Ripple Sounds

Introduction

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FFT-iFFT method

Below is an example of an implementation in matlab. It is based on a broadband signal consisting of pink noise. The input parameters are:

Term	Description
t	time domain array in seconds
octaves	frequency domain array in octaves
ripples_per_sec	the ripple velocity in the time domain
phi	a phase that can be added to the time modulation
ripples_per_octave	the ripple density in the frequency domain
rippleType	determines if the ripple is ascending or descending
modulationDepth	half the amplitude of the modulation

The variables that are sin modulated are denoted by the prefix 'sin_', the cos modulated by '_cos'.
The variables in the time domain are denoted by the suffix '_time' and variables in the frequency domain by the suffix '_freq'.

% Generate array with pink noise
pinkNoise_time = pinknoise(length(t));

% Create modulation functions for time domain (velocity modulation)
sin_modulation_time = sin(2 * pi * ripples_per_sec * t + phi);
cos_modulation_time = cos(2 * pi * ripples_per_sec * t + phi);        

% Create modulation functions for frequency domain (density modulation)
sin_modulation_freq = sin(2 * pi * ripples_per_octave * octaves);
cos_modulation_freq = cos(2 * pi * ripples_per_octave * octaves);
    
% Mirror the frequency modulation components for ifft compatibility
sin_modulation_freq = [sin_modulation_freq, fliplr(sin_modulation_freq)];
cos_modulation_freq = [cos_modulation_freq, fliplr(cos_modulation_freq)];

% Apply time modulation to pink noise in the time domain
sin_modulatedNoise_time = sin_modulation_time .* pinkNoise_time;
cos_modulatedNoise_time = cos_modulation_time .* pinkNoise_time;

% Perform fft to convert the signals to the frequency domain
sin_modulatedNoise_freq = fft(sin_modulatedNoise_time);
cos_modulatedNoise_freq = fft(cos_modulatedNoise_time);
  
% Apply frequency modulation in the frequency domain 
sin_rippledNoise_freq = sin_modulation_freq .* sin_modulatedNoise_freq;
cos_rippledNoise_freq = cos_modulation_freq .* cos_modulatedNoise_freq;   

% Perform ifft to get rippled noise in the time domain
sin_rippledNoise_time = ifft(sin_rippledNoise_freq, 'symmetric');
cos_rippledNoise_time = ifft(cos_rippledNoise_freq, 'symmetric');

% Determine the ripple type (ascending vs. descending)
switch rippleType
    case 'ascending'
        combinedRippledNoise_time = sin_rippledNoise_time + cos_rippledNoise_time;
    case 'descending'
        combinedRippledNoise_time = sin_rippledNoise_time - cos_rippledNoise_time;
end 

% Calculate the final rippled stimulus in the time domain          
rippledStimulus_time = pinkNoise_time + modulationDepth * combinedRippledNoise_time;

N.B. when the density is zero 'rippled_noise' by itself has an envelope of a rectified sine wave (which has double the velocity). Only after adding the original noise the envelope is the correct one.

Band filter method

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References

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