Introduction to Phonetics Week 7 Waveforms Spectra Spectrograms
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Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Today Questions about last week? • Chapter 6 & 7 of Zsiga (2013) • Waves – repeat some issues from last week when the beamer was on strike. • Recording speech • Digitization of speech Introduction Waves Simple harmonic motion Complex waves Intensity Recording Pendulum A pendulum going from left to right and back -1 1 0 References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Pendulum in time Pendulum in time A pendulum in time: Time Introduction Waves Simple harmonic motion Complex waves Intensity Recording Pendulum A pendulum going from left to right and back The pendulum moves from -1 through 0 to 1 and back from 1 through 0 to -1... -1 1 0 References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves The pendulum oscillates. Each movement from −1 through 0 to 1 is called a cycle. Each cycle takes up the same amount of time. • The time for one cycle is called the period • The number of cycles per time unit is called frequency. Frequency = Period = 1 Period 1 Frequency Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Period This is one period – the pressure goes up from 0 to 0.2, back to 0, down to -0,2 and up to 0 – from a wave with a frequency of 100 such periods per second. 100 Hz 1 period Pressure 0.2 0 -0.2 0.1 0.11 Time (s) Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves If a wave repeats 50 times per second, it has a period of 50 cycles (cycle) (per second). Its frequency is 50 1(repetitions) per second. Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Milliseconds In phonetics we often measure time in milliseconds. One millisecond is 1 thousandth of a second. In other words there are 1000 milliseconds in a second. So how many milliseconds is 0.02 seconds? References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Milliseconds In phonetics we often measure time in milliseconds. One millisecond is 1 thousandth of a second. In other words there are 1000 milliseconds in a second. So how many milliseconds is 0.02 seconds? Yes, indeed 20 milliseconds: 20 milliseconds times 50 repetitions = 1.000 = 1 second. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Milliseconds In phonetics we often measure time in milliseconds. One millisecond is 1 thousandth of a second. In other words there are 1000 milliseconds in a second. So how many milliseconds is 0.02 seconds? Yes, indeed 20 milliseconds: 20 milliseconds times 50 repetitions = 1.000 = 1 second. Frequency is expressed in the unit Hertz (Hz) (after Heinrich Hertz). This wave has a frequency of 20 Hz. References Introduction Waves Simple harmonic motion Complex waves Intensity Waves A sine wave This is a sine wave, since it starts at 0. 100 Hz 1 period Pressure 0.2 0 -0.2 0.1 0.11 Time (s) Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves The movement of the pendulum is smallest at the top (0.2) and the bottom (-0.2) and greatest at 0. The points 0.2 and -0.2 are called peak displacement and 0 is called peak velocity. 100 Hz 1 period Pressure 0.2 0 -0.2 0.1 0.11 Time (s) References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves The movement of the pendulum is smallest at the top (0.2) and the bottom (-0.2) and greatest at 0. The points 0.2 and -0.2 are called peak displacement and 0 is called peak velocity. The distance from 0 to peak velocity is the amplitude. 0.2 Amplitude Pressure Amplitude 0 Amplitude -0.2 0.1 0.105 Time 0.11 References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves A system that moves in this way, in a regular fashion from peak displacement through peak velocity back to peak displacement, is called a simple harmonic system. Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Frequency and pitch The higher the frequency, the higher the pitch. 100 200 100 Hertz 200 Hertz 0.6 0.6 0 0 -0.6 0.1 0.2 Time (s) -0.6 0.1 0.2 Time (s) References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Frequency and pitch 300 400 300 Hertz 400 Hertz 0.6 0.6 0 0 -0.6 0.1 0.2 Time (s) -0.6 0.1 0.2 Time (s) References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Excursion You know that short stringed pendulums have a greater frequency than long stringed pendulums. You could compare this with the shorter vocal folds of women and the longer vocal folds of men. These frequencies together make for an amazing dance: pendulum Introduction Waves Simple harmonic motion Complex waves Intensity Recording Complex waves Most waves in nature are more complex than just a simple sine wave. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves Imagine a pendulum going up a mountain road. The road goes up, at some points very steeply and at other points more gradually. You can imagine the position of the bob of the pendulum as a wave (the movement of the pendulum) on top of a wave (the mountain road). This is a complex wave. