Recap the waveform. Complex waves (dạnh sóng phức tạp) and spectra. Recap the waveform

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1 Recap the waveform Complex waves (dạnh sóng phức tạp) and spectra Cơ sở âm vị học và ngữ âm học Lecture 11 The waveform (dạnh sóng âm) is a representation of the amplitude (biên độ) of air pressure perturbations over time. From a waveform, we can distinguish broad classes of speech sounds from one another: vowels from consonants, stops from fricatives, obstruents (âm ồn) from sonorants (âm vang), etc. Recap the waveform The waveform (dạnh sóng âm) is a representation of the amplitude (biên độ) of air pressure perturbations over time. From a waveform, we can distinguish broad classes of speech sounds from one another: vowels from consonants, stops from fricatives, obstruents (âm ồn) from sonorants (âm vang), etc. s k æ n I t scan it.58

2 Recap the waveform Recap the waveform But we can t tell different fricatives from one another, or an [a] from an [e], just by looking at a waveform. For this, we need a different kind of representation. But we can t tell different fricatives from one another, or an [a] from an [e], just by looking at a waveform. For this, we need a different kind of representation. Simple & complex waves We started by looking at simple waves, like this: Simple & complex waves We started by looking at simple waves, like this: Hz pure wave 12 Hz pure wave -1.1 The speech waves you have seen look more like this: -1.1 The speech waves you have seen look more like this: Hz speech wave 12 Hz speech wave

3 Simple & complex waves We started by looking at simple waves, like this: Simple & complex waves We started by looking at simple waves, like this: Hz pure wave 12 Hz pure wave -1.1 The speech waves you have seen look more like this: -1.1 The speech waves you have seen look more like this: Hz speech wave 12 Hz speech wave Color & color perception Color & color perception Colors are created from combinations of more basic colors But we don t perceive these basic components, i.e. we don t see yellow and blue in green We can analyze colors into a color spectrum (quang phổ màu sắc) Colors are created from combinations of more basic colors But we don t perceive these basic components, i.e. we don t see yellow and blue in green We can analyze colors into a color spectrum (quang phổ màu sắc)

4 Color & color perception Color & color perception Colors are created from combinations of more basic colors But we don t perceive these basic components, i.e. we don t see yellow and blue in green We can analyze colors into a color spectrum (quang phổ màu sắc) Colors are created from combinations of more basic colors But we don t perceive these basic components, i.e. we don t see yellow and blue in green We can analyze colors into a color spectrum (quang phổ màu sắc) Complex waves Complex waves Like colors, complex speech sounds are made up of more basic components (thành tố) These basic components are simple waves (sine waves) of different frequencies and amplitudes Like colors, we don t perceive these individual components, but we can decompose complex waves into their component parts. Like colors, complex speech sounds are made up of more basic components (thành tố) These basic components are simple waves (sine waves) of different frequencies and amplitudes Like colors, we don t perceive these individual components, but we can decompose complex waves into their component parts.

5 Complex waves.5 Like colors, complex speech sounds are made up of more basic components (thành tố) These basic components are simple waves (sine waves) of different frequencies and amplitudes Like colors, we don t perceive these individual components, but we can decompose complex waves into their component parts Hz simple wave 1 Hz simple wave Greatest common denominator A complex wave has a fundamental frequency which is the greatest common denominator (ước số chung lớn nhất) of the frequencies of its component waves For example: Component 1: Component 2: Fundamental Frequency (F): 3 Hz 5 Hz

6 Greatest common denominator Greatest common denominator A complex wave has a fundamental frequency which is the greatest common denominator (ước số chung lớn nhất) of the frequencies of its component waves A complex wave has a fundamental frequency which is the greatest common denominator (ước số chung lớn nhất) of the frequencies of its component waves For example: For example: Component 1: Component 2: Fundamental Frequency (F): 3 Hz 5 Hz Component 1: Component 2: Fundamental Frequency (F): 3 Hz 5 Hz 1 Hz Why? Why? Both component waves are periodic (i.e., they repeat themselves in time). The pattern formed by combining these component waves will only start repeating itself when both waves start repeating themselves at the same time. The GCD is the smallest common multiple (bội số chung nhỏ nhất) of the periods of the component waves. (1 chu kỳ là độ dài giữa hai cấu trúc lặp lại.) Both component waves are periodic (i.e., they repeat themselves in time). The pattern formed by combining these component waves will only start repeating itself when both waves start repeating themselves at the same time. The GCD is the smallest common multiple (bội số chung nhỏ nhất) of the periods of the component waves. (1 chu kỳ là độ dài giữa hai cấu trúc lặp lại.)

7 Why? Why? Both component waves are periodic (i.e., they repeat themselves in time). The pattern formed by combining these component waves will only start repeating itself when both waves start repeating themselves at the same time. The GCD is the smallest common multiple (bội số chung nhỏ nhất) of the periods of the component waves. (1 chu kỳ là độ dài giữa hai cấu trúc lặp lại.) Both component waves are periodic (i.e., they repeat themselves in time). The pattern formed by combining these component waves will only start repeating itself when both waves start repeating themselves at the same time. The GCD is the smallest common multiple (bội số chung nhỏ nhất) of the periods of the component waves. (1 chu kỳ là độ dài giữa hai cấu trúc lặp lại.) Kết hợp hai cái sóng 3 Hz và 5 Hz (chu kỳ sóng = 1 giây) (tần số = 1 Hz)

