lecture 4: signal processing een 112: introduction to electrical and computer engineering professor...
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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 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