Sub-Space Filtering

Subspace filtering is a technique used in audio processing to separate a mixture of signals into its individual components.

Applications

1. source separation

2. noise reduction

3. speech enhancement

4. audio compression

The below Figures are in this format

Activity 7

Sub-Space Filtering

[data, Fs] = audioread('sarigamapa.wav');

Time = audioinfo ('sarigamapa.wav').Duration;

N = 10;

signal = data (:,1);

XX = buffer (signal,N,N-1);

X = XX(:,10: end);

S = cov (X');

[V,D] = eigs (S,10);

figure (01);

bar (diag (D))

title('Dominant Eigen Values - diag (D)')

figure (02);

bar (log (diag (D)))

title ('Dominant Eigen Values log (diag (D) ')

eigen_idx = 1

Xhat = V(:,eigen_idx)'*X;

figure (03);

subplot (1,2,1); pspectrum (data (:,1),Fs, 'spectrogram'); title('Before Sub-Space Filtering')

subplot (1,2,2); pspectrum (Xhat, Fs, 'spectrogram'); title('After Sub-Space Filtering')

figure (04);

freqz (1,V(:,eigen_idx))

plot_points = 100000

scatter(signal(1:plot_points)',Xhat(1:plot_points),5)

xlabel('Reconstructed Signal')

ylabel('Orginal Signal')

title('Correlation of Reconstructed Signal and Orginal Signal')

hold on

plot([-0.5,0,0.5],[-0.5,0,0.5],'LineWidth',2,'DisplayName','Y=X Line')

legend('Location','best')

grid on

% audio write

filename = "recontructed_eigen-Filters_3.wav";

audiowrite (filename, Xhat, Fs);

filename = "recontructed_eigen-Filter_1.wav";

audiowrite (filename, Xhat, Fs);

Reference

https://asp-eurasipjournals.springeropen.com/articles/10.1155/2007/45821

https://link.springer.com/chapter/10.1007/3-540-27489-8_7