Beyond Logic Circuits — Next Stop Signal, Systems, and ...eceweb.uccs.edu/~mwickert/ECE2211_Lecture_Demo.pdf · Next Stop Signal, Systems, and Circuits, ... A Career in Electrical

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


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


VLSI Fab


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


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



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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



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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



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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



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Adding Two Signals Together – Hands-on

Time



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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



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Linear Chirp Signals – Hands-on



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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



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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



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Bat Echolocation Signals – Hands-on

Shorter durationchirps givethe bat betterresolution



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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.



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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



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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



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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



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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



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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



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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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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



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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



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Questions?



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Beyond Logic Circuits — Next Stop Signal, Systems, and ...eceweb.uccs.edu/~mwickert/ECE2211_Lecture_Demo.pdf · Next Stop Signal, Systems, and Circuits, ... A Career in Electrical

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