Wave Walker DSP

DSP Algorithms for RF Systems

New Posts Wednesday!

Most Popular

Signal and Noise: The Vocabulary of RF
August 31, 2021

Table of Contents

Introduction

All DSP scenarios will include a signal and noise. But what are they? Using a common set of clearly defined terms is important to properly understand what information is trying to be conveyed.

More posts from the Explaining Why series:

Time-Series

A time-series is a collection of data measured over time. That can be the Dow Jones Industrial Average every day at the closing bell, the temperature every hour or samples from an analog to digital converter (ADC). A time-series might be represented through an array,

(1)   \begin{equation*}x[n] = [0, 0.9511, 0.5878, -0.5878, -0.9511]\end{equation*}

or through an equation,

(2)   \begin{equation*}x[n] = sin\left(2 \pi n/5 \right), n = 0, 1, 2, 3, 4.\end{equation*}

Signal and Noise

I consider a signal to be a time-series which is information bearing. An example of a signal might be your height if you were able to measure it with infinite precision. I consider noise to be a time-series of randomness. Noise can come from many places, including measurement error or environmental variables. Figure 1 is an example of how a height measurement might be effected by noise.

Figure 1: Two time-series demonstrating the difference between a signal and noise. Your actual height over time would be a signal whereas your estimated or measured height would include noise sources.
Figure 1: Two time-series demonstrating the difference between a signal and noise. Your actual height over time would be a signal whereas your estimated or measured height would include noise sources.

A height estimate could have noise or error coming from one or multiple sources:

  • How fine of resolution is your ruler?
  • How accurately was your ruler constructed?
  • Did you forget to take off your shoes?
  • Are you slouching or leaning?

Note that both signals and noise are time-series and their labels are used to represent the expectation about the content of the time-series.

Frequently the term signal is used loosely and acts as a catch-all for any time-series. Consider that a transmit signal is a signal with information while a receive signal is a signal with information and noise. Figure 2 is a simplified version of how a receive signal relates to a transmit signal and noise and Figure 3 is an example of how noise corrupts a receive signal.

Figure 2: Environmental noise is added at the receiver which is a source of error.
Figure 2: Environmental noise is added at the receiver which is a source of error.
Figure 3: Environmental noise corrupts the receive signal. The difference between the transmit signal and receive signal is the error.
Figure 3: Environmental noise corrupts the receive signal. The difference between the transmit signal and receive signal is the error.

Interference

Interference is a signal which is undesired, sometimes referred to as signal not of interest (SNOI). Conversely a signal with information that is desired may be referred to as a signal of interest (SOI) or desired signal.

Signal Processing

The goal of signal processing is to apply effects to a receive signal in order to:

  • Enhance the information within the signal of interest
  • Minimize the impact of noise
  • Minimize the impact of interference

Takeaway

The terms signal and noise are only labels used to express the expectation about the content within a time-series. Noise corrupts a signal through measurement error or other uncontrollable environmental errors.

The Explaining Why category is a good place to start if you are interested in or new to DSP and looking for some answers about common questions.

Leave a Reply