DS-2000 Frequently Asked Questions

Even when displaying the same signal on an FFT analyzer, the peaks of the two waveforms will not coincide because they represent different things in the time domain (time-axis waveform) and the frequency domain (power spectrum). This will be explained next.

The left side of the diagram below shows, from top to bottom, sine waves with amplitudes of 1 V at 100 Hz and 110 Hz, and an enlarged time waveform of their combined form. These can be expressed by the following equations:

 

 

Furthermore, the right-hand figure displays the same time waveform as the left-hand figure on the upper side, and the power spectrum of each waveform on the lower side. Since the Y-axis scales are the same, you should be able to see the differences in the waveforms and their amplitudes when comparing them.

 

Reading the value at the cursor position, the time-domain waveform peak of the composite waveform is 1.994V, and the power spectrum appears as two peaks at 100 Hz and 110 Hz, both of which are 1 Vo-p. The power spectrum represents the amplitude of the sine waves at 100 Hz and 110 Hz, respectively. In other words, the power spectrum can be interpreted as displaying the frequency components and their amplitudes of the time waveform. Conversely, if we consider the frequencies and amplitudes represented by the power spectrum as sine waves, then combining these sine waves will result in the time waveform. This is known as the Fourier transform (frequency domain) and the inverse Fourier transform (time domain). To reiterate, an FFT analyzer displays the time evolution of the signal voltage in the time domain and the frequencies and amplitudes of the sine wave components that make up the time-domain waveform in the frequency domain. Therefore, to find the maximum amplitude value, you should look at the time-domain waveform (time domain), and to find the frequency components, you should look at the power spectrum (frequency domain).

 

 

Since power spectra do not contain phase information, we will omit the explanation of phase. Note that the phase of a sine wave significantly affects the synthesis of sine waves; even with the same frequency and amplitude, different phases result in completely different time waveforms. Please refer to the following document for more details.

 

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