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 Grades Including homework, participation, and lab grades…

SIGNAL PROCESSING

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?

Ways to collect data from sensors in the environment.

Why do we care about signals?

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 Signals Number of bitsNumber of states * 10^19

Digital Signals Representing numbers – How can we encode the values from -1 to 1 in 4 bits?

Digital Sampling

WRAP UP

Upcoming Items of Interest Lab this week – Matlab, intro to signal processing