Using the Frequency Analysis VIs (Sound and Vibration Measurement Suite)
December 2007
NI Part Number:
372416A-01
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This topic provides specific information about using the Frequency Analysis VIs in measurements.
Available Measurements
The following Frequency Analysis VIs provide the same basic measurements but are designed for specific measurement needs:
- Baseband FFT VIs
- Zoom FFT VIs
- Baseband Subset VIs
Each of the three palettes contains a VI for measuring the power spectrum. The SVFA Power Spectrum VI computes the power spectrum of an input signal. The SVFA Power Spectrum Subset VI computes a subset of the power spectrum of the input signal. The SVFA Zoom Power Spectrum VI computes a zoom power spectrum of the input signal.
The Baseband FFT, Baseband Subset, and Zoom FFT VIs all share the same basic relationships between the input signal and the computed spectrum. For the baseband and subset analyses, you can obtain a tighter frequency resolution only by increasing the block size. Increasing the block size results in an FFT computed with more lines. Zoom analysis internally reduces the sampling frequency by decimating the data. In baseband FFT, baseband subset, and zoom FFT analysis, the frequency resolution is the inverse of the measurement duration.
Single-Channel Measurements
You can perform the following single-channel measurements with the Frequency Analysis VIs:
- Power spectrum computes the power present within each spectral bin. All phase information is lost in the computation. Use power spectrum to examine the various frequency components in a signal.
- Power spectral density computes the power present within each bin normalized by the bin width. All phase information is lost in the computation. Use power spectral density to examine the noise floor in a signal or the power in a specific frequency range. Normalizing the power spectrum by the bin width decouples the result of this measurement from the block size N.
- FFT spectrum computes either the magnitude and phase, the real and imaginary parts, or the complex form of the spectrum of the input signal. Phase information is retained depending on the selected averaging mode. Use FFT spectrum in measurements that require magnitude and phase information.
Power Spectrum Measurement
The following block diagram shows how to use the SVFA Power Spectrum VI to perform a single-shot acquisition.
The following block diagram shows using the SVFA Power Spectrum VI to perform a continuous acquisition.
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Note In the previous block diagrams, the output of the DAQmx Read (Analog 1D Wfm NChan NSamp) VI is an array of waveforms. You can wire the output array from the DAQmx Read (Analog 1D Wfm NChan NSamp) VI directly to the SVL Scale Voltage to EU VI. If the DAQmx Read (Analog 1D Wfm NChan NSamp) VI output array contains only a single waveform, use the instance of the polymorphic DAQmx Read VI that returns only a single channel before wiring the waveform to the SVL Scale Voltage to EU VI. |
You can use the Power Spectrum Express VI to configure power spectrum measurements interactively.
Dual-Channel Measurements
Dual-channel measurements differ from single-channel measurements because the output spectrum of dual-channel measurements is dependent on the relationship between two input channels. Typically, the input signals are a stimulus and a response. Some form of broadband excitation usually is required to obtain accurate results. Broadband signals include noise, chirps, multi-tone signals, and impulses.
Use the Frequency Analysis VIs to make the following dual-channel measurements:
- Frequency response computes the transfer function of the response to the stimulus. Use the frequency response as a general tool to characterize the dynamic response of a system. The coherence often is used to validate the frequency response results. The coherence quantifies the portion of the response that is linearly dependent on, or coherent with, the stimulus. The coherence ranges from 0 to 1.
- Cross spectrum computes the cross spectrum of the two inputs. Use the cross spectrum in some advanced analyses. Dynamic data often is stored in terms of cross spectra. Use the cross spectra to compute other useful measurements, such as frequency-response functions.
- Coherent output power computes the portion of the response power that is coherent with the stimulus.
You can view most dual-channel measurement results as magnitude and phase or as real and imaginary parts. Use the view parameter of the Frequency Analysis VIs that return magnitude and phase to specify the following viewing options:
- Whether the magnitude is expressed in decibels. Convert the magnitudes to a logarithmic scale where:
Converting the magnitudes to a logarithmic scale helps to visualize small and large spectrum components at the same time.
- Whether the phase is unwrapped. Unwrapping the phase removes discontinuities greater than
(180?. The phase is wrapped between – and by default. - Whether the phase is returned in degrees or radians.
Frequency Response Function Measurement
Frequency response measurements compare a stimulus signal and a response signal in order to compute the frequency response function (FRF) of the device under test (DUT). The FRF represents the complex ratio of output-to-input in the frequency domain and fully characterizes linear, time-invariant systems.
The magnitude of the FRF is equivalent to the gain expressed as a function of frequency. The phase of the FRF is equivalent to the relative delay of each frequency component through the DUT.
Performing FRF measurements requires a signal source. Valid stimulus signals are usually broadband signals such as white noise, pink noise, impulses, and chirp signals. Broadband signals ensure that all the frequencies of interest are excited during acquisition.
Use the Frequency Response Express VI to develop and interactively configure frequency response measurements.
The following example illustrates a FRF measurement. In this example, an NI PXI-4461 DSA device is used to generate the stimulus signal. The stimulus signal is white noise. The DUT is a notch filter centered at 1 kHz. The following illustration shows the connection scheme used in this example.
