1. Analysis and Digital Implementation of the Talk Box Effect Yuan Chen Advisor: Professor Paul Cuff

2. Introduction  What is a talk box?  Allows a musician to add diction and intelligibility to an instrument’s sound  Motivation?  Popular as an analog device  Application of signal processing  Goals?  Analyze output  Digital implementation Figure 1 – Talk Box

3. Background – Speech and Intelligibility  Human speech production of convolution between source and filter (1)  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

4. 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):  Apply a low quefrency lifter to separate source and filter

5. 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

6. Design Overview  Problem definition:  Implement in MATLAB

7. Vocal Tract Impulse Response Extraction  Calculate cepstrum (eq. 3):  Lifter: Eliminate all quefrency above cutoff n c (eq. 4)  From liftered cepstrum, invert to calculate impulse/frequency response (eq. 5):

8. 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):

9. 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)

10. Synthesis  From causality, output at time n 0 depends only on input occurring no later than n 0  From finite-length impulse response, output at time n 0 depends only on input occurring no earlier than n 0 – M + 1  Closed Form expression for y(n) (eq.11):

11. Design Summary

12. 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

13. 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

14. 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