Input: N - wavetable size. It's recomanded to be a power of 2. This is, usually, a big number (like 262144) samplerate - the samplerate (e.g. 44100) f - frequency of the fundamental note (e.g. 440) bw - bandwidth of first harmonic in cents (e.g. 50 cents) must be greater than zero number_harmonics - the number of harmonics. Of course, number_harmonics<(samplerate/f) A[1..number_harmonics] - amplitude of the harmonics Output smp[0..N-1]- the generated wavetable Internal variables freq_amp[0..N/2-1] = {0,0,0,0,...,0} freq_phase[0..N/2-1] etc... Functions RND() returns a random value between 0 and 1 IFFT() is the inverse fourier transform normalize_sample() normalizes samples profile(fi,bwi){ x=fi/bwi; return exp(-x*x)/bwi; }; Steps FOR nh = 1 to number_harmonics bw_Hz=(pow(2,bw/1200)-1.0)*f*nh; bwi=bw_Hz/(2.0*samplerate); fi=f*nh/samplerate; FOR i=0 to N/2-1 hprofile=profile((i/N)-fi,bwi); freq_amp[i]=freq_amp[i]+hprofile*A[nh]; ENDFOR ENDFOR FOR i=0 to N/2-1 freq_phase[i]=RND()*2*PI; ENDFOR smp=IFFT(N,freq_amp,freq_phase); normalize_sample(N,smp); OUTPUT smp The differences between the extended algorithm and the basic algorithm are minor: There is an additional parameter: bwscale: that specify how much the bandwidth of the harmonic increase according to its frequency. Also, there is defined a function called relF(N) who returns the relative frequency of the N'th overtone. It allows to generate detuned harmonics or even metallic sounds (like bells). The difference between the basic algorithm is at the computation of bw_Hz and fi: bw_Hz=(pow(2.0,bw/1200.0)-1.0)*f*pow(relF(nh),bwscale); fi=f*relF(nh)/samplerate; If the relF(N) function returns N and the bwscale is equal to 1, this algorithm will be equivalent to the basic algorithm. Graphs of the (basic algorithm) freq_amp array for N=262144, f=500 Hz, bw=100 cents, samplerate=44.1 kHz, and A[] where A[n]=1.0/sqrt(n)
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