The magic of adaptive filters in amateur radio

Examples of a speech signal (top),
a sinusoidal, and noise (bottom)

Radio amateurs have been using adaptive noise reduction and adaptive notch filters for decades. They came with the advent of audio digital signal processing. 

Few however, understand how different they are from ordinary frequency selective filters and for many they appear to do something magic, very different from ordinary filters.

Adaptive noise reduction (NR) and adaptive notch filters in today's amateur radio transceivers can be constructed in several ways, but one of the most common ways is to use Finite Impulse Response (FIR) filters. The filter coefficients vary with the signal and are calculated continuously for each incoming sample, so the filter is constantly updating itself. Unlike standard filters with fixed coefficients, the adaptive filters are able to remove unwanted signals even if they overlap in frequency with the desired signal.

Examples of the three types of signals in question are shown in the figure to the right.

What separates the three signal types, speech, sinewave and noise, from each other, is what is called correlation time. This is the key to understanding these filters. It is a measure of the relationship between the samples in the signal. In the top speech signal, two sets of oscillations are seen. The slow one, which repeats with about 13 ms, is the vocal cord vibration, pitch, of about 77 Hz which is in the typical range of a male voice. The faster oscillation between each vocal cord pulse is due to resonances in the oral cavity. In this signal, there is a good correlation between the samples over 5-10 ms, but beyond that it becomes small. In the sinewave, the correlation time is much longer, while in the white noise at the bottom, each sample is independent of each other so the correlation time is almost 0.

An adaptive filter as shown in the figure below figure exploits these differences and, using the algorithm for finding filter parameters, manages to create a filter that makes it possible to subtract the unwanted noise from the signal, leaving you with an improved signal. This applies whether it is white noise with a short correlation time that is to be removed from a speech signal with a medium correlation time, or it is an interfering tone with a long correlation time that is to be removed from a speech signal. The value for the delay, Δ, shown in the lower left corner is set to a value between that of the undesired noise and the desired signal. 

This has been a brief description of the principles behind the LMS (least mean square) adaptive filter and variants of it such as Leaky and Normalized LMS. There are also other kinds of adaptive filters, based on for instance Spectral Subtraction, that can be used for this application.* 

This text has been written for the chapter on digital signal processing in the revised textbook for Norwegian radio amateurs due in 2025.

*A. L. L. Ramos, S. Holm, S. Gudvangen, R. Otterlei, "A Spectral Subtraction Based Algorithm for Real-time Noise Cancellation with Application to Gunshot Acoustics," Int. J. Electron. and Telecomm., 2013.