cs 551/651: structure of spoken language lecture 1: visualization of the speech signal, introductory...
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CS 551/651:Structure of Spoken Language
Lecture 1: Visualization of the Speech Signal,Introductory Phonetics
John-Paul HosomFall 2010
Structure of Spoken Language : Hosom 2
Visualization of the Speech Signal
Most common representations:• Time-domain waveform• Energy• Pitch contour• Spectrogram (power spectrum)
Structure of Spoken Language : Hosom 3
Visualization of the Speech Signal: Time-Domain Waveform
Time-domain waveform is a signal recorded directly from microphone, with time on horizontal axis and amplitude on vertical axis.
“Variations in air pressure in the form of sound waves movethrough the air somewhat like ripples on a pond. … A graphof a sound wave is very similar to a graph of the movementsof the eardrum.” [Ladefoged, p. 184]
“Sound originates from the motion or vibration of an object.This motion is impressed upon the surrounding medium (usuallyair) as a pattern of changes in pressure. … The sound generallyweakens as it moves away from the source and also may besubject to reflections and refractions…” [Moore, p. 2]
Structure of Spoken Language : Hosom 4
Visualization of the Speech Signal: Time-Domain Waveform
Vertical axis: amplitude, relative sound pressuretypical unit: Pa (micro-pascals)
(digital signal usually unitless)quantization (-32768 to 32767)
Horizontal axis: timetypical unit: msec (milliseconds)sampling (8000, 16000, 44.1K samp/sec)
Structure of Spoken Language : Hosom 5
Visualization of the Speech Signal: Energy
“Energy” or “Intensity”:intensity is sound energy transmitted per second (power) through a unit area in a sound field. [Moore p. 9]
intensity is proportional to the square of the pressure variation [Moore p. 9]
normalized energy = intensity
xn = signal x at time sample nN = number of time samples
N
xNt
tnn
12
Structure of Spoken Language : Hosom 6
Visualization of the Speech Signal: Energy
“Energy” or “Intensity”:human auditory system better suited to relative scales:
energy (bels) =
energy (decibels, dB) =
I0 is a reference intensity… if the signal becomes twice aspowerful (I1/I0 = 2), then the energy level is 3 dB (3.01023 dBto be more precise)
Typical value for I0 is 20 Pa.20 Pa is close to the average human absolute threshold for
a 1000-Hz sinusoid.
)(log0
110 I
I
)(log100
110 I
I
Structure of Spoken Language : Hosom 7
Visualization of the Speech Signal: Energy
What is a good value of N? Depends on information of interest:
N=1 msec
N=5 msec
N=20 msec
N=80 msec
Structure of Spoken Language : Hosom 8
Visualization of the Speech Signal: Power Spectrum
What makes one phoneme, /aa/, sound different from anotherphoneme, /iy/?
Different shapes of the vocal tract… /aa/ is produced with the tongue low and in the back of the mouth; /iy/ is produced with the tongue high and toward the front.
The different shapes of the vocal tract produce different“resonant frequencies”, or frequencies at which energy in thesignal is concentrated. (Simple example of resonant energy:a tuning fork may have resonant frequency equal to 440 Hz or “A”).A resonance is the tendency of a system to oscillate with larger amplitude at some frequencies than at others [Wikipedia]
Resonant frequencies in speech (or other sounds) can be displayed by computing a “power spectrum” or “spectrogram,” showing the energy in the signal at different frequencies.
Structure of Spoken Language : Hosom 9
Visualization of the Speech Signal: Power Spectrum
A time-domain signal can be expressed in terms of sinusoidsat a range of frequencies using the Fourier transform:
where x(t) is the time-domain signal at time t, f is a frequencyvalue from 0 to 1, and X(f) is the spectral-domain representation.
note:
One useful property of the Fourier transform is that it is time-invariant (actually, linear time invariant). While a periodic signal x(t) changes at t, t+, t+2, etc., the Fourier transform of this signal is constant, making analysis of periodic signals easier.
t
t
ftj
dtftjfttx
dtetxfX
)2sin()2cos()(
)()( 2
)sin()cos( je j
Structure of Spoken Language : Hosom 10
Visualization of the Speech Signal: Power Spectrum
Since samples are obtained at discrete time steps, and sinceonly a finite section of the signal is of interest, the discreteFourier transform is more useful:
in which x(k) is the amplitude at time sample k, n is a frequencyvalue from 0 to N-1, N is the number of samples or frequency points of interest, and X(n) is the spectral-domain representation ofx(k). Note that we assume that that the series outside the range (0, N-1) is “extended N-periodic,” that is, xk = xk+N for all k.
