-set spectra (norm) enables evaluation of the difference between the pre-set and actual spectrum level. This option is necessary for various types of equipment monitoring, input/output control.

Simultaneous spectral analysis in various frequency bands of one and the same signal allows to observe the spectrum both in the entire frequency band (panoramic mode) and a detailed spectral analysis in the selected frequency bands. It is necessary if the signal has several high or low-frequency discrete constituents.

High-frequency resolution (up to 32,000 bands) allows to accurately determine the frequency of a stationary signal tone and to divide several adjacent frequency components. Such situation often occurs during vibroacoustic analysis of various mechanisms with electric drive. In the range about 50 Hz, several discrete constituents are typically determined, which are related to the electromagnetic blast, mechanical oscillations caused by the rotation of an asynchronous engine. All of these sources are typically located in a band of up to 0.5 Hz.

When analyzing noise components, discrete constituents on the spectrum could be quite disturbing. The program provides an option Clearing spectrum from discrete constituents (DC). This function suppresses all stationary signal tones.

Piezoelectric accelerometers are usually used for vibroacoustic analysis. These sensors send a signal proportional to the acceleration at the attachment point. Norms for vibration levels and their spectral composition are usually determined by the vibrational velocity value. To obtain a vibrational velocity signal, it is necessary to integrate the vibrational acceleration signal based on the time. For balancing, it is necessary to obtain the vibrational displacement value at the sensor attachment point. A vibrational signal time-based double integral allows for obtaining a vibrational displacement signal. These additional signal integration and differentiation functions are available in the described program.

For measuring the discrete constituents level, the root-mean-square (RMS) is usually measured in the filter band. In this case, the level of the discrete constituent does not really change against the analysis band. For measuring the level of noise components, it is necessary to measure the spectral power density (SPD) which is set in ^{unit of measurement}/√Hz. This is necessary because the noise spectral power density does not depend on the analysis band. FFT Analysis allows to calculate the spectra based on RMS, SPD, and amplitude values.

Additional functions of the program

The program FFT analysis allows to implement the following additional functions:

Multi-channel mode
Calculation of resonance frequencies
Synchronization

FFT analysis - Narrow-band spectrum - ZETLAB Software - new functional features

Multi-channel mode of operation

In the case, if it is necessary to calculate signal’s spectra received from a large number of channels, the user can activate the Multi-channel mode function.

In order to enable simultaneous calculation of spectra by several channels, start the program “FFT analysis“, go to the settings of the program, then in the section Multi-channel mode specify the number of channels, select a channel to be displayed, then configure the parameters of the channel in question.

If you want to save the changes in the parameters configuration file, then, upon completion of channel’s parameters configuration, select the check-box Common CFG, and apply the relevant settings.

Synchronization

In pratice, you can often face a task, in which it is necessary to calculate the signal spectra at a particular moment of time, or by certain event, in order to analyze the frequency components of the specimen in question.

The program FFT analysis has the synchronization function available for two modes of operation:

by the channel of RPM transducer;
by a value.

The RPM transducer channel allows to determine the type synchronization labels used. The follow-up frequency of the synchronization labels should not be less than 1,5 Hz. The pulses can be of any polarity and amplitude.

The spectrum is calculated in the narrow band range upon receipt of the signal from the RPM transducer. This type of analysis allows to outline the spectrum segment, having the greatest contribution to the overall distortion level. This option is quite useful in the case of rotary mechanism components research.

Synchronization mode: by the RPM transducer signal

Narrowband spectrum without synchronization mode

Narrowband spectrum with synchronization mode

Synchronization of spectrum calculation can also be implemented by value, in the case if one of the below listed options is selected:

over the positive value;
between the values;
below the negative value;

or by amplitude (in the case if the signal threshold is set):

over the threshold;
below the threshold.

Window functions

The program FFT analysis has a number of window functions available (i.e., data windows, also referred to as tapering windows). The main task addressed by the window functions is to decrease the displacement value of periodogram spectral evaluations. Processing with the use of window functions is used for the control of the defects attributed to the presence of secondary (lateral) lobes in the spectral evaluations. The program has the following discrete time functions available for use in the spectral analysis:

Rectangular window;
Hann window;
Hamming window;
Blackman window;
Bartlett window;
Kaiser window;
Rife-Vincent window;
Blackmann-Harris window;
Nutall window;
Blackman-Nutall window;
Flat-top window;
Sine window;
Asymmetrical window.

Selection of the window function to be used in the program FFT analysis

Below you can see the examples of frequency characteristics obtained with the use of discrete time Fourier transform of each relevant window:

Asymmetrical-window-function-705x496 — Asymmetrical window function

Bartlett-window-function-705x496 — Bartlett window function

Blackman-Harris-window-function-3-705x496 — Blackman-Harris window function 3

Blackman-Harris-window-function-4-705x496 — Blackman-Harris window function 4

Blackman-window-function-705x496 — Blackman window function

Blackman-Nutall-window-function-705x496 — Blackman-Nutall window function

Kaiser-window-function-1-705x496 — Kaiser window function

Nutall-window-function-705x496 — Nutall window function

Flat-top-window-function-705x496 — Flat-top window function

Rectangular-window-function-705x496 — Rectangular window function

Rife-Vincent-window-function-4-705x496 — Rife-Vincent window function 4

Sine-window-function-705x496 — Sine window function

Hann-Hanning-window-function-705x496 — Hann – Hanning window function

Hamming-window-function-705x496 — Hamming window function

Configuration of graph display parameters:

If necessary, the user can configure the graph display parameters in the program FFT analysis. To activate the panel used for graph display parameters configuration, right-click the graph grid area.

