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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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**Additional NotesonWavetable 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 fs • Waveform frequency is fs/N New sample every 1/fs; Table frequency fs/N Wavetable (N) Wavetable Details R. C. Maher**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**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**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**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**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**Wavetable Synthesizer**Attack Wavetable Looped Wavetable Gain Multiplier Sample Increment (SI) Envelope Modulate with sinusoid for vibrato Wavetable Details R. C. Maher**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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