COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X

Page 1 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/1.jpg' width='140' height='200' /> COMPLEX (HILBERT) EOF

X: data matix

Y = X + iXH XH is the Hilbert transform of X

By CEOF:

Y = ∑ (EOF)† (PC) = {re(EOF)re(PC)+im(EOF)im(PC)} + i{-im(EOF)re(PC)+re(EOF)im(PC)}Example: HadiSSTa (50°S-50°N, 30°E-60°W), 1951-1990. Band-pass: [1,40]

Page 2 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/2.jpg' width='140' height='200' /> Page 3 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/3.jpg' width='140' height='200' /> Page 4 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/4.jpg' width='140' height='200' /> Page 5 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/5.jpg' width='140' height='200' /> Page 6 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/6.jpg' width='140' height='200' /> Page 7 <img data-url='document/complex-hilbert-eof-x-data-matix-y-x-ix-h-x-h-is-the-hilbert-transform.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: COMPLEX (HILBERT) EOF X : data matix Y = X + iX H X H is the Hilbert transform of X' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022081513/568151b6550346895dbfe5f6/html5/thumbnails/7.jpg' width='140' height='200' /> -Phase(position) + Phase(t)