Spectral Analysis Feburary 23, 2010 Sorting Things Out 1.On Thursday: back in the computer lab. Craigie Hall D 428 Analysis of Korean stops. 2.Remember:

Spectral Analysis

Feburary 23, 2010

Sorting Things Out1. On Thursday: back in the computer lab.

• Craigie Hall D 428

• Analysis of Korean stops.

2. Remember:

• mid-term next Tuesday

• Check out the review sheet…

3. Course project reports to hand back

• Also note: the last TOBI homework

4. Note: Spectrogram reading challenge!

• For fun and extra credit points

Today• Today:

• Wrap up voice quality discussion

• Begin examination of spectral analysis

• Some leftovers:

1. Ventricular folds video

2. Death Metal

Harsh Voice• A “raucous voice quality” (Holmes, 1932)

• Acoustically: fundamental frequency is aperiodic

• = lots of jitter (variability in time)

• Articulatorily: harsh voice does not add anything new to the voice quality parameters;

• it just increases the intensity of those already in operation.

• Harsh voice “excessive approximation of the vocal folds”

• = high medial compression and high adductive tension

Harsh, continued• “Harshness results from overtensions in the throat and neck; it is often if not usually accompanied by hypertensions of the whole body.” (Gray and Wise, 1959)

• Harsh F0 is usually > 100 Hz

• Creaky F0 is usually < 100 Hz

Voice Quality Summary• So far, we’ve talked about:

AT LT MC Flow

Modal moderate varies moderate med.

Tense high varies high high

Creaky high low high low

Breathy low varies low high

Whisper low N/A high med.

4. Whispery Voice• When we whisper:

• The cartilaginous glottis remains open, but the ligamental glottis is closed.

• Air flow through opening with a “hiss”

• The laryngeal settings:

1. Little or no adductive tension

2. Moderate to high medial compression

3. Moderate airflow

4. Longitudinal tension is irrelevant…

Nodules• One of the more common voice disorders is the development of nodules on either or both of the vocal folds.

• nodule = callous-like bump

• What effect might this have on voice quality?

Last but not least• What’s going on here?

• At some point, my voice changes from modal to falsetto.

5. Falsetto• The laryngeal specifications for falsetto:

1. High longitudinal tension

2. High adductive tension

3. High medial compression

• Contraction of thyroarytenoids

4. Lower airflow than in modal voicing

• The results:

• Very high F0.

• Very thin area of contact between vocal folds.

• Air often escapes through the vocal folds.

Falsetto EGG

• The falsetto voice waveform is considerably more sinusoidal than modal voice.

Some Real EGGs

Modal voice (F0 = 140 Hz)

Falsetto voice (F0 = 372 Hz)

Voice Quality SummaryAT LT MC Flow

Modal moderate varies moderate med.

Tense high varies high high

Creaky high low high low

Breathy low varies low high

Whisper low N/A high med.

Falsetto high high high low

• Last but not least, Korean makes an interesting distinction between “emphatic” (or fortis) obstruents and unaspirated and aspirated (lenis) obstruents.

What’s going on here?• A variety of things occur during the articulation of fortis

consonants in Korean.

1. Glottis is not open as wide (during closure) as in lenis stops.

Voicing begins more quickly after stop release

2. Increased airflow in fortis stops.

Higher F0 after stop release.

3. Vocal folds are “more tense” than in lenis stops.

• = greater medial compression

• = “squarer” glottal waveform

An Actual EGG Waveform• Modal voicing (by me):

• Note: completely closed and completely open phases are both actually quite short.

• Also: closure slope is greater than opening slope.

• Q: Why might there be differences in slope?

A Different Kind of Voicing• The basic voice quality in khoomei is called xorekteer.

• Notice any differences in the EGG waveforms?

• This voice quality requires greater medial compression of the vocal folds.

• ...and also greater airflow

Why Should You Care?• Remember that the most basic kind of sound wave is a sinewave.

time

pressure

• Sinewaves can be defined by three basic properties:

• Frequency, (peak) amplitude, phase

Complex Waves• It is possible to combine more than one sinewave together into a complex wave.

• At any given time, each wave will have some amplitude value.

• A1(t1) := Amplitude value of sinewave 1 at time 1

• A2(t1) := Amplitude value of sinewave 2 at time 1

• The amplitude value of the complex wave is the sum of these values.

• Ac(t1) = A1 (t1) + A2 (t1)

• Note: a harmonic is simply a component sinewave of a complex wave.

Complex Wave Example• Take waveform 1:

• high amplitude

• low frequency

• Add waveform 2:

• low amplitude

• high frequency

• The sum is this complex waveform:

+

=

Another Perspective• Sinewaves can also be represented by their power spectra.

• Frequency on the x-axis

• Intensity on the y-axis (related to peak amplitude)

Waveform Power Spectrum

Putting the two togetherWaveform Power Spectrum

+ +

= =

harmonics

More Combinations

• What happens if we keep adding more and more high frequency components to the sum?

