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 […]

# Free

## 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 […]

## 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 […]

## Fourier Transform Interpretation of Sampling

In the Fourier Transform Interpretation of Sampling lesson you will learn how the Fourier transform of the sampled signal depends on the Fourier transform of the original continuous-time signal. This relationship provides the basis for understanding the sampling theorem, how to reconstruct a continuous-time signal from samples, and how aliasing can distort the frequency content of […]

## 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 […]

## 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 […]