2. SPPA 6010 Advanced Speech Science 1 The Source-Filter Theory: The Sound Source

3. SPPA 6010 Advanced Speech Science 2 Topic 3a: Physical Acoustics Review

4. SPPA 6010 Advanced Speech Science 3 Learning Objectives Outline the physical processes underlying simple harmonic motion using the mass- spring model Describe the molecular basis of sound wave propagation

5. SPPA 6010 Advanced Speech Science 4 Spring Mass Model Mass (inertia) Elasticity Friction

6. SPPA 6010 Advanced Speech Science 5 What is sound? It may be defined as the propagation of a pressure wave in space and time. propagates through a medium

7. SPPA 6010 Advanced Speech Science 6 Sound-conducting media Medium is composed of molecules Molecules have “wiggle room” Molecules exhibit random motion Molecules can exert pressure AB

8. SPPA 6010 Advanced Speech Science 7 Model of air molecule vibration (Time 1) Rest positions Air molecules sitting side by side

9. SPPA 6010 Advanced Speech Science 8 Model of air molecule vibration (Time 2)

10. SPPA 6010 Advanced Speech Science 9 Model of air molecule vibration (Time 3)

11. SPPA 6010 Advanced Speech Science 10 Model of air molecule vibration (Time 4)

12. SPPA 6010 Advanced Speech Science 11 Model of air molecule vibration (Time 5)

13. SPPA 6010 Advanced Speech Science 12 Model of air molecule vibration Time 1 2 3 4 5 Distance abcd

14. SPPA 6010 Advanced Speech Science 13 Wave action of molecular motion Time 1 2 3 4 5 Distance

15. SPPA 6010 Advanced Speech Science 14 Amplitude waveform Position Time

16. SPPA 6010 Advanced Speech Science 15 Amplitude waveform Amplitude Time Question: How long will this last?

17. SPPA 6010 Advanced Speech Science 16 Model of air molecule vibration Time 1 2 3 4 5 Pressure measuring device Questions: Where is a region of compression? Where is a region of rarefaction?

18. SPPA 6010 Advanced Speech Science 17 For example… Pressure Time

19. SPPA 6010 Advanced Speech Science 18 Learning Objectives Define the key characteristics of sinusoidal motion (amplitude, frequency/period and phase) Outline the relationship between the frequency and wavelength of a sound wave

20. SPPA 6010 Advanced Speech Science 19 Pressure vs. time (pressure waveform) Pressure Time Amplitude Period (T) Phase: when a period begins Frequency (F): rate that waveform repeats itself (1/T) Phase (deg)

21. SPPA 6010 Advanced Speech Science 20 Phase

22. SPPA 6010 Advanced Speech Science 21 Initiating a sound waves that differ only in phase A force is applied to molecule at frequency f and time t same force applied at frequency f at time t+a where a < the period of vibration

23. SPPA 6010 Advanced Speech Science 22 Features of a pressure waveform Amplitude –Measured in pressure units –peak amplitude –peak-to-peak amplitude –Instantaneous amplitude Period and Frequency –Period measured in time (basic quantity) –Frequency is a rate measure (per unit time) expressed as Hertz (s -1 ) –May be expressed as octaves, semitones, etc Phase –Measured in degrees (relative to period length) –0-360 degrees

24. SPPA 6010 Advanced Speech Science 23 Spatial variation in pressure wave wavelength ( ) is the distance covering adjacent high and low pressure regions

25. SPPA 6010 Advanced Speech Science 24 For example… Distance Wavelength ( ) Pressure

26. SPPA 6010 Advanced Speech Science 25 Relation between frequency and wavelength =c/F where : wavelength F: is the frequency c: is sound speed in medium (35,000 cm/sec)

27. SPPA 6010 Advanced Speech Science 26 Additional Concepts Propagation of waves –Transmission –Absorption –Reflection –Reverberation

28. SPPA 6010 Advanced Speech Science 27 Learning Objectives Draw and describe time-domain and frequency-domain representation of sound Distinguish between simple and complex sound sounds with regard to physical characteristics and graphical representations Distinguish between periodic and aperiodic sounds with specific emphasis on terms such as fundamental frequency/period, harmonics, and overtones Distinguish between continuous and transient sounds Describe how waves sum, define Fourier's theorem and be able to describe the basics of Fourier analysis