The user can configure the following parameters:

size of vertical and horizontal scales (even, log, dB/1/n-octave);
coordinate grid parameters;
display parameters – type of the lines, graph color, line thickness, etc.;
parameters of grid color and font size;
tooltip windows – a text note on the graph allowing to add comments.

Main Features

signal level measurement in narrow spectral bands. The number of bands can be equal to the power of 2 (64, 128, 256, 512, 1024, 2048, …, 32768) or to an arbitrary integer number (50, 100, 200, 500, …, 50 000);
spectral analysis dynamic range: 170 dB;
averaging of the analyzed signal: from 0,01 up to 1000 seconds;
averaging types: linear, exponential;
implementation of weighting functions: rectangular, Hann, Hamming, Blackmann, Bartlett;
signal integration/ differentiation;
signal processing based on particular algorithms: fast (FFT) and discrete (DFT) Fourier transform;
type of the analyzed signal representation: spectral density, spectral power, RMS or amplitude value;
implementation of median filter for elimination of spectrum discrete components.

calculation and display of signal cepstrum (reverse Fourier transform);
calculation and display of the transient characteristics;
calculation and display of spectral graphs in 2-dimensional format (with color indication of signal level) and in 3-dimensional format;
calculation and display of maximum and averaged values for a set period of time;
graphs overlay option for transient processes analysis;
harmonic components analysis;
recording and reproduction of program configuration for the repeated measurement processes;
integrated correction function for the FR characteristics.

Analysis frequency range of the program Narrow-band spectrum for FFT spectrum analyzers ZET 017-U

Sampling frequency f, Hz	Range, Hz Frequency resolution, Hz
50 000	0…20 000	0…2 000	0…200	0…20	0…2
50 000	from 0,5 up to 500	from 0,05 up to 50	from 0,005 up to 5	from 0,0005 up to 0,5	from 0,00005 up to 0,25
25 000	0…10 000	0…1 000	0…100	0…10	0…1
25 000	from 0,25 up to 250	from 0,025 up to 25	from 0,0025 up to 2,5	from 0,00025 up to 0,25	from 0,000025 up to 0,025
5 000	0…2 000	0…200	0…20	0…2	0…0,2
5 000	from 0,05 up to 50	from 0,005 up to 5	from 0,0005 up to 0,5	from 0,00005 up to 0,05	from 0,000005 up to 0,005
2 500	0…1000	0…100	0…10	0…1	0…0,1
2 500	from 0,25 up to 25	from 0,025 up to 2,5	from 0,0025 up to 0,25	from 0,00025 up to 0,025	from 0,000025 up to 0,0025

Analysis frequency range of the program Narrow-band spectrum for FFT spectrum analyzer А19

Sampling frequency f, Hz	Range, Hz Frequency resolution, Hz
250 000	0…100 000	0…10 000	0…1 000	0…100	0…10
250 000	from 2,5 up to 2500	from 0,25 up to 250	from 0,025 up to 25	from 0,0025 up to 2,5	from 0,00025 up to 0,25
50 000	0…20 000	0…2 000	0…200	0…20	0…2
50 000	from 0,5 up to 500	from 0,05 up to 50	from 0,005 up to 5	from 0,0005 up to 0,5	from 0,00005 up to 0,25
25 000	0…10 000	0…1 000	0…100	0…10	0…1
25 000	from 0,25 up to 250	from 0,025 up to 25	from 0,0025 up to 2,5	from 0,00025 up to 0,25	from 0,000025 up to 0,025
5 000	0…2 000	0…200	0…20	0…2	0…0,2
5 000	from 0,05 up to 50	from 0,005 up to 5	from 0,0005 up to 0,5	from 0,00005 up to 0,05	from 0,000005 up to 0,005
2 500	0…1000	0…100	0…10	0…1	0…0,1
2 500	from 0,25 up to 25	from 0,025 up to 2,5	from 0,0025 up to 0,25	from 0,00025 up to 0,025	from 0,000025 up to 0,0025
500	0…200	0…20	0…2	0…0,2	0…0,02
500	from 0,005 up to 5	from 0,0005 up to 0,5	from 0,00005 up to 0,05	from 0,000005 up to 0,005	from 0,0000005 up to 0,0005
250	0…100	0…10	0…1	0…0,1	0…0,01
250	from 0,0025 up to 2,5	from 0,00025 up to 0,25	from 0,000025 up to 0,025	from 0,0000025 up to 0,0025	from 0,00000025 up to 0,00025

Supported Hardware

Input data for Narrowband spectrum program includes digital data of the ZETLAB server channel.

FFT Analysis is a part of the following software:

ZETLAB BASE – ADC/DAC module software,
ZETLAB ANALIZ – FFT spectrum analyzer software
ZETLAB VIBRO – Shaker controller software,
ZETLAB TENZO – Strain-gauge station software,
ZETLAB SEISMO – Seismic station software,
ZETLAB NOISE – vibration meter-noise meter software,
ZETLAB SENSOR – digital ZETSENSOR sensor software.

Narrowband spectrum analysis is included into the Signal Analysis software group.

FFT Analysis

Additional functions of the program

Multi-channel mode of operation

Synchronization

Window functions

Asymmetrical window function

Bartlett window function

Blackman-Harris window function 3

Blackman-Harris window function 4

Blackman window function

Blackman-Nutall window function

Kaiser window function

Nutall window function

Flat-top window function

Rectangular window function

Rife-Vincent window function 4

Sine window function

Hann – Hanning window function

Hamming window function

Configuration of graph display parameters:

Main Features

Supported Hardware

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