CF-5200 Frequently Asked Questions

2048 points sampled at a frequency range of 2.56 times the sampling frequency are displayed on the time axis, and from that data, a Fourier expansion (Fourier transform) is performed to obtain the Fourier spectrum (pairs of sin and cos coefficients).
In other words, to express it in a Fourier series, we calculate those sin and cos coefficients → Fourier coefficients → Fourier spectrum.

Fourier series is

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

The Fourier spectrum
can conceptually be represented as a vector with the coefficient values Bi of cos on the X-axis as the real part (Re), and the coefficient values Ai of sin on the Y-axis as the imaginary part (Im).
This value is called the Fourier spectrum, and it is displayed on the screen after showing the power spectrum when the REAL button and IMAG button are turned on.

The power spectrum Vr is
obtained as the magnitude of the Fourier spectrum.

Vi = √{Re ² + Im ²} { } indicates the contents inside the square root.

The phase is also determined from the following equation.

tanΘ＝Im÷Re

again

Ai・sinωi＋Bi・cosωi＝Vi・cos（ωi＋Θ）

Therefore, f(t) can be considered as a composition of cosine waveforms for each frequency ωi.
(In the CF5200 series, Vi is displayed as the effective value at the initial setting.)

When the Y-axis is linear, Vi is displayed as is, but when the Y-axis is logarithmic,

Pi＝10LOG（Vi）²

We calculate Pi and display this value.
Since we are taking the square of Vi, the power spectrum generally refers to data in Log representation.

Additionally, the FFT is displayed with a resolution of 800 divisions of the frequency range for 2048 sample points.
Therefore, in the power spectrum display screen, 801 data points are shown on the X-axis from 0Hz to the frequency range.

Chapter of the relevant instruction manual

Setting of analysis data length and resolution