This measurement column addresses frequently asked questions received by our customer support center and provides answers to them. Starting with this issue, we will cover topics related to the measurement of frequency response functions using sweep signals and other methods.
To measure the natural vibration frequency, one method involves exciting the object with a vibrator and determining the frequency response function from the resulting vibration. Similarly, when measuring the frequency response of a filter circuit, a signal is input into the circuit, and the frequency response function is determined from the output signal.
This time, we will introduce some of the input signals used to measure frequency response functions.
Frequency response function and FFT (Fast Fourier Transform)
The frequency response function is a function of frequency and has a complex number value. Because it is a complex number, it has a real part and an imaginary part. It can also be expressed in terms of gain (amplitude) and phase. When a sine wave (a pure sine wave) with an amplitude of 1 at a certain frequency is input to an object, the amplitude of the signal output from the object is the "gain". The time delay (lead) of the output signal is expressed as the "phase". When there is a time delay, the phase has a negative value.
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Figure 1: Example of a frequency response function
To measure the frequency response function, a sine wave of a certain frequency is input to the object, and the output is measured.
We measure a sine wave and then measure the amplitude ratio and phase difference. By changing the frequency of the input sine wave...
By repeating the same measurement, the frequency response function can be obtained. The following measurements are used for this type of measurement:
A signal whose frequency changes sequentially is called a sine sweep signal.
When a time-domain waveform containing multiple frequency components is subjected to an FFT (Fast Fourier Transform), the frequency spectrum is obtained.
It can be obtained by inputting a signal containing broadband frequency components and measuring the output signal.
By performing an FFT on each to obtain the frequency spectrum, the frequency response function can be derived from it.
Yes, it is possible. Broadband signals used in such cases include random signals and swept sine waves.
These include signals and pseudo-random signals. Theoretically, you can input such signals and perform an FFT operation.
The frequency response function can be measured in one go, but in practice, multiple measurements are performed to improve measurement accuracy.
It is calculated by performing an FFT operation and then taking the average of those results.
Signals used to measure frequency response functions
Here are some of the signals used to measure frequency response functions. In particular, the sine sweep signal and the swept sine signal are often confused, but they are clearly distinguished when measuring frequency response functions and other related data.
(1) Sine sweep signal
Figure 2-1 shows an example of a sine sweep signal used for frequency response function measurement using the FFT method. This example shows the first 10 seconds of the waveform when sweeping from 5 Hz to 50 Hz with a frequency range of 1 kHz and 2048 sample points. Under the conditions of a 1 kHz range and 2048 points, 0.8 seconds of data are required to perform one FFT. The analysis device outputs a 5 Hz sine wave for 0.8 seconds to measure the frequency response function of the 5 Hz component. Next, it outputs a 6.25 Hz sine wave for 0.8 seconds, and so on, repeating up to 50 Hz. There are 37 lines from 5 Hz to 50 Hz in 1.25 Hz increments, so measuring these takes 0.8 seconds × 37 = 29.7 seconds. If multiple FFT operations are performed on a single frequency component and the average is taken, the time required will be twice the number of averaging operations.
Measuring the frequency response function using the FFT method with a sine sweep signal requires such a long time.
It takes time. There is also a method called FRA that performs measurements in a shorter time, but the FRA method
We will introduce this in future measurement columns.
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Figure 2-1 Time-domain waveform of a sine sweep signal (partial)
(2) Random signal
A signal generated by random numbers is called a random signal. Among random signals, white noise has the same amplitude for all frequency components when averaged over a long period of time. Figure 2-2 shows the time waveform and spectrum of a random signal with a frequency range of 1 kHz and 2048 sample points.
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Figure 2-2 Time-domain waveform and spectrum of a random signal
(3) Swept sine signal
A sine sweep signal is generally a sine wave whose frequency changes over a period of several tens of seconds or more.
A swept sine wave is a sine wave whose frequency changes from 0 Hz to the upper frequency limit within the time duration of a single FFT operation. Figure 2-2 shows the time waveform and spectrum of a swept sine wave with a frequency range of 1 kHz and 2048 sample points. In Figure 2-2, the frequency of the swept sine wave changes from 0 Hz to 1 kHz in 0.8 seconds.
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Figure 2-3 Time-domain waveform and spectrum of a swept sine signal
(4) Pseudo-random signals
A pseudo-random signal appears random, but it is actually a sum of sine waves of equal amplitude and random phase at various frequencies, resulting in a flat spectrum.
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Figure 2-4 Time-domain waveform and spectrum of a pseudo-random signal.
summary
This time, we introduced the signals used to measure frequency response functions. The time required for measurement differs significantly between measurements using a sine sweep signal and those using broadband signals (random signals, swept sine signals, pseudo-random signals). Also, measurements using a sine sweep signal are complex to set up. Therefore, next time we will introduce the setup, measurement procedures, and precautions for using a sine sweep signal.
(Excerpt from the email newsletter issued on October 22, 2015)
