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Beyond Logic Circuits —Next Stop Signal, Systems,
and Circuits, ... A Career in Electrical and Computer Engineering?
Mark Wickert, Professor (262-3500)Electrical and Computer Engineering Department
April 26, 2012
C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Overview
• The BSEE curriculum
• Moving into signal and systems
– The use of mathematics in signals and systems modeling; yes!
– Signal basics
– Signal processing tools and MATLAB
• Example: Beat notes and trig identities
• Example: Bat echo location
• Example: Compact Disk (CD) digital audio — 2’s complement for signednumbers, is it related?
– PCM and bit errors: MSB vs LSB
– Forward error correction in CD recording
• Example: Frequency tripler circuit and Fourier series mathematics
• Radio signals and spectra
• Questions
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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http://www.eas.uccs.edu/wickert/
Foundation(see catalog)
Fundamentals
Breadth-Lect(min of 12 cr)
Depth(min of 11 cr)
Chemistry Physics Humanities SocialScience
• ECE 1001, Intro to Robotics• ECE 1021, Comp.-Based Mod
& Meth of EngComm.Skills
Math
• ECE 1411 Logic Circuits I• ECE 2411 Logic Circuits II• ECE 2610 Intro Signals & Systems• ECE 2050 Intro Physical Electronics• ECE 2205 & 3205 Ckts & Sys I & II• ECE 3420, Micro Proc Systems Lab
ECE
Bas
ic
• ECE 3020 Semiconductor Devices• ECE 3110 Electromagnetic Fields I• ECE 3210 3220, 3230, & 3240,
Electronics I & II, Labs I & II• ECE 3430 Micro Processor Systems• ECE 3610 Eng. Probability & Statistics
ECE
Adv
.
Breadth-Lab(min of 2 cr)
Capstone Design(4 cr)
Computers• ECE 4480,
Comp Arch
Circuits• ECE 4340 VLSI
4242 Adv Dig
Comm/DSP• ECE 4625/50
Comm I/DSP
Controls• ECE 4510,
Fbk Cntl
EM• ECE 3120,
Emag II
Micro Elect.• ECE 4020,
Semi Dev
Computers• ECE 3440,
Micro Proc
Circuits• ECE 4200,
Dig Dsgn
Comm/DSP• ECE 4670/
80, Com/DSP
Controls• ECE 4530/
60, Anl/Dig
EM• ECE 4150,
EM Meas
Micro Elect.• ECE 4040,
VLSI Fab
Computers• ECE 4320,
4330, 4340, 4362, 4480,
Circuits• ECE 4211,
4220, 4230,, 4250, 4260, 4270
Comm/DSP• ECE 4610,
4615, 4630, 4655, 4660, 4675
Controls• ECE 4520,
4540, 4560
EM• ECE 4110
Micro Elect.• ECE 4070,
4080
• ECE 4890, Senior Seminar• ECE 4899 Senior Design
CU Colorado SpringsBSEE Curriculum
StartCareer
Power• ECE 3910• ECE 4160
Power• ECE 4910
Pwr Sys II
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Sound Waves as Functions of Time
• If a microphone is placed in the path of the sound wave, the time changingpressure results in an electrical signal that changes with time
• Similarly if our ear is in the path of the varying pressure of the sound wave, anerve signal is produced and sent to our brain
• From the electrical signal we can make some basic observations about thesound wave, assuming the wave is periodic, or repeats
Time
Am
plitu
de (
volta
ge)
wavelength (ft) period (sec) 1130 ft/sec=
period in seconds T0=
(seconds)
A
frequency pitch f0 1 T0 1T0------= = = =
signal amplitude
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
The Spectrogram
Time
Am
plitu
de (
volta
ge)
(seconds)
Signal as a Time Function
Spectrogram: Signal Frequency vs Time
A
period T0 frequency 1T0------ f0= ==
0
f0Lower Frequency or pitchF
requ
ency
(H
z)
Time(seconds)
Higher Frequency or pitch
Flat line means steady frequency, f0;Same color means steady intensity, A
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Adding Two Signals Together – Theory
Time
Time
Freq
s1
s2
s1 s2+
A1
A2
SumSignal
1f1----
1f2----
f1
f2
Sp
ectr
og
ram
0
Time
Time
Intensity A2
Intensity A1
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Adding Two Signals Together – Hands-on
Time
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Adding Two Signals – Hands-on (cont.)
Play – Enter at the MATLAB prompt >> two_tone• Listen to the default or start-up signal which has Hz and
Hz
• Compare the spectrogram plot in 2D and 3D to see what a constant frequencysignal looks like in both viewing modes (a line or a 3D wedge)
• Increase so that you can now hear two distinct tones or pitches
Beat Notes• Set Hz so that the pitch of one signal is ‘A’ on the keyboard
• Set Hz, so that the pitch of the second signal is set just 5 Hz above‘A’
– Listen to this signal; what do you hear?
• An alternate mathematical view of the two signals can be obtained via the trigidentity
• We are hearing the average of and times a slow beat at
f1 1000=f2 0=
f2
f1 440=
f2 450=
2f1t sin 2f2t sin+ 2 2 f2 f1– 2 sin 2 f1 f2+ 2 cos=
f1 f2 f2 f1– 2
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Linear Chirp Signals – Hands-on
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Linear Chirp Signals – Hands-on (cont)
Play – Enter at the MATLAB prompt >> linear_chirp• Listen to the default or start-up chirp signal which has Hz and
Hz
• Experiment with different start and stop frequencies, making sure at this pointthat both and are less than 8000/2 = 4000 Hz; the folding frequency
– Consider an up-chirp when
– Consider a down-chirp when
Aliasing• Computer signals are generated/stored for playback as a sequence of samples
• In this demo the sampling rate is samples
• For the signals considered here greater than two samples per waveform periodare required to allow faithful reconstruction of the playback signals
• If we violate this condition aliasing occurs, and the signal is heard at a lowerfrequency
• If you set or above 4000 Hz aliasing occurs and you see a zig-zag
fstart 100=fstop 2000=
fstart fstop
fstop fstartfstop fstart
fs 8000=
fstart fstop
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Animal Echolocation1
• Echolocation, also called biosonar, is the biological sonar used by several ani-mals such as shrews, most bats, and most cetaceans. The term was coined byDonald Griffin, who was the first to conclusively demonstrate its existence inbats.
