L34: Noise and Signal

1. L34: Noise and Signal

2. Announcements • Away next Friday, the class will be taught by …. • No office hours next Wednesday • Assignment 4

3. Smoothing functions • Audio processing • Image processing

4. What does this code do? t=linspace(0,2*pi,101); y=sin(t); y=sin(t)+0.1*(rand(size(t))-0.5); y_mod=y; for i=2:length(t)-1 y_mod(i)=(y(i-1)+y(i)+y(i+1))/3; end

5. Noise vs Signal plots plot(t,y); hold on; plot(t,y_mod,’r’);

6. Other ways of smoothing • Vector additions y_mod=y; y_mod(2:end-1)=(y(1:end-2)+y(2:end-1)+y(3:end))/3; • Convolution/Filtering y_mod=imfilter(y,[1 1 1]/3);

7. What does this code do? t=linspace(0,2*pi,101); y=sin(t)+0.1*(rand(size(t))-0.5); y_mod=y; for i=2:length(t)-1 y_mod(i)=y(i)-y(i-1); end plot(t,y_mod);

8. Other ways of doing the same thing • Vector minus y_mod=y; y_mod(2:end)=y(2:end)-y(1:end-1); • Convolution/Filtering y_mod=imfilter(y,[-1 1]);

9. Takeaways • Averaging smoothens i.e. suppresses high frequency jitter • Differentiating amplifies noise i.e. suppresses low frequency signal

10. Audio processing • Reading in a wav file • [audio_var,fs]=wavread(‘hootie.wav’); • Audio variables are just two column matrices: first column is the left channel and the second column is the right channel • Playing audio • soundsc(audio_var,fs); • soundsc(audio_var(:,1),fs); %plays left channel

11. Vector operations on audio files left=audio_var(:,1); right=audio_var(:,2); plot(left) soundsc(left(end:-1:1,:),fs)

12. Adding echo N=10000; left_echo=left; for i=N+1:length(left) left_echo=left(i)+left(i-N); end

13. Removing vocals • Vocals are, in general, recorded on both the left and right channel. So…. • soundsc(left-right, fs)

14. High frequency (noise) and low frequency (signal) • Suppressing high frequency (smoothing) left_smooth=imfilter(left,ones(10,1)); • Suppressing low frequency (differentiating) left_der=left(2:end)-left(1:end-1);