Signals and signal processing are a constant part of your everyday experience. This lesson introduces you to the incredible breadth of signal-processing applications. An overview of some of the key historical factors that have led to the proliferation of signal processing is also given. This lesson will prepare and motivate you for continued study of this exciting field.

## Ever-Present Noise

The most dominant factors in the field of signal processing are noise and its sister, interference. Noise and interference is the motivating root of almost all signal-processing methods. This lesson introduces you to the notions of noise and interference and explains why they are always present. You will gain an understanding for the context for Read More

## Models, Math, and Real-World Signals

In this third lesson on fundamental signal processing concepts you will learn about the role of mathematical models in signal processing. Models are used to describe characteristics of signals and or noise that are relevant to the information of interest in the signal. Mathematical models underlie all algorithms in signal processing, including separation of signals Read More

## Four Signal-Processing Themes

This lesson introduces you to four common signal-processing problems that transcend many application areas. You will gain a general perspective of the overarching goals of the signal processing without the complications of specific applications and methods. This high level introduction will help you maintain the proper perspective and context when you later immerse yourself in Read More

## Building Signals with Blocks: Basis Expansions

The notion of building complex signals using elementary signals – metaphorical “blocks” – is central to many signal processing tools, such as Fourier transforms, wavelet transforms, and principle component analysis. The details of these different tools vary and can appear complex. This lesson presents a unified, big picture view of this topic that will help Read More

## Signals: The Basics

The field of signal processing has developed notation and terminology for efficient and accurate communication of concepts and ideas. In this lesson you will learn the basic notation and terminology used to describe signals, including concepts such as sampling, period, fundamental frequency, and discrete and continuous independent variables. Understanding these basic concepts and terms will Read More

## Sinusoidal Signals

Sinusoids are arguably the most important type of signal used in signal processing. In this lesson you will learn why sinusoids play such a prominent role, important differences between continuous- and discrete-time sinusoids, and how sampling relates continuous- and discrete-time frequency. Knowledge of sinusoidal signals will allow you to understand important signal processing concepts such Read More

## Sinusoidal Signals Examples

This lesson illustrates sinusoidal signals with two examples drawn from music. In the first example you will see how changing the frequency of sinusoids can generate the notes in a musical scale. The second example previews the important topic of Fourier representations. You will see and hear that as few as eight sinusoids accurately represent Read More

## Complex Sinusoids

At first it might seem that complex sinusoids complicate your study of signal processing. On the contrary, complex sinusoids simplify signal processing analysis and computation. This lesson will provide you with understanding of complex sinusoids that is essential to work and study in the field of signal processing. The real and imaginary parts of a Read More

## Exponential, Step, and Impulse Signals

This lesson introduces you to three additional important types of signals: exponentials, steps, and impulses. These signals serve as useful models for physical phenomena and as building blocks for more complicated signals. Both continuous- and discrete-time versions are defined. Adding knowledge of these signals to your understanding of sinusoids will complete your dictionary of fundamental Read More

## Introduction to Linear, Time-Invariant Systems

Linear, time-invariant (LTI) systems are the primary signal-processing tool for modeling the action of a physical phenomenon on a signal, such as propagation and measurement. LTI systems also are a very important tool for processing signals. For example, filters are almost always LTI systems. In this lesson you will learn the definition of a system Read More

## Introduction to Difference Equation System Descriptions

A difference equation is one of several tools for expressing the output of a linear time-invariant (LTI) system as a function of the input. Difference equations are widely used in computational applications to implement signal-processing algorithms. This lesson provides you with an introduction to the use of difference equations for computing the output of a Read More

## Impulse Response Descriptions for LTI Systems

The impulse response of a system is the output of the system in response to a unit impulse input signal. This lesson introduces you convolution, which expresses the output of an LTI system as a function of its input and impulse response. You will learn how the impulse response reveals whether the system is causal Read More

## Frequency Response Descriptions for LTI Systems

This lesson will introduce you to the most intuitive description for LTI systems used in signal processing. The frequency response of a system defined as the amplitude and phase of the system output in response to a unit complex sinusoid input signal. You will learn how the frequency response is related to the impulse response Read More

## Exercises for Signals: The Basics

The benefit you derive from these exercises is proportional to the effort you put into them. Here are my suggestions: Try to work the problems without looking at the solution. Don't give up easily. Feel free to refer back to the lessons covering this material. If/when you become stuck, then look at the solution, but Read More