### Analysis and Digital Implementation of the Talk

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