+ =

+ =

A Spectral ComparisonWaveform Power Spectrum

What’s the Point?• Remember our EGG waveforms for the different

kinds of voice qualities:

• The glottal waveform for tense voice resembles a square wave.

• lots of high frequency components (harmonics)

What’s the point, part 2• A modal voicing EGG looks like:

• It is less square and therefore has less high frequency components.

• Although it is far from sinusoidal...

What’s the point, part 3• Breathy and falsetto voice are more sinusoidal...

• And therefore the high frequency harmonics have less power, compared to the fundamental frequency.

Let’s Check ‘em out• Head over to Praat and check out the power spectra of:

• a sinewave

• a square wave

• a sawtooth wave

• tense voice

• modal voice

• creaky voice

• breathy voice

Spectral Tilt

• Spectral tilt = drop-off in intensity of higher harmonics, compared to the intensity of the fundamental.

The Source• The complex wave emitted from the glottis during voicing=

• The source of all voiced speech sounds.

• In speech (particularly in vowels), humans can shape this spectrum to make distinctive sounds.

• Some harmonics may be emphasized...

• Others may be diminished (damped)

• Different spectral shapes may be formed by particular articulatory configurations.

• ...but the process of spectral shaping requires the raw stuff of the source to work with.

Spectral Shaping Examples• Certain spectral shapes seem to have particular vowel qualities.

QuickTime™ and a decompressor

are needed to see this picture.

Spectrograms• A spectrogram represents:

• Time on the x-axis

• Frequency on the y-axis

• Intensity on the z-axis

Real Vowels

Ch-ch-ch-ch-changes• Check out some spectrograms of sinewaves which change frequency over time:

The Whole Thing• What happens when we put all three together?

• This is an example of sinewave speech.

The Real Thing

• Spectral change over time is the defining characteristic of speech sounds.

• It is crucial to understand spectrographic representations for the acoustic analysis of speech.

Life’s Persistent Questions• How do we get from here:

• To here?

• Answer: Fourier Analysis

Fourier’s Theorem• Joseph Fourier (1768-1830)

• French mathematician

• Studied heat and periodic motion

• His idea:

• any complex periodic wave can be constructed out of a combination of different sinewaves.

• The sinusoidal (sinewave) components of a complex periodic wave = harmonics

Fourier Analysis• Building up a complex wave from sinewave components is straightforward…

• Breaking down a complex wave into its spectral shape is a little more complicated.

• In our particular case, we will look at:

• Discrete Fourier Transform (DFT)

• Also: Fast Fourier Transform (FFT) is used often in speech analysis

• Basically a more efficient, less accurate method of DFT for computers.

The Basic Idea• For the complex wave extracted from each window...

• Fourier Analysis determines the frequency and intensity of the sinewave components of that wave.

• Do this about 1000 times a second,

• turn the spectra on their sides,

• and you get a spectrogram.

Possible Problems• What would happen if a waveform chunk was windowed like this?

• Remember, the goal is to determine the frequency and intensity of the sinewave components which make up that slice of the complex wave.

The Usual Solution• The amplitude of the waveform at the edges of the window is normally reduced...

• by transforming the complex wave with a smoothing function before spectral analysis.

• Each function defines a particular window type.

• For example: the “Hanning” Window

• There are lots of different window types...

• each with its own characteristic shape

Hamming Bartlett Gaussian

Hanning Welch Rectangular

Window Type Ramifications• Play around with the different window types in Praat.

Ideas• Once the waveform has been windowed, it can be boiled down into its component frequencies.

• Basic strategy:

• Determine whether the complex wave correlates with sine (and cosine!) waves of particular frequencies.

• Correlation measure: “dot product”

• = sum of the point-by-point products between waves.

• Interesting fact:

• Non-zero correlations only emerge between the complex wave and its harmonics!

• (This is Fourier’s great insight.)

A Not-So-Complex Example• Let’s build up a complex wave from 8 samples of a 1 Hz sine wave and a 4 Hz cosine wave.

• Note: our sample rate is 8 Hz.

1 2 3 4 5 6 7 8

1 Hz 0 .707 1 .707 0 -.707 -1 -.707

4 Hz 1 -1 1 -1 1 -1 1 -1

Sum: 1 -.293 2 -.293 1 -1.707 0 -1.707

• Check out a visualization.

Correlations, part 1• Let’s check the correlation between that wave and the 1 Hz sinewave component.

1 2 3 4 5 6 7 8

Sum: 1 -.293 2 -.293 1 -1.707 0 -1.707

1 Hz 0 .707 1 .707 0 -.707 -1 -.707

Dot: 0 -.207 2 -.207 0 1.207 0 1.207

• The sum of the products of each sample is 4.

• This also happens to be the dot product of the 1 Hz wave with itself.

• = its “power”