Ripple Sounds

Introduction

Ripple sounds are temporal and spectral modulated sounds (or noise). They mimic some aspects of vowels. They are often used in experiments for cochlear implant users.

There are basically two methods for creating ripple sounds, which are described in detail below:

• the FFT-iFFT method
• the band-filter method

FFT-iFFT method

The FFT-iFFT method for creating rippled sounds begins by generating two copies of a broad band signal, often noise. Each copy is temporally modulated in the time domain with a sine and a cosine of the same frequency, creating two orthogonal components. Next, the FFT is applied to both modulated signals to obtain their spectra. In the spectral domain, these spectra are modulated by multiplying them sine and cosine functions. The modulated spectra are then transformed back to the time domain using the inverse FFT. The two time-domain signals are either summed or subtracted, which results in ripples that move upward or downward in frequency. Finally, these ripples are scaled by a modulation depth factor (ranging from 0 to 1) and added to the original sound, controlling the intensity of the ripples in the resulting audio.

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 above 100 Hz (half as many points as t)
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 the prefix 'cos_'.
The variables in the time domain are denoted by the suffix '_td' and variables in the frequency domain by the suffix '_fd'.

    % Calculate the number of samples and time vector    
    n             = length(signal);  
    half_n        = floor(n / 2); 
    t             = (1:n)/sampleRate;
    f             = sampleRate * (1:half_n) / n + eps; 
    octaves       = log2(f/100); % octave above 100 Hz

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

    % Create modulation for time domain
    sin_modulation_td = sin(2 * pi * ripples_per_sec * t + phi);
    cos_modulation_td = cos(2 * pi * ripples_per_sec * t + phi);        

    %apply time modulation to noise, 
    sin_modulatedSignal_td = sin_modulation_td .* broadBandSignal_td;
    cos_modulatedSignal_td = cos_modulation_td .* broadBandSignal_td;

    % perform fft 
    sin_modulatedSignal_fd = fft(sin_modulatedSignal_td);
    cos_modulatedSignal_fd = fft(cos_modulatedSignal_td);

    % Create modulation for frequency domain    
    sin_modulation_fd = sin(2 * pi * ripples_per_octave * octaves);
    cos_modulation_fd = cos(2 * pi * ripples_per_octave * octaves);
    
    % Extend the modulation functions for ifft compatibility by adding the mirrored (fliplr) signal
    extended_sin_modulation_fd = [sin_modulation_fd, fliplr(sin_modulation_fd)]; 
    extended_cos_modulation_fd = [cos_modulation_fd, fliplr(cos_modulation_fd)]; 

    % Apply frequency modulation
    sin_rippledSignal_fd = extended_sin_modulation_fd.* sin_modulatedSignal_fd;
    cos_rippledSignal_fd = extended_cos_modulation_fd.* cos_modulatedSignal_fd;
      
    % perform ifft
    sin_rippledSignal_td =  ifft(sin_rippledSignal_fd, 'symmetric');
    cos_rippledSignal_td =  ifft(cos_rippledSignal_fd, 'symmetric');

    % calculate the rippled signal
    switch rippleType
        case 'ascending'
            rippleSignal_td =   sin_rippledSignal_td + cos_rippledSignal_td;  
        case 'descending'
            rippleSignal_td = - sin_rippledSignal_td + cos_rippledSignal_td;  
    end    

    % Calculate the final rippled stimulus in the time domain          
    stimulus = broadBandSignal_td + modulationDepth * rippleSignal_td;    

N.B. It is important that you call the function 'pinknoise' only once and stored the result in broadBandSignal_time. If you instead call the function pinknoise again in the last line it gives a wrong result, because each call creates a new random array and this will destroy the necessary interference in the last line.

Band filter method

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References

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