Lecture 3: Time Signals in the Frequency DomainAnnouncementsPlan for TodayKey Points from Last LectureHarmonicsPeriodic vs. Aperiodic SignalsPeriodic ExamplesAperiodic ExamplesGenerating MusicComplexities of Real NotesEnvelopeFrequency Content vs. TimeTime-Varying Frequency ContentZooming in on the TubaExample: SpeechZooming In…Not all aperiodic sounds are high frequencyTime vs. Frequency CharateristicsCharacteristics of SoundWays to Change a SignalMusic Signal ProcessingLecture 3: Time Signals in the Frequency DomainThe Digital World of MultimediaProf. Mari OstendorfEE299 Lecture 311 Jan 2008Announcements HW1 due next week – books are optional MATLAB: If you want to do the labs at home…you can get the student edition for your PC from the UW Bookstore Technology Center ($99.95) Labs: If you finish Lab 1 early, you can get started on Lab 2 – will be posted on Monday EE computer account: If you aren’t an EE student, you can get an account by going to EEB 307G during 9-12,1-5, bring student IDEE299 Lecture 311 Jan 2008Plan for Today Review: Sounds as sinusoids Representing signals in the frequency domain Ways to change a time signalEE299 Lecture 311 Jan 2008Key Points from Last Lecture X(t) = cos(2πf0t) can be described by f0 Interesting signals can be built from combinations of sinusoids440Hztime signalfrequency representationtime signalfrequency representationEE299 Lecture 311 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 harmonicsfrequency representationEE299 Lecture 311 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 speechEE299 Lecture 311 Jan 2008Periodic ExamplesTIMEFREQflute‘ae’ as in ‘bat’fundamental frequencyharmonics…fundamental periodEE299 Lecture 311 Jan 2008Aperiodic Examples‘s’ as in ‘sit’TIMEFREQPop of a balloon in a showerEE299 Lecture 311 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 beethoven.mAdding the complexity of real instruments Harmonics  EnvelopeEE299 Lecture 311 Jan 2008Complexities of Real NotesEE299 Lecture 311 Jan 2008Envelope Natural sounds also have patterns of turning on or off The overall shape is called the “envelope”EE299 Lecture 311 Jan 2008Frequency Content vs. Time Take a Fourier Transform over a Window (chunk) of the signal Slide the window over, allowing some overlap Display magnitude of Fourier transform via color Matlab command: spectrogram(x,window,overlap,Nfft,Fs,’yaxis”)slidingwindowoverlap in # of samplesput time on x-axis, frequency on y-axisEE299 Lecture 311 Jan 2008Time-Varying Frequency ContentFluteTubatime signalspectrogram: frequency vs. timeEE299 Lecture 311 Jan 2008Zooming in on the TubaEE299 Lecture 311 Jan 2008Example: Speechthe first initiativeballotadoptedby Bay Statersss zshvowelsBDP/TBBTstop consonantsTxTzoom inEE299 Lecture 311 Jan 2008Zooming In…AE in ‘ballot’, periodicS in ‘first’, aperiodicEE299 Lecture 311 Jan 2008Not all aperiodic sounds are high frequencyBay StatersEE299 Lecture 311 Jan 2008Time vs. Frequency Charateristics Slow, smooth movements in time have low frequencies Fast, wiggly movements in time have high frequencies Narrow in time, wide in frequency Wide in time, narrow in frequencyttttffffEE299 Lecture 311 Jan 2008Characteristics of Sound Voices are in lower frequency bands Clicks have wide range of frequency … What does this tell you about speaker design? How good you speaker needs to be at different frequencies depends on the type of music you listen to.EE299 Lecture 311 Jan 2008Ways to Change a Signal Changing the time envelope Multiplying by a fading function or sinusoid Changing the time scale (speed up or slow down) and the pitch Reverse time  Filtering: changing the frequency content Smoothing (getting rid of noise) Sharpening (emphasizing contrasts) Boosting particular frequency ranges Adding duplicate copies (echo)EE299 Lecture 311 Jan 2008Music Signal Processing Guitar & castanets Same sound played in reverse Speech Speech reversed Flute Flute