29. SPPA 6010 Advanced Speech Science 28 Graphic representation of sound Time domain –Called a waveform –Amplitude plotted as a function of time Frequency domain –Called a spectrum –Amplitude spectrum amplitude vs. frequency –Phase spectrum phase vs. frequency –May be measured using a variety of “window” sizes

30. SPPA 6010 Advanced Speech Science 29 Same sound, different graphs Time domain Frequency domain From Hillenbrand

31. SPPA 6010 Advanced Speech Science 30 Classification of sounds Number of frequency components –Simple –Complex Relationship of frequency components –Periodic –Aperiodic Duration –Continuous –Transient

32. SPPA 6010 Advanced Speech Science 31 Simple periodic sound Simple: one frequency component Periodic: repeating pattern Completely characterized by –amplitude –period (frequency) –phase Other names: sinusoid, simple harmonic motion, pure tone

33. SPPA 6010 Advanced Speech Science 32 Simple periodic sound: Graphic appearance From Hillenbrand

34. SPPA 6010 Advanced Speech Science 33 Complex periodic sounds Complex: > one frequency component Periodic: repeating pattern Continuous Frequencies components have a special relation –Lowest frequency: fundamental frequency Symbol: f o Frequency component with longest period –Higher frequency components: harmonics integer (whole number) multiples of the f o

35. SPPA 6010 Advanced Speech Science 34 Complex periodic sounds: Graphic appearance Time domain: –repeating pattern of pressure change –within the cycle, things look complex Frequency domain: –spectral peaks at evenly spaced frequency intervals –“picket fence” appearance Auditory impression: sounds ‘musical’

36. SPPA 6010 Advanced Speech Science 35 Complex periodic sounds: Graphic appearance From Hillenbrand

37. SPPA 6010 Advanced Speech Science 36

38. SPPA 6010 Advanced Speech Science 37 Amplitude vs. Phase Spectrum Amplitude spectrum: different Phase spectrum: same

39. SPPA 6010 Advanced Speech Science 38 Amplitude vs. Phase Spectrum Amplitude spectrum: same Phase spectrum: different

40. SPPA 6010 Advanced Speech Science 39 (Complex) Aperiodic sounds Complex: > one frequency component Aperiodic: Does not repeat itself Frequency components are not systematically related May be –Continuous –Transient

41. SPPA 6010 Advanced Speech Science 40 Aperiodic sounds: Graphic appearance Time domain: –no repeating pattern of pressure change Frequency domain: –the spectrum is dense –No “picket fence” Auditory impression: sounds ‘noisy’

42. SPPA 6010 Advanced Speech Science 41 Aperiodic sounds: Graphic appearance From Hillenbrand

43. SPPA 6010 Advanced Speech Science 42 Analysis of complex waves Waves can be summed Complex waves are the sum of simple waves Fourier: French Mathematician: –Any complex waveform may be formed by summing sinusoids of various frequency, amplitude and phase Fourier Analysis –Provides a unique (only one) solution for a given sound signal –Is reflected in the amplitude and phase spectrum of the signal –Reveals the building blocks of complex waves, which are sinusoids

44. SPPA 6010 Advanced Speech Science 43 Learning Objectives Draw and differentiate the waveform and the waveform envelope Draw and differentiate the amplitude spectrum, the phase spectrum and the spectrum envelope Differentiate between short-term and long- term average amplitude spectra

45. SPPA 6010 Advanced Speech Science 44 The “envelope” of a sound wave Waveform envelope: –imaginary smooth line that follows the peak of the amplitude of a sound pressure waveform Spectrum envelope: –Imaginary smooth line drawn on top of the amplitude spectrum

46. SPPA 6010 Advanced Speech Science 45 Waveform envelope From Hillenbrand

47. SPPA 6010 Advanced Speech Science 46 Waveform envelope Time

48. SPPA 6010 Advanced Speech Science 47 Spectrum envelope From Hillenbrand

49. SPPA 6010 Advanced Speech Science 48 Thought Question Can an aperiodic and complex periodic sound have identical spectrum envelopes?