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves four simple sine waves 220 Hz 110 Hz 440-Hz 220-Hz 0.8 0.8 0 0 -0.8 0.2 0.225 Time (s) -0.8 0.2 0.225 Time (s) Introduction Waves Simple harmonic motion Complex waves Intensity Complex waves Combining simple waves 220 + 440 Hz. 220-440-combined 0.2 0.7534 0.21 0 -0.4869 0.2 0.21 Time (s) Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves four simple sine waves 440 Hz 330 Hz 440-Hz 330-Hz 0.8 0.8 0 0 -0.8 0.2 0.225 Time (s) -0.8 0.2 0.225 Time (s) Introduction Waves Simple harmonic motion Complex waves Intensity Complex waves Combining simple waves 330 + 440 Hz: 0.5721 heinrich3_heinrich4 0.140903488 0 -0.5388 0.1318 0.15 Time (s) Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Complex waves The complex waves are not sinusoidal, but they are periodic. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Complex waves The complex waves are not sinusoidal, but they are periodic. All complex waves can be analyzed in the simple waves they consist of. References (blue), harmonic 250 Hz (red) Introduction50 Hz (green), Waves 100 HzSimple motion Pressure 1.5 Intensity Recording References Complex waves 0.75 3 waves 2 3 waves and its complex wave 50 Hz (green), 100 Hz (blue), 250 Hz (red) 0 -1 -2 0.1 3 simple waves (red, blue, green) and its complex wave (black) 2 Amplitude (Pressure) 1 Pressure Complex waves 0.105 0.11 1 0 -1 -2 1 1.05 Time 1.1 Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves Spectrum Complex wave alone One complex wave (of the three simple waves of before) Its spectrum Spectrum of a complex wave (3 component waves) 2.5 Amplitude (Pressure) Amplitude (Pressure) 2 1 0 -1 2 1.5 1 0.5 0 -2 1 1.05 Time 1.1 0 50 100 150 200 Frequency (Hz) 250 300 Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves The complex wave is periodic: It repeats itself in a regular fashion. The frequency of the repetition is called the fundamental frequency. Introduction Waves Simple harmonic motion Complex waves Intensity Recording Complex waves The fundamental frequency (notated as F0) of a complex wave determines its pitch. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves Suppose we have a complex wave that is made up of a wave of 80 Hz, 200 Hz and 340 Hz: This is what the combination sounds like combined. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Complex waves Suppose we have a complex wave that is made up of a wave of 80 Hz, 200 Hz and 340 Hz: This is what the combination sounds like combined. The fundamental frequency of a complex wave equals the greatest common denominator; in this case 20 Hz. 20 is the largest number that all components (80, 200 and 340) can be divided by. Introduction Waves Simple harmonic motion Complex waves Intensity Recording Waves Loudness The loudness of a wave is called its intensity. It is a function of amplitude and frequency. The intensity is expressed in decibels (dB), which is a ratio of two sound intensities. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Loudness Loudness is the way in which we perceive intensity, which is the energy that a sound has. The energy of the loudest sound we can perceive, a jet engine at three meters, is 10 watt per m2 . The energy of the softest sound we can perceive (a mosquite of three meters) is 10−12 watt per m2 . Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Loudness Loudness is the way in which we perceive intensity, which is the energy that a sound has. The energy of the loudest sound we can perceive, a jet engine at three meters, is 10 watt per m2 . The energy of the softest sound we can perceive (a mosquite of three meters) is 10−12 watt per m2 . These difference are large numbers therefore they are expressed as logarithms. Introduction Waves Simple harmonic motion Complex waves Waves Loudness The decibel scale Number 1 10 100 1.000 10.000 100.000 1.000.000 1.000.000.000 is logarithmic. exponential logarithm 100 0 1 10 1 102 2 103 3 4 10 4 105 5 6 10 6 109 9 Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Intensity is a ratio If sound A has an intensity that is 10.000 times greater than sound B, the ratio is 10.000:1. And 10.000 = 104 . So sound A is 4 bels louder than sound B. However, we express loudness in decibels, so we have to multiply 4 by 10 = 40. Sound A is 40 dB louder than sound B. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Waves Intensity is a log ratio If sound A has twice as much intensity as sound B than is is 3 dB louder: 10 times the log of the ratio 2:1 = 2 = 10.3 . 0.3 * 10 = 3. One ticking watch is 20 dB, two ticking watches are 23 dB. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Source filter theory The vocal tract is the source of energy for air molecules and the energy that is added to the molecules is filtered by the vocal tract. This is the source-filter theory. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Source filter theory The vibration of the molecules has a certain frequency and can be described as a complex wave. Some parts of the wave are reinforced and other parts are dampened. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Source filter theory Which parts are reinforced and which part are dampened depends on the length of the column of air in the mouth and the position of the articulators. