Transcript Analysis and Digital Implementation of the Talk

Analysis and Digital Implementation
of the Talk Box Effect
Yuan Chen
Advisor: Professor Paul Cuff
Introduction
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What is a talk box?
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Motivation?
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Allows a musician to add
diction and intelligibility to
an instrument’s sound
Popular as an analog device
Application of signal
processing
Goals?
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Analyze output
Digital implementation
Figure 1 – Talk Box
Background – Speech and Intelligibility
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Human speech production of convolution between
source and filter (1)
s(n)  e(n)  (n)
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Not really time invariant
Only valid for voiced speech
Frequencies of formant peaks account for intelligibility of
speech (Lingard, McLoughlin)
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Most important are F2, F3 formants which occur in frequency
band 800 Hz – 3 kHz
Complex Cepstrum
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Formant peaks arise from  , need a way to “deconvolve”
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Intuitively source excitation varies quickly in frequency,
vocal tract response varies slowly in frequency (Deller)
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Complex Cepstrum (eq. 2) (Deller):
1
 s ( n) 
2
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  log S ( )e

jn
d
Apply a low quefrency lifter to separate source and filter
Analysis Results – Vowel Sounds
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Talk box most successfully impresses F2, F3 peaks
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Relative Error in peak frequency: F1 – 19.6%, F2 – 9.33%, F3 –
6.22%
Error due to inability to replicate sound
For voice, ~90% of energy in 0 Hz – 1000 Hz
For talk box, ~10% of energy in 0 Hz – 1000 Hz
Design Overview
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Problem definition:
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Implement in MATLAB
Vocal Tract Impulse Response Extraction
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Calculate cepstrum (eq. 3):
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Lifter: Eliminate all quefrency above cutoff nc (eq. 4)
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From liftered cepstrum, invert to calculate
impulse/frequency response (eq. 5):
Impulse Response Preprocessing
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Calculated impulse response has too high low frequency
(0 – 1000 Hz) magnitude
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Different frames of speech have different energy levels
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Speech input should not directly determine output amplitude
Normalize, preprocess in frequency domain (eq. 6):
Synthesis
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50% overlap between successive frames
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Define system response to be linear interpolation of
vocal tract impulse responses in overlapping region (eq.
7):
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α: relative index (eq. 8)
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p: frame index (eq. 9)
Synthesis
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From causality, output at time n0 depends only on input
occurring no later than n0
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From finite-length impulse response, output at time n0
depends only on input occurring no earlier than
n0 – M + 1
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Closed Form expression for y(n) (eq.11):
Design Summary
Performance
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F2, F3 peaks on vowel speech inputs:
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Static implementation relative error: 3.0% F2, 3.5% F3
Dynamic implementation relative error: 3.7% F2, 3.2% F3
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Qualitatively, output has similar intelligibility to analog talk
box
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Dynamic implementation can produce voiced non-vowel
phonemes and whole words
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Not always consistent, depends on alignment in time
Performance Issues
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Even with linearly-interpolated system impulse response,
noticeable transitions between frames
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Computationally expensive: 2 FFTs, 2 IFFTs per frame
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In MATLAB, computation time takes longer than duration of
the frame
Performance dependent on alignment of input signals
Conclusions and Further Considerations
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Dynamic implementation closely models performance of
analog talk box:
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Can produce vowels and voiced phonemes
Real-time setup
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Demonstrate possibility of fully digital implementation of
talk box using speech input
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Further considerations:
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Improve transitions between frames
Decrease calculation time
Physical implementation