ELEC484Phase Vocoder

Kelley Fea

Overview

Analysis Phase Synthesis Phase Transformation Phase

Time Stretching Pitch Shifting Robotization Whisperation To Do

Denoising Stable/Transient Components Separation

Analysis Phase

Analysis Phase

Based on Bernardini’s documentpv_analyze.m

Inputs: inx, w, Ra Uses hanningz.m to create window Modulates signal with window Performs FFT and fftshift Outputs: Mod_y, Ph_y

(Moduli and Phase)

pv_analyze.m

function [Mod_y, Ph_y] = pv_analyze(inx, w, Ra)% pv_analyze.m for ELEC484 Project Phase 1% Analysis phase... based on Bernardini% inx = original signal% w = desired window size% Ra = analysis hop size % Get size of inx; store rows and columns separately[xrow, xcolumn] = size(inx); % Create Hanning window% using the hanningz code found in Bernardiniwin = hanningz(w);

pv_analyze.m

% Figure out the number of windows requirednum_win = ceil( (xrow - w + Ra) / Ra ); % Matrix for storing time slices (ts)ts = zeros(w, num_win); % Modulation of the signal with the window happens herecount = 1;for i = 0:num_win% the frame ends... frame_end = w - 1;

pv_analyze.m

% checks to see where the end of the frame should be% if the count + frame_end goes outside of the size limitations do... if ( count + frame_end >= size(inx,1)) frame_end = size(inx,1) - count; end% determine where the end of the window is win_end = frame_end+1;% Set value of the time slice to match the windowed segment ts = inx( count : count + frame_end ) .* win( 1 : win_end );

pv_analyze.m

% FFT value of ts using fftshift which moves zero frequency component

Y( 1 : win_end,i+1 ) = fft( fftshift(ts) );% Increment count by hop size count = count + Ra;end % End for loop

% Set output values for Moduli and Phase and return the matricesMod_y = abs(Y);Ph_y = angle(Y);end % End ph_analyze.m

Synthesis Phase

Synthesis Phase

Also based on Bernardini’s documentpv_synthesize.m

Inputs: Mod_y, Ph_y, w, Rs, Ra Uses hanningz.m to create window Calculates difference between actual and target

phases (delta phi) Recombines Moduli and Phase into Array of

complex numbers

Synthesis Phase

Performs IFFT and Overlap add Sum all samples using tapering window Final result is divided by absolute of the maximum

value Output: outx

pv_synthesize.m

function outx = pv_synthesize( Mod_y, Ph_y, w, Rs, Ra )% pv_synthesize.m for ELEC484 Project Phase 1 % Set number of bins and frames based on the size of the phase

matrix[ num_bins, num_frames ] = size (Ph_y);% Set matrix delta_phi to roughly the same size as the phase matrixdelta_phi = zeros( num_bins, num_frames-1 );% PF same size as Ph_yPF = zeros( num_bins, num_frames );% Create tapering windowwin = hanningz(w);

pv_synthesize.m

% Phase unwrapping to recover precise phase value of each bin% omega is the normal phase increment for Ra for each binomega = 2 * pi * Ra * [ 0 : num_bins - 1 ]' / num_bins; for idx = 2 : num_frames ddx = idx-1;% delta_phi is the difference between the actual and target phases% pringcarg is a separate function delta_phi(:,ddx) = princarg(Ph_y(:,idx)-Ph_y(:,ddx)-omega);% phase_inc = the phase increment for each bin phase_inc(:,ddx)=(omega+delta_phi(:,ddx))/Ra;end % End for loop

pv_synthesize.m

% Recombining the moduli and phase...% the initial phase is the samePh_x(:,1) = Ph_y(:,1); for idx = 2:num_frames ddx = idx - 1; Ph_x(:,idx) = Ph_x(:,ddx) + Rs * phase_inc(:,ddx);end% Recombine into array of complex numbersZ = Mod_y .* exp( i * Ph_x );% IFFT and overlap add% Create X of specified sizeX = zeros( ( num_frames * Rs ) + w, 1);

