SV SLA-PA201, Manual, Page: 43 / 88

43
2. 3 Averaging of FFT Spectrum
The reason of averaging spectrum is to remove noises in the spectrum. There are linear averaging,
exponential averaging and peak hold averaging.
2. 3. 1 Linear Averaging
Let’s suppose that
1
FFT
is FFT spectrum of the first time signal buffer,
2
FFT
is FFT spectrum
of the second time signal buffer and so on as [Fig. V-2-8]. Linear averaging is the arithmetic average
of spectrums at each frequency. On other words, you have to sum all of spectrums at special
frequency, and then divide summed values with averaging number like the equation below.
1
1
( ) ( )
a
n
i
i
a
FFT k FFT k
n
=
=
∑
,
0
2
N
k
≤ ≤
<Eq. V-2-3>
where
FFT
is the averaged spectrum of FFT.
a
n
is averaged number.
N
is buffer size.
Time1 Time2 Time3
…
FFT
1
FFT
2
FFT
3
[Fig. V-2-8] Instantaneous FFT Spectrum
2. 3. 2 Exponential Averaging
Exponential averaging is calculated from the exponential averaged spectrum at each frequency
using <Eq. V-2-4>. Exponential averaging emphasizes recent spectrum in all of spectrums.
1
0
( ) 1 ( )
T iT
i i
i
FFT k e e FFT k
τ τ
∞
− −
−
=
⎛ ⎞
= − ⋅
⎜ ⎟
⎝ ⎠
∑
,
0
2
N
k
≤ ≤
<Eq. V-2-4>
where
i
FFT
is the averaged spectrum of FFT at present.
1 i
FFT
−
is the proceeding averaged
spectrum.
T
is the total time of one buffer per second. And
τ
is time constant per second.