1 / 15

I is the unit matrix and  are the EOFs

I is the unit matrix and  are the EOFs. Eigenvalue problem corresponding to a linear system:. Sometimes use another complex form of EOFS. Apply the Hilbert Transform of U to understand a bit more about the phase of propagation of the phenomenon.

ryu
Download Presentation

I is the unit matrix and  are the EOFs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. I is the unit matrix and  are the EOFs Eigenvalue problemcorresponding to a linear system:

  2. Sometimes use another complex form of EOFS. Apply the Hilbert Transformof U to understand a bit more about the phase of propagation of the phenomenon In essence, the Hilbert transform of a signal (time series) produces a complex variable with real part identical to the time series and the imaginary part is shifted 90º from the original (sometimes called the analytical signal): >> t=[1:1:1000]; >> u1=sin(2*pi*t/200); >> plot(t,u1,’LineWidth’,3) u1 t

  3. >> t=[1:1:1000]; >> u1=sin(2*pi*t/200); >> plot(t,u1,’LineWidth’,3) >> >> u2=hilbert(u1); >> hold on; >> plot(real(u2),'r--','LineWidth',3) u t

  4. >> t=[1:1:1000]; >> u1=sin(2*pi*t/200); >> plot(t,u1,’LineWidth’,3) >> >> u2=hilbert(u1); >> hold on >> plot(real(u2),'r--','LineWidth',3) >> plot(imag(u2),'g','LineWidth',3) u t

  5. Hilbert Transformof U can be regarded as the convolution of U with h(t) = 1/(t) P is the Cauchy principal value (assigns values to improper integrals) • hilbert uses a four-step algorithm: • 1. It calculates the FFT of the input sequence, storing the result in a vector x. • 2. It creates a vector h whose elements h(i) have the values: • 1 for i = 1, (n/2)+1 • 2 for i = 2, 3, ... , (n/2) • 0 for i= (n/2)+2, ... , n • 3. It calculates the element-wise product of x and h. • 4. It calculates the inverse FFT of the sequence obtained in step 3 and returns the first n elements of the result.

  6. Echo Intensity in a Fjord

  7. Mean Profile 10 log (echo)

  8. Anomaly from Mean

  9. 18% 60% 9%

  10. Hilbert EOF 18% 6% 64%

More Related