Connexions

You are here: Home » Content » Information and Signal Theory » Introduction to Convolution

Recently Viewed

This feature requires Javascript to be enabled.

Inside Collection (Course):

Course by: Anders Gjendemsjø. E-mail the author

Introduction to Convolution

Module by: Anders Gjendemsjø. E-mail the author

Summary: Introduction to the convolution chapter

In addition to the operations performed on signals in the Signals chapter there are several more. The most important operation is linear filtering, which can be performed by convolution. The reason that linear filtering is so important to signal processing is that it solves many problems and that is relatively simple to describe mathematically. In this chapter we will be looking at convolution.

Convolution helps to determine the effect a system has on an input signal. It can be shown that a linear, time-invariant system is completely characterized by its impulse response. Using the sampling property of the delta function for for continuous time signals and the unit sample for discrete time signals we can decompose a signal into an infinite sum / integral of scaled and shifted impulses. By knowing how a system affects a single impulse, and by understanding the way a signal is comprised of scaled and summed impulses, it seems reasonable that it should be possible to scale and sum the impulse responses of a system in order to determine what output signal will results from a particular input. This is precisely what convolution does - convolution determines the system's output from knowledge of the input and the system's impulse response.

Content actions

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks