lecture 2: intro to frequency - university of...
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Lecture 2: Intro to Frequency
The Digital World of MultimediaProf. Mari Ostendorf
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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
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EE299 Lecture 29 Jan 2008
Plan for TodayGoals of course (missed this last week)Analog vs. digital (cont.)Music as sinusoidsRepresenting general signals in the frequency domain
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
Things You Will Do
Music SynthesisZeldaBuilt from one “doh”
Image Processing
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
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)
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EE299 Lecture 29 Jan 2008
Causes of the RevolutionHardware: Invention of the transistor & Moore’s law
Signal processing:Shannon’s sampling theoremLeveraging imperfect human perception
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EE299 Lecture 29 Jan 2008
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,…
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
Sinusoids of different frequencies
Hz440
880Hz
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EE299 Lecture 29 Jan 2008
Orchestras tune to A = 440 Hz
Sinusoid 440 cycles per second(440 Hz)
amplitude
Hz, sinusoidal frequency440
time
pressure
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
Signals in the frequency domain
Hz440 880
time
time
time
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
Trumpet signals in time & frequency
Note determines fundamental frequency, which gives spacing between harmonics.
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EE299 Lecture 29 Jan 2008
More Examples
TIME
FREQ
flute ‘ae’ as in ‘bat’
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EE299 Lecture 29 Jan 2008
An artificial example: square wave
You can build a square wave out of sinusoids! (but it takes an infinite number)
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EE299 Lecture 29 Jan 2008
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
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EE299 Lecture 29 Jan 2008
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
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