pv_synthesize.m

count = 1;for idx = 1:num_frames endx = count + w - 1; real_ifft = fftshift( real( ifft( Z(:,idx) ))); X( [count:endx] )= X(count:endx) + real_ifft .* win; count = count + Rs;end % sum of all samples multiplied by tapering windowk = sum( hanningz(w) .* win ) / Rs;X = X / k;% Dividing by the maximum keeps things in proportionoutx = X/abs(max(X));end % end ph_synthesize.m

hanningz.m

Used because hann() gives incorrect periodicity:

w = .5*(1 - cos(2*pi*(0:n-1)'/(n)));

princarg.m

Returns the principal argument of the nominal initial phase of each frame

a=Phasein/(2*pi);k=round(a);Phase=Phasein-k*2*pi;

Cosine Wave Test 1 (w = Ra = Rs)

Cosine Wave Test 1 (w = Ra = Rs)

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Spectrum of Waveforms For Circular Convolution

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Cosine Wave (Ra = Rs = w/8)

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Waveforms For Circular Convolution

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Cosine Wave – Zoom

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Waveforms For Circular Convolution

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Toms Diner

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Waveforms For Circular Convolution

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Piano

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Waveforms For Circular Convolution

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Figure 8.1 (DAFX)

Time Stretching

Modify hop size ratio between analysis (Ra) and synthesis (Rs)

% Analysis function[Mod_y, Ph_y] = pv_analyze(inx, w, Ra);% Do Time Shifting here %% Modify hop size ratio hop_ratio = Rs / Ra;hop_ratio = 2;Rs = hop_ratio * Ra;% Synthesis functionX2 = pv_synthesize( Mod_y, Ph_y, w, Rs, Ra );

Ratio = Rs/Ra = 0.5

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Waveforms For Time Stretching - 0.5

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Toms Diner

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Waveforms For Time Stretching - 0.5

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Piano

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Waveforms For Time Stretching - 0.5

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Ratio = Rs/Ra = 2

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Waveforms For Time Stretching - 2

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Toms Diner

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Waveforms For Time Stretching - 2

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Piano

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Waveforms For Time Stretching - 2

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Pitch Shifting

Attempted to multiply a factor by the phase

Pitch Shifting

% Analysis function[Mod_y, Ph_y] = pv_analyze(inx, w, Ra);% Do Pitch Shifting here %Ph_y = princarg(Ph_y*1.5);% Synthesis functionX4 = pv_synthesize( Mod_y, Ph_y, w, Rs, Ra );

Pitch Shifting – Cosine

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Waveforms For Pitch Shifting - 0.5

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Pitch Shifting – Toms Diner

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Waveforms For Pitch Shifting - 0.5

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Pitch Shifting – Piano

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Waveforms For Pitch Shifting - 0.5

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Robotization

Set phase (Ph_y) to zero

% Analysis function

[Mod_y, Ph_y] = pv_analyze(inx, w, Ra);

% Do Robotization here %

Ph_y = zeros(size(Ph_y));

% Synthesis function

xout = pv_synthesize( Mod_y, Ph_y, w, Rs, Ra );

Robotization – Cosine

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Waveforms For Robotization

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Robotization – Toms Diner

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Waveforms For Robotization

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Robotization – Piano

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Waveforms For Robotization

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Whisperization

deliberately impose a random phase on a time-frequency representation

% Analysis function

[Mod_y, Ph_y] = pv_analyze(inx, w, Ra);

% Do Whisperization here %

Ph_y = ( 2*pi * rand(size(Ph_y, 1), size(Ph_y, 2)) );

% Synthesis function

xout = pv_synthesize( Mod_y, Ph_y, w, Rs, Ra );

Whisperization – Cosine

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Waveforms For Whisperization

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Whisperization – Toms Diner

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Waveforms For Whisperization

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Whisperization – Piano

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Waveforms For Whisperization

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Denoising

emphasize some specific areas of a spectrum

Stable Components Separation

Calculate the instantaneous frequency by making the derivative of the phase along the time axis.

Check if this frequency is within its “stable range”.

Use the frequency bin or not for the reconstruction.

Transient Components Separation

Conclusion

Rest of effects need to be properly implemented:Stable/Transient Components SeparationDenoising

Questions?

Thank you!