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 SignalsLecture 2: Intro to FrequencyThe Digital World of MultimediaProf. Mari OstendorfEE299 Lecture 29 Jan 2008Announcements You 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 internetEE299 Lecture 29 Jan 2008Plan for Today Goals of course (missed this last week) Analog vs. digital (cont.) Music as sinusoids Representing general signals in the frequency domainEE299 Lecture 29 Jan 2008Goals of this Course Technical literacy:  Learn basic concepts of multimedia signal processing and communication Develop an appreciation for how this technology impacts society Skill development: Learn basic computer skills in MATLAB Portfolio building: Create your own digital art and music Develop an appreciation for synergy of art and engineeringEE299 Lecture 29 Jan 2008Things You Will DoMusic SynthesisZeldaBuilt from one “doh”Image ProcessingEE299 Lecture 29 Jan 2008Analog vs. DigitalAnalog X(t), t = a real number Audio file stored on a (vinyl) record Electric signal driving the speakers in a sound system Systems tend to be large & consume lots of energy Systems are hard to modify Communication and storage is sensitive to physical conditionsDigital X(n), n = an integer Audio file stored on a CD or DVD Binary number sequence transmitted in streaming over the internet Systems tend to be small with low energy usage Systems are easy to reprogram Communication and storage is very reliableEE299 Lecture 29 Jan 2008Music Evolution Records Cassete tapes CDs MP3, music over the internet Turntables Cassette deck, Sony Walkman Sony Discman IPODsEntertainment evolution more generally: • move to digital images, videos, TV, …• media on demand• interactive mediaSmaller Players (portability)Smaller format (storage)EE299 Lecture 29 Jan 2008Causes of the Revolution Hardware: Invention of the transistor & Moore’s law Signal processing: Shannon’s sampling theorem Leveraging imperfect human perceptionEE299 Lecture 29 Jan 2008Analog vs. Digitalanalog signalx(t)digital signalx(n)tncontinuous in timediscrete in timeSAMPLINGcontinuous in amplitudediscrete in amplitudeQUANTIZATIONSound 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,…EE299 Lecture 29 Jan 2008From analog to digital Continuous-to-discrete in time (or space)  Sampling Need to understand about frequency Continuous-to-discrete in amplitude Quantization Need to take advantage of perceptionTODAYEE299 Lecture 29 Jan 2008Key Ideas Behind Frequency X(t) = cos(2πf0t) can be described by f0 Interesting signals can be built from combinations of sinusoids440Hztime signalfrequency representationtime signalfrequency representationEE299 Lecture 29 Jan 2008Sinusoids of different frequenciesHz440880HzEE299 Lecture 29 Jan 2008Orchestras tune to A = 440 HzSinusoid 440 cycles per second(440 Hz)amplitudeHz, sinusoidal frequency440timepressureEE299 Lecture 29 Jan 2008Examples:• 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 Vibrations How do you capture sound?  Microphone: transduce air vibrations How do you play sound? Speaker: reverse microphoneEE299 Lecture 29 Jan 2008Signals in the frequency domainHz440 880timetimetimeEE299 Lecture 29 Jan 2008Generating Music The simple synthesizer: 1 note = 1 sinusoid  Notes in the 220-440Hz octave: A = 220 Hz, A# = 220*21/12, B = 220*22/12, etc MATLAB synthesis demo major_scale.m, beethoven.mAdding the complexity of real instruments Harmonics EnvelopeTODAYEE299 Lecture 29 Jan 2008Harmonics Oscillating sounds (like musical notes) typically have frequencies that are integer multiples of the lowest frequency These are called “harmonics” & the lowest harmonic is often called the “pitch” or “fundamental frequency” Different instruments have different patterns of harmonicsEE299 Lecture 29 Jan 2008Trumpet signals in time & frequencyNote determines fundamental frequency, which gives spacing between harmonics.EE299 Lecture 29 Jan 2008More ExamplesTIMEFREQflute‘ae’ as in ‘bat’EE299 Lecture 29 Jan 2008An artificial example: square waveYou can build a square wave out of sinusoids! (but it takes an infinite number)EE299 Lecture 29 Jan 2008Another Example‘s’ as in ‘sit’TIMEFREQWhat 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 atEE299 Lecture 29 Jan 2008Periodic vs. Aperiodic Signals Periodic 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 speech Aperiodic signals: not perfectly repeating, e.g. single square pulse, decaying exponential Frequency content is spread across a continuum Examples: cymbal, click, “s” sound in