Source/Filter Theoryand Vowels

February 4, 2010

Some Lab Notes

Some Lab Notes

Some Lab Notes

Some Lab

Notes

Some Lab Notes

Some Lab Notes• Also: the whisper video

• One point: ranges

• Check out the EGG audio recording, too.

Open Tube Resonances• For the first three resonances in an open tube, the standing waves will look like this:

= 4L

L

= 4L / 3

= 4L / 5

closed

end

open

end

Open Tube Resonances• Last time, we learned that, for open tubes, the frequency of the nth resonance of the tube was determined by the following equation:

• fn = (2n - 1) * c

4L• For an open tube of length 17.5 cm, this would yield formant frequencies of:

• F1 = 500 Hz

• F2 = 1500 Hz

• F3 = 2500 Hz

• Important: vowel formants correspond to the resonant frequencies of the vocal tract “tube”

My “Open Tube” Vowel

formants

Note: the vowel produced by an unperturbed human vocal tract sounds like /schwa/

Spectral Analysis: Vowels• Remember: Fourier’s theorem breaks down any complex sound wave (e.g., speech) into its component sinewaves.

• For each component sinewave (harmonic), this analysis shows us:

• its frequency

• its amplitude (intensity)

• In vowels:

• resonating harmonics have higher intensity

• other harmonics will be damped (have lower intensity)

My Open Tube Profile

Note:

F0 160 Hz

F1

F2

F3 F4

Source/Filter Theory• The combination of harmonics + resonances in the vowel /schwa/ lays the foundation for the source-filter theory of vowel production.

• Developed by Gunnar Fant (1960)

• The shape of the vocal tract filters this complex wave to amplify the intensity of some harmonics and diminish the intensity of others.

• For speech, the source of sound = complex waves created by periodic opening and closing of the vocal folds

“Filters”• For any particular vocal tract configuration, certain frequencies will resonate, while others will be damped.

• analogy: natural variation/environmental selection

• This graph represents how much the vocal tract would resonate for sinewaves at every possible frequency.

Source + Filter = Output

+

=

Schwa at different pitches

100 Hz 120 Hz

150 Hz

“Filters”?• A filter is a tool used in both electronic engineering and

digital signal processing to shape the spectrum of a complex sound.

• A filter removes harmonic components of certain frequencies in the signal.

• There are different types of filters:

1. Low-pass filters

• Allow low frequencies to pass through the filter.

• And remove high frequencies from the signal.

2. High-pass filters:

• Allow high frequencies to pass through filter.

• And remove low frequencies.

Low-Pass Filter in Action• Power spectrum of 100 Hz + 1000 Hz combo:

• Filter passes 100 Hz component, but not 1000 Hz component.

• Demo: Low-pass filter some noisy EGG waveforms.

Band-Pass Filters• A band-pass filter combines both high- and low-pass filters.

• It passes a “band” of frequencies around a center frequency.

Band-Pass Filtering

• Basic idea: components of the input spectrum have to conform to the shape of the band-pass filter.

Bandwidth• Filters can differ not only in terms of which frequencies they allow to pass, but also in terms of their bandwidth.

• Bandwidth is the range of frequencies over which a filter will respond at .707 of its maximum output.

bandwidth• Half of the acoustic energy passed through the filter fits within the bandwidth.

• Bandwidth is measured in Hertz.

Different Bandwidths

narrow band wide band

Your Grandma’s Spectrograph

• Originally, spectrographic analyzing filters were constructed to have either wide or narrow bandwidths.

Narrow-Band Spectrogram• A “narrow-band spectrogram” clearly shows the harmonics of speech sounds.

• …but the formants are less distinct.

harmonics

• Also: temporal resolution is not very good.

Wide-Band Spectrogram• By changing the parameters of the Fourier analysis, we can get a “wide-band spectrogram”

• This shows the formants better than the harmonics.

formants

Wide-Band Spectrogram• By changing the parameters of the Fourier analysis, we can get a “wide-band spectrogram”

• This shows the formants better than the harmonics.

formants

F1

F2

F3

voice bars (glottal pulses)

Also: temporal resolution is better.

The Other Half• Source-filter theory holds that:

• Resonance effectively creates a series of band-pass filters in our mouths.

+ =

• Wide-band spectrograms help us see properties of the vocal tract filter.

Formants• Rather than filters, though, we may consider the vocal tract to consist of a series of resonators.

• With center frequencies

• And particular bandwidths

• The characteristic resonant frequencies of a particular articulatory configuration are called formants.

• Questions to answer:

• What formant frequencies are characteristic of each vowel?

• How can we change the resonant frequencies of the vocal tract? (i.e., make spectral changes)

Different Vowels,Different Formants

• The formant frequencies of resemble the resonant frequencies of a tube that is open at one end.

• For the average man (like Peter Ladefoged or me):

• F1 = 500 Hz

• F2 = 1500 Hz

• F3 = 2500 Hz

• However, we can change the shape of the vocal tract to get different resonant frequencies.

• Vowels may be defined in terms of their characteristic resonant frequencies (formants).

Artificial Examples• The characteristic resonant frequencies (formants) of the “corner” vowels:

“[i]” “[u]”

“ ”

Real Vowels

Real Vowels

Vowel Acoustics• If you look at enough of these, you will start to notice a pattern.

• The first formant (F1) of “high” vowels tends to be lower than the F1 of /schwa/.

• …while the first formant of “low” vowels tends to be higher than the F1 of /schwa/.

• The first formant (F2) of “front” vowels tends to be higher than the F2 of /schwa/.

• The second formant (F2) of “back” vowels tends to be lower than the F2 of /schwa/.

• So…what should the F1 and F2 values of my [æ] be?

Things to Keep in Mind• Resonant frequencies (formants) are primarily based on the length of the speaker’s vocal tract.

• (the length of the open tube)

• The longer the vocal tract, the lower the formant frequencies.

• Thought Question #1:

• What effect might lip rounding have on formant frequencies?

Things to Keep in Mind• Thought Question #2:

• How might formant frequencies differ between men and women?

Male Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

[i][u]

[æ]

Female Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

[i] [u]

[æ]

Combined Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

Women and Men• The acoustics of male and female vowels differ

reliably along two different dimensions:

1. Sound Source

2. Sound Filter

• Source--F0: depends on length of vocal folds

shorter in women higher average F0

longer in men lower average F0

• Filter--Formants: depend on length of vocal tract

shorter in women higher formant frequencies

longer in men lower formant frequencies

Prototypical Voices• Andre the Giant: (very) low F0, low formant frequencies

• Goldie Hawn: high F0, high formant frequencies

F0/Formant mismatches• Source and filter characteristics are independent of each other

...and can sometimes “mismatch” in men and women:

• Julia Child: high F0, low formant frequencies

• Popeye: low F0, high formant frequencies