1
0
1
0
2
)]2
sin()2
)[cos((1
1,0for)(1
)(
N
k
N
k
N
knj
N
knj
N
knkx
N
NnekxN
nX
Structure of Spoken Language : Hosom 11
Visualization of the Speech Signal: Power Spectrum
• The sampling frequency is the rate at which samples are recorded; e.g. 8000 Hz = 8000 samples per second.
• Shannon’s Sampling Theorem states that a continuous signal must be discretely sampled with at least twice the frequency of the highest frequency present in the signal. So, the signal must not contain any data above Fsamp/2 (the Nyquist frequency). If it does, use a low-pass filter to remove these higher frequencies.
• Because the signal is assumed to be periodic over length N, but this assumption is usually false, then the signal is weighted with a window so that both edges of the signal taper toward zero:
Hamming window:
1...01
2cos460540 )()(
Nn
N
n..nxnxw
Structure of Spoken Language : Hosom 12
Visualization of the Speech Signal: Power Spectrum
The magnitude and phase of the spectral representation are:
Phase information is generally considered not important inunderstanding speech, and the energy (or power) of the magnitude of F(n) on the decibel scale provides most relevant information:
Note: usually don’t worry about reference intensity I0 (assume a value of 1.0); the signal strength (in Pa) is unknown anyway.
))(
)((tan
))()()()(()(
1
5.0
)(
)(
nF
nFphase
nFnFnFnFnFmagnitude
real
imagF
imagimagrealrealF
n
n
))()((log10 2210)(
nFnFrumPowerSpect imagrealF n
absolute value of complex number
Structure of Spoken Language : Hosom 13
Visualization of the Speech Signal: Power Spectrum
The power spectrum can be plotted like this (vowel /aa/):
time-domain
amplitude
spectralpower
(dB)(512 samp)
0 Hz 4000 Hz
73 dB
frequency (Hz)
Structure of Spoken Language : Hosom 14
Visualization of the Speech Signal: Power Spectrum
If the speech signal is periodic and the number of samples in the window is large enough, then harmonics are seen:
periodic signal/aa/ periodic signal /aa/ aperiodic signal /sh/128 samples 2048 samples 2048 samples
(frequency range is 0 to 4000 Hz in all plots)
A harmonic is a strong energy component at an integer multipleof the fundamental frequency (pitch), F0.
Structure of Spoken Language : Hosom 15
Visualization of the Speech Signal: Formants
Note that the resonant frequencies, or formants, for the two vowels /aa/ and /iy/ can be identified in the spectra.
For recognition of phonemes, the spectral envelope is important (envelope = shape of spectrum without harmonics)
/aa/ 2048 samples /iy/ 2048 samples
?
envelope
?
0 1K 2K 3K 4K 0 1K 2K 3K 4K
Structure of Spoken Language : Hosom 16
Visualization of the Speech Signal: Formants
The harmonics, which are dependent on F0, are not, in theory, significantly related to the resonant frequencies, which are dependent on the vocal tract shape (or phoneme)
0 1K 2K 3K 4KHz
/aa/F0=80Hz
/aa/F0=164Hz
Structure of Spoken Language : Hosom 17
Visualization of the Speech Signal: Spectrograms
Many power spectra can be plotted over time, creating a “spectrogram” or “spectrograph” (pre-emphasis = 0.97):
/aa/
freq
(H
z)
amp
/iy/
freq
(H
z)
amp
time (msec)
(FFT size = 10 msec)
Structure of Spoken Language : Hosom 18
Visualization of the Speech Signal: Formants
These formants can be modeled by a “damped sinusoid”, whichhas the following representations:
where S(f) is the spectrum at frequency value f, A is overallamplitude, fc is the center frequency of the damped sine wave, and is a damping factor. [Olive, p. 48, 58]
2222
22
2)()2sin()(
cc
cc
t
fff
AffStfAetx
time (msec)
pow
er (
dB)
ampl
itud
e
frequency (Hz)
center freq. fc
0 dB0
Structure of Spoken Language : Hosom 19
Visualization of the Speech Signal: Formants
The bandwidth is defined as the width of the spectral peakmeasured at the point where the linear spectral magnitude value is ½ the maximum value. A reduction of the signal by a factor of 2 is equivalent to a 3 dB change.
