1. Additional Notes on Wavetable Synthesis R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2002

2. ECEN4002 Spring 2002Wavetable Details R. C. Maher2 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 Wavetable (N) New sample every 1/f s ; Table frequency f s /N

3. ECEN4002 Spring 2002Wavetable Details R. C. Maher3 Frequency Control (cont.) In order to have a waveform frequency different than f s /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:

4. ECEN4002 Spring 2002Wavetable Details R. C. Maher4 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, f s =48000: 2.7940x10 -6 Hz Ex: N=256, L=8, f s =48000: 0.7324 Hz

5. ECEN4002 Spring 2002Wavetable Details R. C. Maher5 Aliasing due to resampling The discrete-time signal represented by the wavetable has a spectrum that may occupy the entire bandwidth from 0 - f s /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

6. ECEN4002 Spring 2002Wavetable Details R. C. Maher6 Linear Interpolation LUA fraction is used to interpolate the table. Effectively convolving stored samples with triangle, so spectrum modified by sinc 2 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 LL+1L + fract y[L+1] y[L]

7. ECEN4002 Spring 2002Wavetable Details R. C. Maher7 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

8. ECEN4002 Spring 2002Wavetable Details R. C. Maher8 Wavetable Synthesizer Sample Increment (SI) Looped Wavetable Envelope Gain Multiplier Modulate with sinusoid for vibrato Attack Wavetable

9. ECEN4002 Spring 2002Wavetable Details R. C. Maher9 Other enhancements Layer multiple wavetables Stereo wavetables Add a dynamic filter Velocity dependence Pitch dependence Other real time controls