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

• t = time domain array
• octaves = frequency domain array
• ripples_per_sec = the ripple velocity
• phi = a phase that can be added to the time modulation
• ripples_per_octave = the ripple density
• ripple_type = determines if the ripple is ascending or descending
• modulation_depth = half the amplitude of the modulation

The variables in the time domain are denoted by '_time' at the end and variables in the frequency domain by '_freq'.

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

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

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

% Apply time modulation to pink noise in the time domain
modulated_noise_sin_time = modulation_sin_time .* pink_noise_time;
modulated_noise_cos_time = modulation_cos_time .* pink_noise_time;

% Perform fft to get the signals in the frequency domain
modulated_noise_sin_freq = fft(modulated_noise_sin_time);
modulated_noise_cos_freq = fft(modulated_noise_cos_time);
  
% Apply frequency modulation in the frequency domain 
rippled_noise_sin_freq = mirrored_mod_sin_freq .* modulated_noise_sin_freq;
rippled_noise_cos_freq = mirrored_mod_cos_freq .* modulated_noise_cos_freq;   

% Perform ifft to get rippled noise in the time domain
sin_rippled_noise = ifft(sin_rippled_noise_freq , 'symmetric');
cos_rippled_noise = ifft(cos_rippled_noise_freq , 'symmetric');

% Determine the ripple type (ascending vs. descending)
switch ripple_type
    case 'ascending'
        combined_rippled_noise = sin_rippled_noise  + cos_rippled_noise;
    case 'descending'
        combined_rippled_noise = sin_rippled_noise  - cos_rippled_noise;
end 

% Calculate the final rippled stimulus          
rippled_stimulus = pink_noise + modulation_depth * combined_rippled_noise;

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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