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

    % Generate array with pink noise
pink_noise = pinknoise(n);

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

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

% Apply time modulation to pink noise
modulated_noise_sin_time = time_modulation_sin .* pink_noise;
modulated_noise_cos_time = time_modulation_cos .* pink_noise;

% Perform FFT  
fft_sin_modulated_noise_time = fft(modulated_noise_sin_time);
fft_cos_modulated_noise_time = fft(modulated_noise_cos_time);
  
% Apply frequency modulation 
fft_modulated_noise_sin_time_freq = mirrored_freq_mod_sin .* fft_sin_modulated_noise_time;
fft_modulated_noise_cos_time_freq = mirrored_freq_mod_cos .* fft_cos_modulated_noise_time;   

% Perform IFFT to get rippled noise in the time domain
sin_rippled_noise = ifft(fft_modulated_noise_sin_time_freq, 'symmetric');
cos_rippled_noise = ifft(fft_modulated_noise_cos_time_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 modulated 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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