# Connexions

You are here: Home » Content » Digital Signal Processing » Introduction to Digital Signal Processing

• Introduction to Digital Signal Processing

### Recently Viewed

This feature requires Javascript to be enabled.

Inside Collection (Course):

Course by: Mark A. Davenport. E-mail the author

# Introduction to Digital Signal Processing

Module by: Mark A. Davenport. E-mail the author

## Information, Signals and Systems

Signal processing concerns primarily with signals and systems that operate on signals to extract useful information. In this course our concept of a “signal” will be very broad, encompassing virtually any data that can be represented as an organized “collection” of data.

### Example 1

• A continuous function f(t)f(t)
• A sequence of discrete data points f[n]f[n]
• A multi-dimensional array of data
• Audio, images, video, voltage of antenna
• Stock prices, potassium concentration in a neuron

Our concept of a “system” will be a black box that takes a signal as input and provides another signal as output.

### Example 2

• Filters
• Decimators/Interpolators
• Matched filters
• Face recognition systems

In this course we will approach signal processing from the point of view that signals are vectors living in an appropriate vector space, and systems are operators that map signal from one vector space to another. This allows us to use a common mathematical framework to talk about how to:

• represent signals
• measure similarity/distance between signals
• transform signals from one representation to another
• understand the operation of linear systems on the signals

Since the ficus of this course in on digital signal processing, this will also allow us to use tools from linear algebra to facilitate this understanding.

## Digital Signal Processing

DSP is often presented as an alternative to analog signal processing, i.e., instead of a purely analog system as in Figure 1, we can build a digital implementation of an analog system as in Figure 2. This can be advantageous since high-precision analog components are expensive (even compared to the cost of an ADC/DAC).

However, the success of DSP derives to a much greater extent from the facts that:

1. Discrete-valued signals can be more robust to noise, as illustrated in Figure 3. In Figure 3(a), noise may be impossible to eliminate, but in Figure 3(b) noise can be eliminated entirely by exploiting the discrete structure of the signal.
2. Once we have a digital, discrete-time signal, we can store it in memory and perform highly complex processing.

In this course we will consider signal processing systems beyond simple LTI filters. Themes of the course include:

• Signals as vectors, vector space geometry
• Signal representations and bases
• Linear systems analysis and linear algebra
• “Optimality” in signal processing (e.g., optimal filter design)

## 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

### Reuse / Edit:

Reuse or edit collection (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.

| Reuse or edit module (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.