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Audio Filter Project

Audio Filter Project. Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah. CO NC EPT U AL TOOLS. Goal: Build filter to pass low or high frequencies in audio signal Equivalent to bass/treble controls on MP3 player. Overview.

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Audio Filter Project

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  1. Audio Filter Project Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah

  2. CONCEPTUAL TOOLS • Goal: • Build filter to pass low or high frequencies in audio signal • Equivalent to bass/treble controls on MP3 player Overview http://www.guardian.co.uk/music/blog/2009/dec/21/jazz-purist-found-wynton-marsalis http://www.thatcable.com/category/ 6-35mm-(1-4inch)-Plug-to-Plug/sub http://salestores.com/gegsdu153w60.html http://www.ebay.com/bhp/f3-cellphone-watch http://news-releases.theurbanmusicscene.com/2009/01/27/pedro-giraudo-jazz-orchestra--el-viaje.aspx

  3. CONCEPTUAL TOOLS • Goal: • Build filter to pass low or high frequencies in audio signal • Equivalent to bass/treble controls on MP3 player • Each group of students will design/build low-pass filter (more bass) or high-pass filter (more treble) Overview

  4. CONCEPTUAL TOOLS • Goal: • Build filter to pass low or high frequencies in audio signal • Equivalent to bass/treble controls on MP3 player • Each group of students will design/build low-pass filter (more bass) or high-pass filter (more treble) • Theory first: • Sound waves = sums of sinusoids (Fourier theory) • Complex numbers can represent sinusoids (Phasors) • Electronic components alter sinusoids— resistors, inductors, capacitors • Filter design = sinusoid analysis (circuit theory) Overview

  5. Sound and Sinusoids Neil E. Cotter ECE Department UNIVERSITYOFUTAH necotter@ece.utah.edu

  6. CONCEPTUAL TOOLS Resonances [1]

  7. CONCEPTUAL TOOLS Vocal Tract [2] • Pipe organ • Driven by puffs of air

  8. CONCEPTUAL TOOLS Formants [3] • Frequency response • Vowel = musical chord

  9. CONCEPTUAL TOOLS Glottal Pulses [4] • Rate = voice pitch • Shape varies slightly

  10. CONCEPTUAL TOOLS Speech Waveform [5] [7] • Vowel repetitive • Plosive explosive [6] • Fricatives noisy

  11. CONCEPTUAL TOOLS [1] http://www.nmha.org/go/bell [2] http://www.vocalclinic.net/ [3] http://people.ece.cornell.edu/land/courses/ece4760/FinalProjects/s2011/wd65_yz526/wd65 and yz526/highlevel.html [4] http://www.jr.ietejournals.org/article.asp?issn=0377-2063;year=2011;volume=57;issue=4;spage=363;epage=371;aulast=Raj [5] http://web.science.mq.edu.au/~cassidy/comp449/html/comp449.html [6] http://folk.uio.no/ristoh/aspiration/analysis.html [7] http://www.phon.ucl.ac.uk/home/johnm/siphtra/plostut2/plostut2-5.htm References Neil E. Cotter necotter@ece.utah.edu

  12. Fourier Theory Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah

  13. CONCEPTUAL TOOLS Fourier Theory Any function of time = sum of sinusoids

  14. CONCEPTUAL TOOLS • Example: create a square wave • Use a graphing calculator to plot ƒ(t): • Replace t with x. Use x range of -0.5 to 1.5 • Use y range of -2 to +2. Plot the first term (sinusoid), • then two terms, and then three terms. • Observe how waveform becomes more square Fourier Theory

  15. CONCEPTUAL TOOLS • Function of time = sum of sinusoids • Application: • Sound = air pressure changes versus time • Sound = function of time • Sound = sum of sinusoids Fourier Theory

  16. CONCEPTUAL TOOLS • Filter = change sinusoids, depending on frequency • Result = change in waveform • Example: remove low frequency from square wave • Waveform now has sharp edges (more high frequencies) • Application: emphasize or attenuate notes in music • Equalizer = set of filters • Treble and bass controls = filters Fourier Theory

  17. Phasors Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah

  18. CONCEPTUAL TOOLS • Consider one frequency at a time in circuit • Sum of sinusoids of same frequency is single sinusoid • Use complex numbers to represent sinusoids • Capture magnitude • Capture phase shift • Use j for √-1 (because i was used for current) • Use phasor transform: • P[Acos(2πft +Φ)] = Aejø = a + jb =aAcosΦ +jAsinΦ Phasors

  19. CONCEPTUAL TOOLS • Treat complex numbers as vectors • Sum like vectors (a+jb)+(c+jd) = a+c + j(b+d) • Use polar or rectangular form • Rectangular form: a+jb • Polar form: Aejø • Use right triangle trigonometry to covert forms: • Rectangular from polar: a = AcosΦ and b = AsinΦ • Polar from rectangular: A = √a2 + b2and Φtan-1(b/a) Phasors

  20. CONCEPTUAL TOOLS • Sum of sinusoids becomes sum of complex numbers • Example: • express v(t) in form Phasors

  21. Electronics Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah

  22. CONCEPTUAL TOOLS Voltage

  23. CONCEPTUAL TOOLS Current

  24. CONCEPTUAL TOOLS Resistor

  25. CONCEPTUAL TOOLS Resistor Resistor reduces current flow Water analogy: flow less for winding river

  26. CONCEPTUAL TOOLS Ohm’s Law Current in resistor = voltage / resistance (Ohm's law) Water analogy: flow = altitude drop / length of river

  27. CONCEPTUAL TOOLS Capacitor

  28. CONCEPTUAL TOOLS Capacitor Current flow = tank area times rate of height change i = C dv/dt

  29. CONCEPTUAL TOOLS Inductor http://www.magnariders.com/html/Rides/rally/2005_Rally.html

  30. CONCEPTUAL TOOLS Inductor http://www.magnariders.com/html/Rides/rally/2005_Rally.html Pressure on paddles = moment of wheel times rate of flow change v = L di/dt

  31. CONCEPTUAL TOOLS LED http://www.furuier.com/english/product/index0.htm http://www.xmission.com/~m3lody/junk/xmas2002/lit_waterfall1.jpg

  32. CONCEPTUAL TOOLS Op-Amp

  33. RLC Filter Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah

  34. CONCEPTUAL TOOLS RLC Filter Circuit

  35. CONCEPTUAL TOOLS • Vo = IR = voltage across R Ohm’s Law

  36. CONCEPTUAL TOOLS • Gain is size of output relative to input • Gain = |Vo|/|Vi| where |a + jb| = √a2+b2 = A for polar form Gain or or

  37. CONCEPTUAL TOOLS • Gain is max at “center frequency” denoted by ωo • Gain is max/√2 at “cutoff frequencies” denoted by ωC1 and ωC2 Gain versus Frequency

  38. CONCEPTUAL TOOLS • Center frequency, ωo, where gain is max • Occurs where gain = 1 • Solve for ωo using following equation: Center Frequency

  39. CONCEPTUAL TOOLS • Cutoff frequencies, ωC1 and ωC2, where gain is max/√2 • Occurs where gain = 1/√2 • Solve for cutoff frequencies using following equation: Cutoff Frequencies • Bandwidth = β = ωC2 – ωC1 • Bandwidth is roughly frequency range that gets through filter

  40. CONCEPTUAL TOOLS • Find R and C value for assigned filter: • Low-pass filter: • ωo= 2π·500 r/s • β = 2π·1600 r/s • High-pass filter: • ωo= 2π·16,000 r/s • β = 2π·1600 r/s Filter Design

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