8 The (Fourier) spectrum Jean Baptiste Joseph Fourier ( ): a French mathematician who served under Napolean Fourier s theorem: all complex waves can be regarded as a sum of a (possibly infinite) number of sine waves. Fourier analysis is a mathematical technique for decomposing a complex wave into its component sine waves Fourier spectrum: the result of Fourier analysis of sound. Represents harmonics (tần số cộng hưởng) of the fundamental (f, tần số cơ bản) and their amplitudes (biên độ). A spectrum is like a snapshot of a sound wave over a short period of time, with frequency on the x-axis. Fourier analysis is a mathematical technique for decomposing a complex wave into its component sine waves Fourier spectrum: the result of Fourier analysis of sound. Represents harmonics (tần số cộng hưởng) of the fundamental (f, tần số cơ bản) and their amplitudes (biên độ). A spectrum is like a snapshot of a sound wave over a short period of time, with frequency on the x-axis. Fourier analysis is a mathematical technique for decomposing a complex wave into its component sine waves Fourier spectrum: the result of Fourier analysis of sound. Represents harmonics (tần số cộng hưởng) of the fundamental (f, tần số cơ bản) and their amplitudes (biên độ). A spectrum is like a snapshot of a sound wave over a short period of time, with frequency on the x-axis.

9 .5 2 Hz pure wave Fourier spectrum Representations for speech analysis Complex wave consisting of 2 Hz + 1 Hz pure tones Sound pressure level (db/hz) Waveforms Show amplitude over time Distinguish major classes of speech sounds Distinguish timing of component waves (phase) Cannot be used to distinguish different members of the same class Spectra Show amplitude over frequency Show details of the energy components of complex waves Distinguish timing of component waves (phase) Cannot show a sound changes over time or relative timing differences Frequency (Hz) Representations for speech analysis Spectra and speech sounds Waveforms Show amplitude over time Distinguish major classes of speech sounds Distinguish timing of component waves (phase) Cannot be used to distinguish different members of the same class Spectra Show amplitude over frequency Show details of the energy components of complex waves Distinguish timing of component waves (phase) Cannot show a sound changes over time or relative timing differences All periodic (speech) waves are complex waves - so they can be analysed as a combination of simple waves. A spectrum representation allows us to see this component energy structure very clearly Vowels are distinguishable from one another by their frequency component structure, as shown in a spectrum.

10 Spectra and speech sounds Spectra and speech sounds All periodic (speech) waves are complex waves - so they can be analysed as a combination of simple waves. A spectrum representation allows us to see this component energy structure very clearly Vowels are distinguishable from one another by their frequency component structure, as shown in a spectrum. All periodic (speech) waves are complex waves - so they can be analysed as a combination of simple waves. A spectrum representation allows us to see this component energy structure very clearly Vowels are distinguishable from one another by their frequency component structure, as shown in a spectrum. Intensity (db) Some real speech spectra Spectra of the vowels [a] and [i] A. Spectrum of the vowel [a] Frequency (Hz) Intensity (db) B. Spectrum of the vowel [i] Frequency (Hz) Harmonics (tần số cộng hưởng) When the glottal folds vibrate they produce a sawtooth-shaped waveform: a complex wave wit many components These frequency components have an important In naturally occurring property: vibrations, they appear there at is a regular a harmonic distance at from o each integer multiple another(bội số nguyên) of the fundamental frequency (f). H2 H3 E.g. if f is 1 Hz, its harmonics are 2 Hz, 3 Hz, 4 Hz, 5 Hz... What characteristic do these vowel spectra These have in don t common? look like very well-behaved complex waves... James Kirby L2B AcPh Lec2 17 James Kirby f = H1 L2B AcPh Lec2

11 Harmonics (tần số cộng hưởng) Harmonics In naturally occurring vibrations, there is a harmonic at each integer multiple (bội số nguyên) of the fundamental frequency (f). E.g. if f is 1 Hz, its harmonics are 2 Hz, 3 Hz, 4 Hz, 5 Hz... The amplitudes of harmonics decrease as the frequency increases. (Càng lên tần số, càng giảm cường độ của tần số cộng hưởng) Idealised Fourier spectrum showing fundamental frequency (1 Hz) and higher harmonics. In the case of voicing... From Johnson (23) Acoustic & Auditory Phonetics. (Idealised) Fourier spectrum of glottal source wave (sóng nguồn). Fourier spectrum of [i]. Actual glottal vibration is highly complex and not completely periodic, only quasi-periodic (hầu như là theo chu kỳ).

12 Quasi-periodicity (Idealised) Fourier spectrum of glottal source wave (sóng nguồn). When glottal folds vibrate, they produce a complex wave with many irregular component frequencies If these irregularities are small enough in amplitude, we still perceive the sound as periodic. Fourier spectrum of [i]. Actual glottal vibration is highly complex and not completely periodic, only quasi-periodic (hầu như là theo chu kỳ). Furthermore, the frequency structure (cấu trúc tần số) of the speech wave is shaped as it travels through the vocal tract. (more after the break...) Quasi-periodicity Quasi-periodicity When glottal folds vibrate, they produce a complex wave with many irregular component frequencies If these irregularities are small enough in amplitude, we still perceive the sound as periodic. Furthermore, the frequency structure (cấu trúc tần số) of the speech wave is shaped as it travels through the vocal tract. (more after the break...) When glottal folds vibrate, they produce a complex wave with many irregular component frequencies If these irregularities are small enough in amplitude, we still perceive the sound as periodic. Furthermore, the frequency structure (cấu trúc tần số) of the speech wave is shaped as it travels through the vocal tract. (more after the break...)

13 Quasi-periodicity When glottal folds vibrate, they produce a complex wave with many irregular component frequencies If these irregularities are small enough in amplitude, we still perceive the sound as periodic. Furthermore, the frequency structure (cấu trúc tần số) of the speech wave is shaped as it travels through the vocal tract. (more after the break...)