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

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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

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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

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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

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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

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Design Overview Problem definition: Implement in MATLAB

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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):

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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):

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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)

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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):

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Design Summary

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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

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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

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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

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