Applied Signal Processing - Lecture 1

Digital Signal Processing:

Mathematical and algorithmic manipulation of

discretized and

quantized

or

naturally digital

signals in order to extract the most

relevant and pertinent information that is carried by the signal.

What is a signal?

What is a system?

What is processing?

Applied Signal Processing - Lecture 1

Examples of signals:

Applied Signal Processing - Lecture 1

Characterization of signals:

Continuous time

signals vs.

discrete time

signals

e.g. Temperature in the building at any time

Continuous valued

signals vs.

digital

signals

e.g. Amount of current drawn by a device; average exam grades

- Continuous time and continuous valued:

Analog signal

- Continuous time and discrete valued:

Quantized signal

- Discrete time and continuous valued:

Sampled signal

- Discrete time and discrete values:

Digital signal

(CD audio)

Real-valued

signals vs.

complex-valued

signals

Single channel

vs.

multi-channel

signals

e.g. Blood pressure signal – 128 channel EEG

Deterministic

vs.

random

signal

One-dimensional

vs.

two-dimensional

vs.

multi-dimensional

signals

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

- Any physical quantity that is represented as a function

of an independent variable is called a

signal

.

independent varables can be time, frequency, space etc.

- Every signal carries

information

. However, not all that

information is typically of interest to the user. The goal of

signal processing is to extract the

useful information

from the signal

- The part of the signal that is not useful is called

noise

.

Noise is not necessarily noisy. Any part of the signal we are not

interested in is by definition noise.

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Sinusoids play a very important role in signal

processing, because

They are easy to generate

They are easy to work with; their mathematical properties

are well known

Most importantly: all signals can be written as a sum of

sinusoids, through Fourier transforms (later).

In continuous time:

Applied Signal Processing - Lecture 1

- A discrete-time signal, commonly referred to as a

sequence

, is only defined at discrete time instances,

where

t

is defined to take integer values only.

- Discrete-time signals may also be written as a sequence

of numbers inside braces:

{x[n]} = {..., -0.2,

2.2

, 1.1, 0.2, -3.7, 2.9, ...}

n indicates discrete time, in integer intervals, the bold-face number

is at t=0.

Applied Signal Processing - Lecture 1

- Discrete-time signals are often generated from

continuous time signals by

sampling

, which can roughly be

interpreted as quantizing the independent variable (time).

{x[n]} = x(nT

S

) =

x

t

∣

t=nT

S

n= ...,-2,-1,0,1,2,...

T

S

= Sampling interval/period

f

S

= 1/T

S

= Sampling frequency

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Applied Signal Processing - Lecture 1

Analysis of ECG Signals

Applied Signal Processing - Lecture 1

Analysis of seismic waves:

study the structure of the

soil by analyzing seismic

waves, wither natural (earthquakes,

volcanic eruptions) or man-made

(explosions etc.)

Useful e.g. for exploration of oil.

Depending on the material in

the soil the reflected waves have

different frequencies (modes).

Applied Signal Processing - Lecture 1

travel

time

Seismic signals as a function of position

Applied Signal Processing - Lecture 1

Dolby Noise Reduction Scheme

A Compressor

Applied Signal Processing - Lecture 1

Dolby Noise Reduction Scheme

Applied Signal Processing - Lecture 1

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