LING330: Quiz #6 Flashcards
Natural resonance frequency
Every object has a basic (or set of) frequency at which it will naturally oscillate when energy is applied
Standing waves
Patterns of vibration that are sustained by continual self-reinforcement in an oscillating system
Explain resonance
Swing pushing metaphor
When energy is applied in resonance with a natural frequency, the amplitude of the movement at that frequency is increased because both forces are acting together
When not in resonance with natural frequency -> energy dissipates quickly because the forces are cancelling each other out and amplitude at that frequency dies out
Free vibration
When you strike a tuning fork/push a swing
Frequency depends on mass, shape and stiffness of object that you are applying the energy to
Two options of what can happen when the sound energy “beats” on an object they encounter
1- if it has had a broad frequency response (like an eardrum or a microphone), it will mimic the vibration of the air particles accurately (within a broad range)
2- other objects are “tuned” to resonate only in a narrow frequency band so if the frequency of the “driving” sound energy happens to match the natural resonant frequency of the object, the object will vibrate in resonance with the sound, passing along the pattern of vibration at a high amplitude
If sound frequency doesn’t match=sound energy dissipated + pattern of vibration dies out
Resonating body acts as a FILTER (some frequencies get through, if resonant=amplified and others lost)
Source-filter theory
Vocal tract: resonating system (filter)
Vibrating vocal folds: driving force for sound, induces resonance in the air trapped in the vocal tract, creates sound (energy output) (source)
Vocal tract sound sources
Can be periodic or APERIODIC
Periodic: sonorants
Aperiodic: obstruents
What does which frequencies are passed through the filter or cancelled depend on?
- shape of body of air contained in vocal tract
- position of the articulators
What is the tube in the vocal tract?
Tube/column of air inside vocal tract
Length of this column determines resonance frequency
What happens when sound waves are in a small, enclosed space
Bounce off walls and interact with each other
Can either cancel each other out or both waves could be pushing in the same direction at the same time = maintains high amplitude (creates standing wave aka resonance)
Formants
Amplified resonance frequencies
How are different shaped tubes of air created?
Moving tongue and lips
What makes our voices sound human rather than robotic ?
Soft sides of vocal tract have deviations that make perfect symmetry + irregular shape and imperfect vibrations of vocal folds
What patterns of vibration will set themselves up as standing waves in a column or tube of air ?
Certain wavelengths interact positively where the interacting forces reinforce each other, pushing or pulling simultaneously
Tube of air=open on one end, closed on other
Conditions to hold resonance for this tube=closed end is a VELOCITY NODE and open end must be a VELOCITY ANTINODE
Particles of air at closed end have nowhere to move, open end=max freedom of movement
Particle movement and pressure at lips and vocal folds is…?
Lips: Max particle movement = minimum pressure change
Vocal folds: minimum particle movement = maximum pressure change
Distance from node to antinode is how much of a wavelength?
1/4 of the wavelength
General principle of a standing wave
Standing wave is set up when the tube length is equal to odd multiples of the quarter wavelength
Perturbation theory
Focuses on location of nodes + antinodes in standing waves and on the inverse relationship between pressure + frequency (a pressure node = a velocity antinode and vice versa)
Where are the nodes and antinodes in a waveform?
Antinodes (maximum velocity variation) = occur at places where line is in middle of tube
Crucial insight of perturbation theory
Increasing the pressure (making a constriction) near a velocity antinode will DECREASE particle velocity and thus frequency
That means INCREASE pressure near a velocity node will RAISE the frequency
Relative amplitude
Differences in amplitude between comparable speech segments
Problem with using peak amplitude as a measure
It doesn’t match how humans perceive loudness (actually depends on frequency and amplitude)
Root mean square (RMS) method
Amplitude measure that corresponds most closely to the perception of loudness
To compute this over a certain window of time, must:
Take set of samples
Square each value
Find the mean
Take the square root (working with squared values makes negative and positive comparable)
Pitch track
Graph of f0 values over time
Autocorrelation
A common computational method of creating pitch tracks
Analysis consists of correlating a signal with a delayed version of itself
Relies on the definition of periodicity (pattern of a certain duration repeats itself)
This analysis finds the duration of that chunk of the waveform that most clearly repeats
How does the autocorrelation algorithm work?
Tries out a range of periods and calculates which one best matches the actual repeating pattern
The computer chooses a certain period, delays the windowed waveform by exactly that much and then compares the offset waveform to the original
If selected lag time matches actual period -> delayed waveform and original will still line up and their values will correlate
Lag time doesn’t correspond to actual period -> two waves will be out of sync
Two downsides to f0 analysis
1- autocorrelation analysis is error prone, especially when the SNR is low or voicing is irregular
2- sudden and implausible jumps in F0 (especially to half or double the previous value) should be corrected by adjusting window size to rule out implausible values
Pitch halving vs pitch doubling
Pitch halving= algorithm returns the best correlation over two periods
Pitch doubling= same thing but over half a period
Fourier analysis
Mathematical analysis of a complex wave into its component frequencies
Fast Fourier Transform (FFT)
Computer performs this algorithm that transforms the signal from the time domain into the frequency domain (Transform)
Fourier because original math goes back to Jean baptiste Fourier
Fast because the algorithm uses some mathematical shortcuts to make waveforms with a large number of samples more easily computable
Explain the correlation part of Fourier analysis
Signal not correlated with itself, but with a series of sine waves
If complex signal has a high amplitude component at a given frequency-> strong correlation between the complex signal and a sinusoid of that frequency
Higher amplitude = higher correlation
Linear predictive coding (LPC)
Different algorithm for spectral analysis of a digital signal
Relies on definition of a periodic signal (certain patterns repeat at regular intervals and the intervals correspond to the periods of the component frequencies)
A type of autocorrelation (samples separated by one period will be highly correlated with each other)
Works by computing the intervals at which sample values are most highly correlated
Diffs between FFT and LPC analysis
LPC:
Smaller intervals examined
More precise (shows exact number for hertz, not just a band) therefore can separate Formants that are close in frequency and that may seem on a spectrogram to have merged
Not more accurate
Will return exactly as many formant frequencies as requested
FFT:
Can be used to confirm the accuracy of LPC analysis (best used together!)
Both:
Can be computed over just one window or can be repeated sequentially to show change over time
