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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?. What is a signal?.
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Lecture 4: Signal Processing EEN 112: Introduction to Electrical and Computer Engineering Professor Eric Rozier, 2/18/13
Current Class Grades Including homework, participation, and lab grades…
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.
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 • Representing numbers • How can we encode the values from -1 to 1 in 4 bits?
Upcoming Items of Interest Lab this week – Matlab, intro to signal processing