What are Single-Tone and Multi-Tone Signals?

Single Tone Signal

A single-tone signal is a signal that consists of a single frequency and is represented graphically by a sinusoidal wave. These are pure sinusoidal, periodic signals with single-frequency components.

In the time domain, it can be represented as:

where A is the amplitude of the signal, f is the frequency, t is the time in seconds, and ϕ is the phase angle of the signal.

In the frequency domain, it can be represented as:

where A is the amplitude of the signal, δ is the Dirac delta function centered around the frequency f_o.

In audio testing, single-tone signals are used to calibrate audio equipment like speakers, amplifiers, etc. It is also used by technicians and sound engineers to test the performance of a system by sending the signal at a specific frequency. In communication systems, they are used in dial-up modems and tone-based telecommunication systems. In acoustics, it is used to study the behavior of sound waves. 

As the single tone signals consist of a single frequency component, they provide limited information as compared to multi-tone frequency system. Besides, these signals are vulnerable to noise which can affect the integrity of the signal.

Multi-Tone Signal

Multi-tone signals, unlike single-tone signals, are composed of multiple single sine waves or tones with a unique amplitude, phase and frequency of each wave respectively. In the frequency domain, the multiple tones are present at unique frequencies respectively, but in the time domain, they will form a composite signal in which each of the tones will add or cancel. They are generated by Continuous Wave (CW) generators and Arbitrary Waveform generators (AWG).

In the time domain, it can be represented as:

where A is the amplitude of the signal, f is the frequency, t is the time in seconds and, ϕ is the phase angle of the signal.

A composite signal made from various time-domain signals

In the frequency-domain, it can be represented as:

Where A is the amplitude of the signal, δ is the Dirac delta function centered around the frequency f_i.

Frequency domain representation of multi-tone signal

Two-tone and multi-tone signals are used in the telecommunications industry to test for non-linear distortions in amplifiers, receivers, etc. They are used in modern audio measurements to test consumers and professional audio devices, broadband devices, and internet audio. Also, they can be used in an open-loop test where the analyzer does not have to sync up with the generator, this allows an audio signal to be tested over a long distance. Standard multi-tone signals have evenly spaced tones with equal amplitude. They are also used to test the frequency response of a device and measure the intermodulation distortion.

Comparison between single-tone and multi-tone signals