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Correlation and Power Spectra

Correlation and Power Spectra. Application 5. Zero-Mean Gaussian Noise. Power Spectrum. E{P n ( k )} = s 2 = 1.12 = R n (0). Auto-correlation. R n (0) = s 2 = 1.12. >> for j = 1:256, R(j) = sum(n.*circshift(n',j-1)'); end. Window Selection: Hamming. y = filter(Hamming,1,n);.

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Correlation and Power Spectra

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  1. Correlation and Power Spectra Application 5

  2. Zero-Mean Gaussian Noise

  3. Power Spectrum E{Pn(k)} = s2 = 1.12 = Rn(0)

  4. Auto-correlation Rn(0) = s2 = 1.12 >> for j = 1:256, R(j) = sum(n.*circshift(n',j-1)'); end

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

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

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

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

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

  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

  20. Window Conditions

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