• Echolocating animals emitcalls out to the environmentand listen to the echoes ofthose calls that return fromvarious objects in the envi-ronment. They use theseechoes to locate, range, andidentify the objects. Echolo-cation is used for navigationand for foraging (or hunting)in various environments.
1. http://en.wikipedia.org/wiki/Animal_echolocation
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Bat Echolocation Signals – Hands-on
Shorter durationchirps givethe bat betterresolution
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Bat Signals – Hands-on (cont)
Problem• Bats typically echolocate at ultrasonic frequencies
• To allow humans to listen to these signals they have been translated (moved)in frequency to a lower frequency
Play – Enter at the MATLAB prompt >> bat_chirp• Listen to the default or start-up signal which is a recording of fruit bats feed-
ing a single piece of cantaloupe hanging in the middle of their bat cave1
A Single Bat Echolocating• Display the One bat recording by clicking the radio button in the upper left
• This is a recording of a single isolated bat flying across the bat cave echolo-cating (the playback speed has been slowed by a factor of four)
• Each chirp in the series of three become more rapid, thus allowing forincreased resolution, as in an electronic radar
1. These recordings were made at the Cheyenne Mountain Zoo Bat Cave using an ultrasound microphone array incombination with a frequency translating device.
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Radio Waves and Sound Waves
• When we watch TV or listen to the radio we rely on the reception of wavestraveling through the air similar to the way sound waves travel through the air
• We can again use mathematics to describe radio waves as signals that varywith time, and then view these signals in terms of their frequency spectrum
Fre
qu
ency
Sp
ectr
um
Frequency
Sounds welisten to
0 20,000
AM Radio
540,000 1600,000
CellPhones
FM Radio
88 MHz 108 MHz
1 MHz 106
1 000 000 Hz = =
1850 MHz 1990 MHz
PCS
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
CD (Compact Disc) Digital Signals
• We take for granted placing a music CD into a player and then hearing highquality music
• How does digital signal processing make this possible?
• The continuous signals we have talked about up to this point are sampled at44.1 thousand times per second to produce a sequence of number that can bestored and played back on a computer
Analog toDigital
Converter
Digital toAnalog
Converter
Time
TimeTimeDiscrete
TimeDiscrete
TimeSampledSignal
Signal Sequence
Signal Sequence
Continuous Signal
Continuous Signal
Samples stored on CD for playback
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Digital Audio (cont.)
• The A/D converts the audio samples into digital words, of finite precision,using pulse-code modulation (PCM)
• From logic circuits and C programming you know that signed numbers aretypically represented using a 2’s complement format
– Each audio sample represented as a twos-complement number of B totalbits, e.g., 16 bits
>> x_bits = PCM_encode([0.34539 -.786],8)
x_bits = 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 MSB LSB
>> x_bits = PCM_decode(x_bits,8)
x_bits = 0.34375 -0.7890625
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Digital Audio (cont.)
• The signal sample is stored with error control coding on the disc as asequence of pits that can be read back off of the disc using a laser beam1
1. Ken C. Pohlmann, Principles of Digital Audio, Sams, Indianapolis, IN, 1985.
LaserPickup
Pits on the CD and the laser spot
Pits on Disc
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Digital Signal Processing in the Lab
• A computer with a real-time digital signal processor will be used to demon-strate some signal processing concepts
• We will be able to listen to sound waves, see the time signals, and the spectralcontent on a graphical display
Spectral Inversion
Reverberation
TimeDiscrete
TimeDiscrete
TimeDiscrete
InputSignal
Sequence
+1
-1
Multiply TwoSignals Together
DelaySignal
Multiply bya constant k
OutputSignal
Sequence
Spe
ctru
m
Normal
Spe
ctru
m
Reversed
Freq. Freq.0 0
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
A Frequency Multiplication System/Circuit
• In ECE 2610 we introduce the Fourier series of a periodic signal
• The mathematical model helps understand how we can design a circuit to per-form frequency multiplication
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� � �
� �� � � �� ����� �� �
�������� �
�������� ������
���
� ����------���
�������������
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Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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C o m m u n i c a t i o n s a n d S i g n a l P r o c e s s i n g G r o u p
Radio Waves in the Lab
• In the communications lab you will see a spectrum analyzer, which is aninstrument that can display the frequency spectrum of the signals present at itsinput (in this case an antenna)
• You will listen to local FM radio broadcast stations, and a locally generatedFM radio signal
Spectrum Analyzer
Antenna
SignalGenerator
TransmitAntennaFM Broadcast Signal
Local FM Stations
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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The Anechoic Chamber
• An environment where radio wave, and to a large extent sound wave, echoesdo not exist
• The anechoic chamber tries to approximate a free space environment, wherethere are no objects present that will reflect radio and sound waves back at anobject being tested
Door
Quiet ZoneTest Area
Radio signal absorbing cones on walls, floor, and ceiling
AntennaUnder test
Waves absorbedWaves
absorbedWaves
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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Questions?
Prepared by Mark Wickert — April 26, 2012Electrical and Computer Engineering Department
University of Colorado – Colorado SpringsColorado Springs, Colorado 80933-7150
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