The dynamic signal acquisition (DSA) device converts the stimulus signal from digital to analog. Analog output channel 0, AO0, sends the stimulus signal to the DUT. Analog input channel 0, AI0, receives the stimulus signal. Analog input channel 1, AI1, receives the response of the DUT.
The following block diagram shows the VI that performs the FRF measurement.
The AO physical channel control is set to Dev1/ao0. The AI physical channels control is set to Dev1/ai0:1. The sampling frequency (fs) is 51,200 Hz and is the same for the output and input channels. This sampling frequency means the measurement is performed in the audio domain. The buffers are automatically configured by NI-DAQmx.
The While Loop in the previous block diagram controls both the generation and the acquisition of the signal. For each iteration of the While Loop, the Uniform White Noise Waveform VI generates a white-noise signal. The white-noise signal is sent to the DUT on analog output channel 0, AO0. Analog input channel 0, AI0, acquires the same number of samples as the buffer that is generated. Simultaneously, analog input channel 1, AI1, acquires the response signal from the DUT. The following front panel shows the measured time-domain stimulus and response signals.
Notice that you cannot interpret the time-domain signals in the previous front panel. Looking at the results in the frequency domain provides more insight into the DUT dynamic response.
Effect of Averaging and Frequency Resolution on FRF Results
Understanding the effects that averaging and frequency resolution have on FRF measurement results is important when performing FRF measurements. The following examples illustrate the effects averaging and frequency resolution have on FRF measurement results.
Both examples use the block diagram in the previous section with a sampling frequency of 51,200 Hz and a block size of 1,024 samples. Audio or acoustic applications commonly use this sampling frequency. The 51,200 Hz sampling frequency and the 1,024 sample buffer size permit 400 alias-free spectral lines up to 20 kHz.
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Note The SVFA Frequency Response (Mag-Phase) VI uses the stimulus and response signals from the DUT to compute the FRF. In the following examples, only the magnitude of the frequency response function is displayed. |
The following front panel shows the frequency response of a notch filter measured without averaging.
You can use averaging to improve the FRF measurement. The following front panel shows the frequency response obtained by applying RMS averaging over 100 measurements.
Using averaging improves the results as compared to the results obtained with no averaging.
Improving Frequency Resolution by Increasing the Number of Samples
At a constant sampling rate, the number of samples used to process the FFT determines the frequency resolution of any FFT-based measurement. For example, assume that the filter used in the averaged FRF example is meant to provide attenuation better than 50 dB at the notch frequency. The notch frequency is 1 kHz in this example. The averaged measurement shown in the previous front panel only indicates an attenuation slightly better than 40 dB at 1 kHz. The 1,024 samples and the 51,200 Hz sampling frequency lead to a 20 ms block of data and a frequency resolution of 50 Hz. However, the filter has a very narrow stopband. A better frequency resolution is needed to perform a more accurate measurement in the region of the notch.
If the processing buffer is increased to 4,096 samples and the sampling frequency is kept at 51,200 Hz, the frequency resolution becomes 12.5 Hz. The following front panel displays the averaged measurement obtained with the new block size.
Increasing the frequency resolution results in a more accurate measurement of the attenuation of the filter around its notch frequency.
The following table shows the multichannel frequency response measurements.
| Instance of the SVFA Frequency Response VI | Test Type | Common Use Cases |
|---|---|---|
| 1x1 | Single-Input, Single-Output (SISO) | Validating single-channel devices such as audio filters, amplifiers, equalizers, speakers, and cell phones |
| NxM | Multiple-Input, Multiple-Output (MIMO) | Performing structural tests, or any type of test with multiple excitation locations and multiple response locations, such as a ground vibration test (GVT) for airplanes, bridge response, and modal analysis |
| N pairs | SISO with n number of DUTs | Validating multiple single-channel devices |
| Nx1 | Single-Input, Multiple-Output (SIMO) | Performing structural tests with a single excitation location and multiple response locations |
| 1xM | Multiple-Input, Single-Output (MISO) | Performing structural tests with multiple excitation locations and a single response location |
Cross Spectrum
A cross spectrum measurement is an important building block for other measurements. Typically, you do not use the cross power spectrum as a direct measurement. The magnitude of the cross spectrum is equivalent to the power spectrum when the two input signals to the cross spectrum are the same signal. For the general case, the magnitude of the cross spectrum is the product of the RMS amplitudes of the input signals, X and Y. The phase of the cross spectrum is equal to the phase of the frequency response.
Coherence
The coherence function indicates the portion of the response energy correlated to the stimulus energy. You can use the coherence function to identify excess noise and to identify which of the multiple stimulus inputs is contributing to the response signal. The coherence equation always yields a value for coherence between zero and one. A value of one at a given frequency indicates that all of the response energy is due to the stimulus signal and that no interference is occurring at that frequency. A value of zero indicates that no correlation exists between the response signal and the stimulus signal at that frequency. Use coherence with averaged measurements. The coherence is unity at all frequencies for applications with only one average.
Coherent Output Power
The coherent output power returns the power in the response signal correlated to the stimulus signal.