pow
er (
dB)
frequency (Hz)
bandwidth
0 dB
3 dB
Also, the resonator must have a value of 0 dB at 0 Hz.
Structure of Spoken Language : Hosom 20
Visualization of the Speech Signal: Formants
• Formants are specified by a frequency, F, and bandwidth, B.
• A neutral vowel (/ax/) theoretically has formants at 500 Hz, 1500 Hz, 2500 Hz, 3500 Hz, etc. The first formant is called F1, the second is called F2, etc. (The fundamental frequency, or pitch, is F0.)
• F1, F2, and sometimes F3 are usually sufficient for identifying vowels.
• Formants can be thought of as filters, which act on the source waveform. For vowels, the source waveform is air pushed through the vibrating vocal folds. Energy is lost (hence a damped sinusoid model) by sound absorption in the mouth.
• A digital model of a formant can be implemented using an infinite-impulse response (IIR) filter.
Structure of Spoken Language : Hosom 21
Visualization of the Speech Signal: Excitation/Source
The vocal-fold vibration source looks like this:
(Note: there are some gross simplifications here… we’ll go intomore detail later in the course.)
In fricatives and other unvoiced speech, the source is turbulent air:
time (msec)
ampl
itud
e
frequency (Hz)
-6 dB/octave
pow
er (
dB)
frequency (Hz)
flat slopepo
wer
(dB
)
time (msec)
ampl
itud
e
Structure of Spoken Language : Hosom 22
Visualization of the Speech Signal: Pre-Emphasis
Because the source for voiced sounds decreases at –6 dB/octave,a simple filter can be used to increase the spectral tilt by +6 dB/octave, thereby making voiced sounds spectrally flatand easier to visualize. (NOTE: unvoiced sounds then have spectral slope of + 6 dB/octave)
frequency (Hz)
0 dB/octave
frequency (Hz)
pow
er (
dB)
-6 dB/octave
97.0
)1()()(
a
nxanxnx
where x(n) is the time-domain speech signal at sample number n,and x(n) is the pre-emphasized speech signal at sample n.
Structure of Spoken Language : Hosom 23
Visualization of the Speech Signal: Spectrograms
The FFT window size has a large impact on visual properties:
/aa/
freq
(H
z)
am
p
/aa/
freq
(H
z)
“wideband” = small time window = small FFT size
“narrowband” = large time window = large FFT size
(FFT size = 5 msec)
(FFT size = 33 msec)
Structure of Spoken Language : Hosom 24
Spectrogram Reading: Vowels
Vowel formant frequencies:
Structure of Spoken Language : Hosom 25
Spectrogram Reading: Vowels
Vowel formants (averages for English, male vs. female):
310
2790
3310
430
2480
3070
610
2330
2990
860
2050
2850
760
1400
2780
850
1220
2810
470
1160
2680
370
950
2670
0
500
1000
1500
2000
2500
3000
3500
iy ih eh ae ah aa uh uw
*from Peterson, G.E., and Barney, H.L. (1952). "Control methods used in the study of vowels", Journal of the Acoustical Society of America, 24,175-184.
Structure of Spoken Language : Hosom 26
Spectrogram Reading: Vowels
Vowel formants, Peterson and Barney data:
Structure of Spoken Language : Hosom 27
Spectrogram Reading: Vowels
Ratios of 1st and 2nd formant, from Miller (1989) based onPeterson and Barney (1952) data:
Structure of Spoken Language : Hosom 28
Spectrogram Reading: Vowels
Observed values from vowel midpoints from a single speaker,speaking both “clearly” and “conversationally”, in different phonetic contexts:
iy
ih
uw
uh
eh ae
ah
aa
(from Amano-Kusumoto, PhD thesis 2010)
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