Digital filters

What Is a Digital Filter?

A digital filter is a signal processing technique for removing unwanted noise from a signal or extracting only specific frequency components. PLC analog input values often contain noise, and low-pass or notch filters make stable control and measurement possible.

Overview

This page introduces digital filter sample programs that can be used on the OMRON NX/NJ series.
To remove noise from analog inputs and extract specific frequency components, low-pass filters (LPF), high-pass filters (HPF), band-pass filters (BPF), notch filters and more are implemented as function blocks.
The operating waveforms of each filter and the sample programs are provided, so use them as a reference for signal processing and analog data analysis on PLCs.

Creates simple digital filters

Original waveform

The original waveform contains a 30 Hz sine wave with 500 Hz noise
We apply the following 8 types of filters

Low-pass filter

Cuts off frequencies above 100 Hz to remove noise

High-pass filter

Cuts off frequencies below 100 Hz to remove noise

Band-pass filter

Passes one octave of frequencies around 30 Hz

Notch filter

Removes one octave of frequencies around 30 Hz

Low-shelf filter

Amplifies frequencies below 100 Hz

High-shelf filter

Amplifies frequencies above 100 Hz

Peaking filter

Amplifies one octave of frequencies around 30 Hz

All-pass filter

Shifts the phase around the cutoff frequency

Symbols

Input/output variables common to all functions

The sampling frequency defaults to the task period of the executing task; for high-speed analog units that acquire multiple analog values per scan, enter the sampling frequency (Hz) according to the setting
The graphs below show a 30 Hz + 500 Hz waveform collected at a sampling frequency of 10000 Hz and passed through the filters

LPF (low-pass filter)

A filter that passes frequencies below the cutoff frequency

HPF (high-pass filter)

A filter that passes frequencies above the cutoff frequency

BPF (band-pass filter)

A filter that passes only the bandwidth around the cutoff frequency
With a cutoff frequency of 30 Hz and a bandwidth of 1 octave, the range is 30/2 to 30x2, so 15 Hz to 60 Hz is passed

NotchF (notch filter)

A filter that passes everything except the bandwidth around the cutoff frequency
The opposite of BPF, it passes everything except 15 Hz to 60 Hz

LowShelfF (low-shelf filter)

A filter that amplifies frequencies below the cutoff frequency by the specified gain

HiShelfF (high-shelf filter)

A filter that amplifies frequencies above the cutoff frequency by the specified gain

PeekingF (peaking filter)

A filter that amplifies the bandwidth centered on the cutoff frequency by the specified gain

AllPassF (all-pass filter)

A filter that changes only the phase around the cutoff frequency

Example

Ladder logic

Applies a filter that passes only frequencies of 100 Hz or less to the AnalogIn data and outputs it to FilterAnalog

Source

Low-pass filter (LPF)

As an example, the low-pass filter is calculated as follows

q := 0.7; // q value IF SampFreq = 0.0 THEN Samplerate := 1.0 / (LINT_TO_REAL(TimeToNanoSec(GetMyTaskInterval())) / REAL#10.0**9); ELSE Samplerate := SampFreq; END_IF; omega := 2.0 * pi * Freq / Samplerate; alpha := SIN(omega) / (2.0 * q); a0 := 1.0 + alpha; a1 := -2.0 * COS(omega); a2 := 1.0 - alpha; b0 := (1.0 - COS(omega)) / 2.0; b1 := 1.0 - COS(omega); b2 := (1.0 - COS(omega)) / 2.0; //Biquad filter // in1 = buf[0] // in2 = buf[1] // out1 = buf[2] // out2 = buf[3] LPF := b0 / a0 * In + b1/a0 * buf[0] + b2/a0 * buf[1] - a1/a0 * buf[2] - a2/a0 * buf[3]; buf[1] := buf[0]; buf[0] := In; buf[3] := buf[2]; buf[2] := LPF;

Related pages

• FFT (fast Fourier transform)
• Analog graphs
• Ring buffer

Download

SampleAnalogFilter.zip

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References

Implementing simple digital filters (Japanese)