App-44
IM 701210-06E
Differentiation on DSP Channels
Differentiation Characteristics
In the differentiation on DSP channels, computation is performed using the 5th order
Lagrange Interpolation Formula. The 5th order Lagrange Interpolation Formula is as
follows. For details, see App-16 page.
f
n
' = 1/(12T
s
){f
n-4
–8f
n-3
+8f
n-1
–f
n
}
The amplitude characteristics and the ideal differentiation characteristics when the 5th
order Lagrange Interpolation Formula is used are indicated below.
-60
-40
-20
0
20
0.001 f
0.010 f
0.100 f
1.000 f
dB
Lagrange Interpolation Formula
Ideal differentiation characteristics
Frequency Characteristics of Differentiation
(f: sampling frequency [Hz])
The differentiation characteristics are approximately equal to the ideal differentiation
characteristics until the input frequency is 20% of the sampling frequency. At higher
frequencies, the high frequency characteristics of the Lagrange Interpolation Formula
suppress the high frequency components.
Computation Delay
The computation delay is as follows.
Computation delay = (4 + 2
1
)
×
sampling period
1. 2 = delay due to the Lagrange Interpolation
However, if the sampling frequency exceeds 100 kHz, it is fixed to 100 kHz (10
µ
s).
It is also fixed to 100 kHz (10
µ
s) when in envelope mode.
Low-Pass Filter Function
In the differentiation on DSP channels, differentiation can be performed after passing the
input signal through a low-pass filter. The low-pass filter used is a SHARP low-pass
filter.
For the characteristics of the SHARP low-pass filter, see page app-25.
When the low-pass filter is turned ON, the computation delay increases. The
computation time can be derived from the following equation.
{(Order of the SHARP low-pass filter – 1)/2 }
×
sampling period
For the order corresponding to the specified cutoff frequency, see page app-27.
Appendix 6 DSP Channel Computation (Optional)
