Analysis and Digital Implementation of the Talk Box Effect

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 nc (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 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):

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