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Smooth random LFO Generator

References : Posted by Rob Belcham

Notes :
I've been after a random LFO that's suitable for modulating a delay line for ages ( e.g for chorus / reverb modulation) , so after i rolled my own, i thought i'd better make it my first contribution to the music-dsp community.

My aim was to achive a sinusoidal based random but smooth waveform with a frequency control that has no discontinuities and stays within a -1:1 range. If you listen to it, it sounds quite like brown noise, or wind through a microphone (at rate = 100Hz for example)

It's written as a matlab m function, so shouldn't be too hard to port to C.

The oscillator generates a random level stepped waveform with random time spent at each step (within bounds). These levels are linearly interpolated between and used to drive the frequency of a sinewave. To achive amplitude variation, at each zero crossing a new random amplitude scale factor is generated. The amplitude coefficient is ramped to this value with a simple exponential.

An example call would be,
t = 4; Fs = 44100;
y = random_lfo(100, t*Fs, Fs);
axis([0, t*Fs, -1, 1]);
plot(y)

Enjoy !


Code :
% Random LFO Generator
% creates a random sinusoidal waveform with no discontinuities
% rate = average rate in Hz
% N = run length in samples
% Fs = sample frequency in Hz
function y = random_lfo(rate, N, Fs)

step_freq_scale = Fs / (1*rate);
min_Cn = 0.1 * step_freq_scale;
An = 0;
lastA = 0;
Astep = 0;
y = zeros(1,N); % output
x = 0; % sine phase
lastSign = 0;
amp_scale = 0.6;
new_amp_scale = 0.6;
amp_scale_ramp = exp(1000/Fs)-1;
for (n=1:N)
if (An == 0) || (An>=Cn)
% generate a new random freq scale factor
Cn = floor(step_freq_scale * rand());
% limit to prevent rapid transitions
Cn = max(Cn, min_Cn);
% generate new value & step coefficient
newA = 0.1 + 0.9*rand();
Astep = (newA - lastA) / Cn;
A = lastA;
lastA = newA;
% reset counter
An = 0;
end
An = An + 1;
% generate output
y(n) = sin(x) * amp_scale;
% ramp amplitude
amp_scale = amp_scale + ( new_amp_scale - amp_scale ) * amp_scale_ramp;
sin_inc = 2*pi*rate*A/Fs;
A = A + Astep;
% increment phase
x = x + sin_inc;
if (x >= 2*pi)
x = x - 2*pi;
end
% scale at each zero crossing
if (sign(y(n)) ~= 0) && (sign(y(n)) ~= lastSign)
lastSign = sign(y(n));
new_amp_scale = 0.25 + 0.75*rand();
end;
end;



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