lecture 2: intro to frequency - university of...

Lecture 2: Intro to Frequency

The Digital World of MultimediaProf. Mari Ostendorf

EE299 Lecture 29 Jan 2008

AnnouncementsYou need an EE account for the lab. Please see EE web page about getting an account.You should all have access to the lab. I will look into why you don’t.About the book(s)….

It’s really hard for books to keep up, so texts are optional and are on reserve. They are great for basics, less good for applications.Orzak et al. better on signal processing; Cyganksi & Orr are better on networks & the internet


Plan for TodayGoals of course (missed this last week)Analog vs. digital (cont.)Music as sinusoidsRepresenting general signals in the frequency domain


Goals of this CourseTechnical literacy:

Learn basic concepts of multimedia signal processing and communicationDevelop an appreciation for how this technology impacts society

Skill development:Learn basic computer skills in MATLAB

Portfolio building:Create your own digital art and musicDevelop an appreciation for synergy of art and engineering


Things You Will Do

Music SynthesisZeldaBuilt from one “doh”

Image Processing


Analog vs. DigitalAnalog

X(t), t = a real numberAudio file stored on a (vinyl) recordElectric signal driving the speakers in a sound systemSystems tend to be large & consume lots of energySystems are hard to modifyCommunication and storage is sensitive to physical conditions

DigitalX(n), n = an integerAudio file stored on a CD or DVDBinary number sequence transmitted in streaming over the internetSystems tend to be small with low energy usageSystems are easy to reprogramCommunication and storage is very reliable


Music Evolution

RecordsCassete tapesCDsMP3, music over the internet

TurntablesCassette deck, Sony WalkmanSony DiscmanIPODs

Entertainment evolution more generally: • move to digital images, videos, TV, …• media on demand• interactive media

Smaller Players (portability)

Sm

aller format (storage)


Causes of the RevolutionHardware: Invention of the transistor & Moore’s law

Signal processing:Shannon’s sampling theoremLeveraging imperfect human perception


Analog vs. Digitalanalog signalx(t)

digital signalx(n)

t

n

continuous in time

discrete in timeSAMPLING

cont

inuo

us in

am

plitu

dedi

scre

te in

am

plitu

deQ

UA

NTI

ZATI

ON

Sound wave, heart beat, temperature fluctuation, image on film, human arm motion, AM radio, …

Audio file on a CD, video on a DVD, Dow Jones daily average, image from a digital camera, HDradio,…


From analog to digitalContinuous-to-discrete in time (or space)

SamplingNeed to understand about frequency

Continuous-to-discrete in amplitudeQuantizationNeed to take advantage of perception

TODAY


Key Ideas Behind FrequencyX(t) = cos(2πf0t) can be described by f0

Interesting signals can be built from combinations of sinusoids

440 Hz

time signal

frequency representation

time signal frequency representation


Sinusoids of different frequencies

Hz440

880Hz


Orchestras tune to A = 440 Hz

Sinusoid 440 cycles per second(440 Hz)

amplitude

Hz, sinusoidal frequency440

time

pressure


Examples:• Carbon microphones (traditional telephones):

Carbon granules get compressed or decompressed by sound (your

voice); compression changes their resistance.

• Dynamic microphones (recording studios):Diaphragm has little magnet; sound moves diaphragm, magnet moves with

it past a wire, induces charge: sound waves transduce

to electric signal.

Sounds as VibrationsHow do you capture sound?

Microphone: transduce air vibrations

How do you play sound?Speaker: reverse microphone


Signals in the frequency domain

Hz440 880

time

time

time


Generating MusicThe simple synthesizer:

1 note = 1 sinusoid Notes in the 220-440Hz octave:

A = 220 Hz, A# = 220*21/12, B = 220*22/12, etcMATLAB synthesis demo

major_scale.m, beethoven.m

Adding the complexity of real instrumentsHarmonicsEnvelope

TODAY


HarmonicsOscillating sounds (like musical notes) typically have frequencies that are integer multiples of the lowest frequencyThese are called “harmonics” & the lowest harmonic is often called the “pitch” or “fundamental frequency”Different instruments have different patterns of harmonics


Trumpet signals in time & frequency

Note determines fundamental frequency, which gives spacing between harmonics.


More Examples

TIME

FREQ

flute ‘ae’ as in ‘bat’


An artificial example: square wave

You can build a square wave out of sinusoids! (but it takes an infinite number)


Another Example‘s’ as in ‘sit’

TIME

FREQ

What is different about this sound?

• no repeating pattern in time; no harmonics in frequency

• a lot more energy in the high frequency range than other signals we’ve looked at


Periodic vs. Aperiodic SignalsPeriodic signals: repeating pattern

Frequency content is isolated to specific frequencies, i.e. can be built with a countable number of sinusoids

Note: even square waves can be built with sinusoids (but you need an infinite number)

Examples: musical notes, vowels in speechAperiodic signals: not perfectly repeating, e.g. single square pulse, decaying exponential

Frequency content is spread across a continuumExamples: cymbal, click, “s” sound in speech

Lecture 2:�Intro to FrequencyAnnouncementsPlan for TodayGoals of this CourseThings You Will DoAnalog vs. DigitalMusic EvolutionCauses of the RevolutionAnalog vs. DigitalFrom analog to digitalKey Ideas Behind FrequencySinusoids of different frequenciesOrchestras tune to A = 440 HzSounds as VibrationsSignals in the frequency domainGenerating MusicHarmonicsTrumpet signals in time & frequencyMore ExamplesAn artificial example: square waveAnother ExamplePeriodic vs. Aperiodic Signals

lecture 2: intro to frequency - university of...

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