SV SLA-PA201, Руководство пользователя

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39
V. Real Time FFT Spectrum
x
Spectrogram and Octave Analysis
1. Understanding of Frequency Analysis
The shape of the time signal is so complex that we can’t see the information of frequency in the
measured time signal. Therefore, we have to calculate FFT (Fast Fourier Transform) analysis to get
the information of frequency-the periodicity of time signal. Frequency analysis is classifying the
magnitude of time signal as frequency like [Fig. V-1-1]
Frequency
Spectrum
FFT
Frequency
Frequency
FFT
FFT
Frequency
Spectrum
FFT
=
+
+
+…
[Fig. V-1-1] Concept of Frequency Analysis
2. Fast Fourier Transform
Frequency analysis usually uses Fast Fourier Transform which is abbreviated to FFT. The basic
assumption to calculate FFT is that time signal has infinite periodicity. Here is the calculating
equation below :
1
2
0
[ ] ( ) , 0 1
k
N
j n
N
n
X k x n e k N
π
⎛ ⎞
−
−⎜
⎟
⎝ ⎠
=
⎡ ⎤
= ≤ ≤ −
⎢ ⎥
⎢ ⎥
⎣ ⎦
∑
<Eq. V-2-1>
where
( ) x n
is discrete time signal,
N
is the buffer size of FFT. And
[ ] X k
is the calculated
result of FFT. In general,
N
has the number of
2
n
-512, 1024, 2048, 4096. The parameters of FFT
are listed in <Table V-2-1>.
The calculation of FFT accomplishes after an allocated buffer is filled with data. This procedure is
shown in [Fig. V-2-1].
1
FFT
is calculated after the first buffer is filled with data, and then
2
FFT
is
calculated after the second buffer is filled with data. This procedure is continuous, so we can see the
FFT results as real-time data.