50. SPPA 6010 Advanced Speech Science 49 Amplitude Spectrum: Window Size “short-term” vs. “long-term average” amplitude spectrum

51. SPPA 6010 Advanced Speech Science 50 “Instantaneous” Amplitude Spectra

52. SPPA 6010 Advanced Speech Science 51 (Long Term) Average Amplitude Spectrum

53. SPPA 6010 Advanced Speech Science 52

54. SPPA 6010 Advanced Speech Science 53 The Spectrogram

55. SPPA 6010 Advanced Speech Science 54 Rotate 90 degrees F A F A

56. SPPA 6010 Advanced Speech Science 55 Rotate it so that The amplitude is Coming out of the page F A This is really narrow because it is a slice in time F Time

57. SPPA 6010 Advanced Speech Science 56 Dark bands = amplitude Peaks Time Frequency

58. SPPA 6010 Advanced Speech Science 57 Two main types of spectrograms Wide-band spectrograms –Akin to spectrum envelopes “lined up” –Frequency resolution not so sharp Narrow-band spectrograms –Akin to amplitude spectrums “lined up” –Frequency resolution is really sharp

59. SPPA 6010 Advanced Speech Science 58 Highlights harmonic structure Highlights spectrum envelope

60. SPPA 6010 Advanced Speech Science 59 Learning Objectives Define an acoustic filter Draw and label a frequency response curve Draw and differentiate different types of acoustic filters Define terms such as cutoff frequency, center frequency, roll off rate, gain, and bandwidth Define and draw a basic filter system and relate that to the source-filter theory of speech production

61. SPPA 6010 Advanced Speech Science 60 What is an “Acoustic” Filter holds back (attenuates) certain sounds and lets other sounds through - selective.

62. SPPA 6010 Advanced Speech Science 61 Why might we be interested in filters? Human vocal tract acts like a frequency selective acoustic filter Human auditory system behaves as a frequency selective filter helps us understand how speech is produced and perceived.

63. SPPA 6010 Advanced Speech Science 62 Frequency Response Curve (FRC) Frequency lowhigh Gain + - Center frequency lower cutoff frequency upper cutoff frequency passband 3 dB

64. SPPA 6010 Advanced Speech Science 63 Operation of a filter on a signal NOTE: Amplitude spectrum describes a sound Frequency response curve describes a filter

65. SPPA 6010 Advanced Speech Science 64 Kinds of frequency selective filters Low-pass filters –Lets low frequencies “pass through” and attenuates high frequencies High-pass filters –Lets high frequencies “pass through” and attenuates low frequencies Band-pass filters –Lets a particular frequency range “pass through” and attenuates other frequencies

66. SPPA 6010 Advanced Speech Science 65 Low Pass Filters Frequency lowhigh Gain + -

67. SPPA 6010 Advanced Speech Science 66 High Pass Filters Frequency lowhigh Gain + -

68. SPPA 6010 Advanced Speech Science 67 Band Pass Filter Frequency lowhigh Gain + -

69. SPPA 6010 Advanced Speech Science 68 Learning Objectives Define resonance, free and forced vibration Outline how acoustic resonators behave like acoustic filters

70. SPPA 6010 Advanced Speech Science 69 Free vibration objects tend to vibrate at a characteristic or resonant frequency (RF)

71. SPPA 6010 Advanced Speech Science 70 Forced vibration A vibrating system can force a nearby system into vibration The efficiency with which this is accomplished is related to the similarity in the resonant frequency (RF) of the two systems

72. SPPA 6010 Advanced Speech Science 71 Forced vibration If the RF of the two systems are the same, the amplitude of forced vibration will be large If the RF of the two systems are quite different, the amplitude of forced vibration will be small or nonexistent

73. SPPA 6010 Advanced Speech Science 72 Resonance refers to Natural vibrating frequency of a system The ability of a vibrating system to force another system into vibration

74. SPPA 6010 Advanced Speech Science 73 Resonance Acoustic (Cavity) Resonators Transmit sound frequencies with more or less efficiency, depending upon the physical characteristics Therefore, they act as filters, passing through (and even amplifying) some frequencies and attentuating others.

75. SPPA 6010 Advanced Speech Science 74 Resonance Acoustic (Cavity) Resonators And since they act as filters, they have most of the same features of a filter, even though we might use different names. Center frequency is often termed the resonant frequency. Frequency response curve often termed the resonance curve. Resonators may be sharply or broadly “tuned” which refers to the roll-off frequency

76. SPPA 6010 Advanced Speech Science 75 Resonator Features Sharply tuned Broadly tuned

77. SPPA 6010 Advanced Speech Science 76 Resonator Features An example of the resonance characteristics of the human vocal tract Frequency Gain