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# Additional Notes on Wavetable Synthesis

Additional Notes on Wavetable Synthesis. R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2003. Wavetable Frequency Control. Assume table is length N , holds one period of the signal, and the sample rate is f s Waveform frequency is f s / N. New sample every 1/f s ; Table frequency f s / N.

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## Additional Notes on Wavetable Synthesis

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1. Additional NotesonWavetable Synthesis R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2003

2. Wavetable Frequency Control • Assume table is length N, holds one period of the signal, and the sample rate is fs • Waveform frequency is fs/N New sample every 1/fs; Table frequency fs/N Wavetable (N) Wavetable Details R. C. Maher

3. Frequency Control (cont.) • In order to have a waveform frequency different than fs/N, need to re-sample the waveform: this implies sample rate conversion • Typically use a phase counter or look-up accumulator to hold current re-sampling location. LUA is incremented by the sample increment value, defined by: Wavetable Details R. C. Maher

4. Wavetable Frequency Resolution • Given an [integer:fraction] SI representation, the frequency resolution of the wavetable is determined by the number of fractional bits • Ex: N=1024, L=24, fs=48000: 2.7940x10-6 Hz • Ex: N=256, L=8, fs=48000: 0.7324 Hz Wavetable Details R. C. Maher

5. Aliasing due to resampling • The discrete-time signal represented by the wavetable has a spectrum that may occupy the entire bandwidth from 0 - fs/2 • Re-sampling the waveform to change its period can result in aliasing if the wavetable is not properly bandlimited • Aliasing generally limits how far we can “re-tune” a wavetable Wavetable Details R. C. Maher

6. Linear Interpolation • LUA fraction is used to interpolate the table. • Effectively convolving stored samples with triangle, so spectrum modified by sinc2 shape • Need to handle “end of table” issue: LUA may point to region between last stored sample and the start of the table • Distortion due to difference between “true” value and linear interpolation estimate can be audible y[L+1] y[L] L L + fract L+1 Wavetable Details R. C. Maher

7. Improved wavetable synthesis • A single stored cycle of a timbre sounds too regular, and sample rate conversion distorts spectral envelope • Generally make recordings of a real instrument at a variety of musical pitches in order to limit the amount of re-tuning • Most musical instruments have an aperiodic attack interval followed by a quasi-periodic sustain interval: synthesizer splits signal into a “one-shot” attack spliced to a looped sustain • Modulate SI and amplitude with some vibrato, tremolo, and random fluctuations Wavetable Details R. C. Maher

8. Wavetable Synthesizer Attack Wavetable Looped Wavetable Gain Multiplier Sample Increment (SI) Envelope Modulate with sinusoid for vibrato Wavetable Details R. C. Maher

9. Other enhancements • Layer multiple wavetables • Stereo wavetables • Add a dynamic filter • Velocity dependence • Pitch dependence • Other real time controls Wavetable Details R. C. Maher

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