1. Correlation and Power Spectra Application 5

2. Zero-Mean Gaussian Noise

3. Power Spectrum E{P n  k  2 = 1.12 = R n (0)

4. Auto-correlation >> for j = 1:256, R(j) = sum(n.*circshift(n',j-1)'); end R n  2 = 1.12

5. Window Selection: Hamming y = filter(Hamming,1,n);

6. Hamming Filtered Power Spectrum

7. White Noise Auto-Covariance vs. Hamming Filtered Noise

8. 2D Power Spectra and Filtering Application 4

9. Image Noise Field Autocovariance Filtered N_autocov = xcorr2(Noiseimage); figure;imagesc(N_autocov/(128*128));colormap(gray);axis('image')

10. Image Noise Field Power Spectrum Unfiltered figure;imagesc(fftshift(abs(fft2(N_autocov/(128*128)))));colormap(gray);axis('image')

11. Image Noise Field Autocovariance Filtered (wc = 0.6; order 20; Hamming Window) N_autocov = xcorr2(Noiseimage_filtered); figure;imagesc(N_autocov/(128*128));colormap(gray);axis('image')

12. Image Noise Field Power Spectrum Filtered (wc = 0.6; order 20; Hamming Window) N_autocov = xcorr2(Noiseimage_filtered); figure;imagesc(N_autocov/(128*128));colormap(gray);axis('image')

13. Image Filtered Image Filtered (wc = 0.6; order 20; Hamming Window) Rose_filtered = filter2(Z,Roseimage,'same');

14. Application 5 Type “sptool” Load in signal –Import into sptool: startup.spt as a “signal” –Sampling frequency is 1kHz (i.e. Fs = 1000) View signal Back to startup.spt, under “spectra” hit create and view. Analyze spectrum as described in the Application

15. Step 1: Load in signal

16. View Signal

17. Create and View Spectrum

18. Measure frequency content

19. Window Conditions