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Source filter theory The waves create echoes. They interact: some waves cancel each other out and other waves reinforce each other. Introduction Waves Simple harmonic motion Complex waves Assignment • Question 2 - 7 Zsiga (2013, 118) Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording before computers • Sound is transferred to a durable medium • wax • plastic • kymograph • oscilloscope • sound spectrograph Recording References Introduction Waves Simple harmonic motion Complex waves Kymograph Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Oscilloscope Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Recording speech • Nowadays we use computers • We sample speech. • We measure at regular intervals. Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Recording speech • If you want to measure something that changes, you measure at regular intervals: • temperature • speed • sound Introduction Waves Simple harmonic motion Complex waves Recording speech An example sample Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording speech Sampling • High frequency sounds change more often. • low frequency sounds change less often. Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording speech Sampling Higher frequency Lower frequency Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Recording speech Nyquist frequency How often do we need to sample to accurately represent all frequencies? • The human ear can hear frequencies up to 20000 Hz. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Recording speech Nyquist frequency How often do we need to sample to accurately represent all frequencies? • The human ear can hear frequencies up to 20000 Hz. 1 • This has a period of 20000 which is 0.00005 seconds (so 1 period takes 0.00005 seconds in which the wave goes from 0 to its highest amplitude to 0 to its lowest amplitude and back to 0 again). Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Recording speech Nyquist frequency How often do we need to sample to accurately represent all frequencies? • The human ear can hear frequencies up to 20000 Hz. 1 • This has a period of 20000 which is 0.00005 seconds (so 1 period takes 0.00005 seconds in which the wave goes from 0 to its highest amplitude to 0 to its lowest amplitude and back to 0 again). • It turns out that to same speech accurately you need to sample twice in a period (once for the up stroke and once for the down stroke). Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Recording speech Nyquist frequency How often do we need to sample to accurately represent all frequencies? • The human ear can hear frequencies up to 20000 Hz. 1 • This has a period of 20000 which is 0.00005 seconds (so 1 period takes 0.00005 seconds in which the wave goes from 0 to its highest amplitude to 0 to its lowest amplitude and back to 0 again). • It turns out that to same speech accurately you need to sample twice in a period (once for the up stroke and once for the down stroke). • 2*0.00005 = so every 0.000025 seconds, which is with a frequency of 1 0.000025 = 40000 Hz. Introduction Waves Simple harmonic motion Complex waves Intensity Recording References Recording speech Nyquist frequency So, we can hear up to 20000 Hz and to accurately represent 20000 Hz we need to sample at least 40000 times per second (in other words: we need a sampling frequency of 40000 Hz). This is called the Nyquist frequency: You have to sample with 2 * the maximal frequency you’re interested in. Introduction Waves Simple harmonic motion Complex waves Intensity Recording Aliasing What happens if you don’t stick to the Nyquist frequency? References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Aliasing What does it sound like if you don’t sample enough? A demonstration to show what it sound like. • open Praat, the program that will change your life. • create sound • establish sampling frequency • change sampling frequency • play same sound References Introduction Waves Simple harmonic motion Complex waves Intensity Speech recording Bits per sample • What we record are sound pressure levels. Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Speech recording Bits per sample • What we record are sound pressure levels. • A computer stores sound pressure levels as a number. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Speech recording Bits per sample • What we record are sound pressure levels. • A computer stores sound pressure levels as a number. • The larger this number can be, the more information can be stored. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Speech recording Bits per sample • What we record are sound pressure levels. • A computer stores sound pressure levels as a number. • The larger this number can be, the more information can be stored. • Most computers nowadays can store a number with 216 = 65.536 digits. References Introduction Waves Simple harmonic motion Complex waves Intensity Recording Speech recording Bits per sample • What we record are sound pressure levels. • A computer stores sound pressure levels as a number. • The larger this number can be, the more information can be stored. • Most computers nowadays can store a number with 216 = 65.536 digits. • High quality recordings are those made with a sampling frequency of 40000 Hz and store the numbers with 216 bits. References Introduction Waves Simple harmonic motion Complex waves Assignment • Question 4d–g Zsiga (2013, 144) Intensity Recording References Introduction Waves Simple harmonic motion Complex waves Intensity Recording References References Zsiga, E. C. (2013). The Sounds of Language: An Introduction to Phonetics and Phonology. Wiley-Blackwell.
