Lecture 4: Signal Processing

EEN 112: Introduction to Electrical and Computer Engineering

Professor Eric Rozier, 2/18/13

MIDTERM RESULTS

Quiz and Midterm

Current Class GradesIncluding homework, participation, and lab grades…

SIGNAL PROCESSING

What is a signal?

What is a signal?

• Functions of one or more independent variables– Often encode/contain information about the

behavior of some phenomenon.– Air pressure inside a trumpet: p(x,t) where x is the

location in the tube, and t is time.

Why do we care about signals?

Why do we care about signals?

• Ways to collect data from sensors in the environment.

Why do we care about signals?

Why do we care about signals?

Why do we care about signals?

Why do we care about signals?

Signals Example

Signals Example

Signals Example

Signals Example

Signals Example

Dimensionality

• One dimensional signals– f(x) – single independent variable, “Temperature

at Miami International Airport at time t”– Intensity seen by a Kepler sensor

• Two dimensional signals– V(x,y) – color of an image sensor at position x,y.

Dimensionality

• One-dimensional signals– Amplitude or intensity is described as a function of

time, single dimension.• Audio• Speech• Seismic data• Sonar• etc

Dimensionality

• Three-dimensional signals– Take a picture, add time…– Video, v(x,y,t)

Continuous vs. Discrete

• A variable is continuous if it can assume any real value within a permissible range.– Air temperature in Miami during a day which

ranges from 60F – 80F. What values can it take on?

Continuous vs. Discrete

• A variable is continuous if it can assume any real value within a permissible range.– Air temperature in Miami during a day which

ranges from 60F – 80F. What values can it take on?

• A variable is discrete if it can assume values from a specified set.– Day of the month of February. What values can it

take on?

Continuous vs. Discrete

• Analog signal – continuous in amplitude and time– All signals that occur naturally are analog– Acoustic signals – continuous fluctuations in air

pressure or particle velocity.– If the acoustic signal has energy between 20Hz

and 24 kHz, it is audible to the human ear.

Analog Signals

• Decibel scale – logarithmic response of the human ear to changes in sound intensity/pressure.– Intensity J dB = 10 log (J/J0), where J is the sound

intensity and J0 is the intensity of the faintest audible sound

– Pressure P dB = 20 log (P/P0), where P is the sound pressure and P0 is the sound pressure of the faintest audible sound

Analog Signal

• Acoustic transducers - Microphones and speakers– Microphones convert an acoustic signal into an

electric signal, with corresponding amplitude or variation.

– Speakers convert electric signals into acoustic signals, with corresponding pressure variation.

• Allow us to convert audio signals to and from electrical signals for processing.

A problem…

• Let’s say we have an 8-bit machine, trying to record audio signals.– What inherent limits are we imposing?

Discrete-time/Digital

• Discrete-time – a signal that is continuous in amplitude and discrete in time.

• Digital – a signal that is discrete in both amplitude and time.

Digital Signals

• Computers have revolutionized our ability to store and manipulate signals.

• But… we have to store them as bits…

Digital SignalsNumber of bits Number of states

1 2

2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1024

32 4294967296

64 1.8446744 * 10^19

Digital Signals

• Representing numbers– How can we encode the values from -1 to 1 in 4

bits?

Digital Sampling

Digital Sampling

WRAP UP

Upcoming Items of Interest

Lab this week – Matlab, intro to signal processing