7-4. FFT and Bandpass Filters
In the previous lesson, we learned that in FFT, the X-axis is represented by discrete points with intervals of f0. So, what happens to the components of a signal whose frequencies fall between these intervals? This time, we'll consider this.
An FFT analyzer performs an FFT by setting the frequency range and the number of sample points. The period T and frequency resolution f0 are determined by these settings. To analyze high frequencies with high resolution, it is necessary to set a large number of sample points. However, it is not always necessary to have an accuracy of, for example, 9.72 Hz for natural frequencies; in practical terms, knowing 10.0 Hz is often sufficient. Therefore, the measurement conditions should be set and measured according to the purpose.
Now, regarding the f0 mentioned at the beginning, what happens to the component C at frequencies f that are not integer multiples of f? It is displayed as C1 and C2 at the frequencies k f0 and (k+1) f0 on both sides of f. The spectrum C1 of k f0 is displayed as larger the closer f is to k f0, and as farther away it is, as small the value of C1. When f = k f0, C1 coincides with C. The spectrum of k f0 is exactly the magnitude of the signal (power spectrum) after passing through a bandpass filter centered on f0. This is illustrated in Figure 7-4. From this, we can think of the power spectrum display of an FFT analyzer as "a series of bandpass filters" (Figure 7-5).
The shape and bandwidth of this bandpass filter are determined by the window function, which will be explained in the next section (Figure 7-6).
As a side note, in the field of acoustics, 1/3 octave band and 1/1 octave band analysis are frequently used, but in contrast to this, FFT is sometimes referred to as "narrowband" because it is a bandpass filter with an extremely narrow bandwidth.
In IT terminology, "narrowband" is often used alongside "broadband" (high-speed communication) to refer to low-speed communication lines such as telephone lines. However, in this context, "narrowband" refers to a narrow frequency band.
<Key Points>
The Fast Fiscal Format (FFT) represents the power of a signal passed through a series of bandpass filters. The shape of the bandpass filters is determined by a window function.
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Figure 7-4: FFT and bandpass filter
The power spectrum of k f0 in the FFT represents the power of the signal after passing through a bandpass filter.
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Figure 7-5: Conceptual diagram of FFT
The FFT is like having a series of bandpass filters lined up, and you're trying to find the power of each bandpass filter.
Yes.
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Figure 7-6: Shape of a bandpass filter using a window function.
The shape of a bandpass filter is determined by the window function.
(Excerpt from the email newsletter issued on July 19, 2007)
