Single Frequency Filter

The Single Frequency Filter (or Notch Filter) is a specialized digital filter designed to attenuate a very narrow band of frequencies, effectively "notching out" a single periodic component from a signal.

This is extremely useful for:

• Removing 50Hz/60Hz power line noise from sensor data.
• Eliminating fixed-frequency acoustic or electrical interference.
• Restoring signals corrupted by a single-tone oscillator.

Interactive Demo

The demonstration below uses a High-Performance Toggle Interface to switch between Time and Frequency domains within the same chart instance:

1. Oscilloscope Mode: Observe the sum of 3 base frequencies vs the interference-corrupted signal.
2. Spectrum Mode: Visualize the frequency components and see the Notch Filter create a surgical "hole" at your target frequency.

Try it out

Move the Target Frequency slider to change the interference frequency, and watch how the filter adapts to remove it! Use Bandwidth to control how sharp the filter is.

Initialising Charting Engine...

Interference50 Hz

Bandwidth2 Hz

Implementation

The filter is implemented as a 2nd Order IIR Notch Filter. It provides a zero-phase frequency response when applied using the filtfilt (forward-backward) technique, ensuring no time-shifting of your data.

API Usage

You can use the filter as a standalone function or through the PluginAnalysis.

1. Standalone Function

import { singleFrequencyFilter } from 'scichart-engine';

const filteredData = singleFrequencyFilter(noisyBuffer, {
  frequency: 50,      // Hz to remove
  sampleRate: 1000,   // Hz
  bandwidth: 1.0      // Hz (width of the notch)
});

2. Via Analysis Plugin

import { PluginAnalysis } from 'scichart-engine/plugins';

chart.use(PluginAnalysis());

// Later in your code
const filtered = chart.analysis.singleFrequencyFilter(data, {
  frequency: 60,
  sampleRate: 500
});

How it Works

The filter uses a transfer function in the Z-domain:

$$H(z) = \frac{1 - 2\cos(\omega_0)z^{-1} + z^{-2}}{1 - 2r\cos(\omega_0)z^{-1} + r^2z^{-2}}$$

Where:

• $\omega_0 = 2\pi \frac{f}{f_s}$ is the normalized angular frequency.
• $r$ is the pole radius (calculated from bandwidth), which determines the sharpness of the notch.
• $f$ is the target frequency.
• $f_s$ is the sample rate.

The numerator creates zeros on the unit circle at $\omega_0$ (perfect attenuation), while the denominator creates poles very close to those zeros to keep the rest of the frequency response flat.