CF-5200 Frequently Asked Questions

2048 points, converted using AD conversion at a sampling frequency 2.56 times the frequency range, are displayed on the time axis. A Fourier expansion (Fourier transform) is then performed on this data to obtain the Fourier spectrum (pairs of sine and cosine coefficients).
In other words, in order to express it as a Fourier series, we find the coefficients of its sine and cosine, which in turn become the Fourier coefficients, and then the Fourier spectrum.

Fourier series

f(t)=A0+Σ{Ainωi+Bicosωi}
ωi: 2π×(each frequency f)

The Fourier spectrum is
Conceptually, it can be represented as a vector with the cosine coefficient Bi as the real part (Re) on the X-axis and the sinine coefficient Ai as the imaginary part (Im) on the Y-axis.
This value is called the Fourier spectrum, and it will be displayed on the screen after the power spectrum is displayed and the REAL and IMAG buttons are turned on.

Power spectrum Vr is
This is determined as the magnitude of the Fourier spectrum.

Vi = √{Re ² + Im ²} { The expression inside the braces { } represents what is inside the square root.

The phase is calculated using the following equation.

tanΘ＝Im÷Re

Also

Ai・sinωi＋Bi・cosωi＝Vi・cos（ωi＋Θ）

Since it can be converted in this way, f(t) can be considered to be a composite of cosine waveforms of each frequency ωi.
(In the CF5200 series, Vi displays the RMS value by default.)

When the Y-axis is Lin, Vi is displayed as is, but when the Y-axis is Log...

Pi＝10LOG（Vi）²

Calculate Pi and display this value.
Since we are taking the square of Vi, the power spectrum generally refers to data in logarithmic form.

Furthermore, with 2048 samples, the FFT displays a resolution of 800 equal parts of the frequency range.
Therefore, the power spectrum display screen shows 801 data points from 0Hz to the frequency range on the X axis.

Related instruction manual chapters

3.6 Setting the Analysis Data Length and Resolution