- #1
ramdas
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- 0
Hello everyone have a look at this video of Fourier Decomposition of an image.also we know that Fourier series is given in the image as
http://data:image/jpeg;base64,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
Here in the above formula there are summation terms of cosine and sine functions.I want to ask few queries regarding it.
1.In the given video at bottom middle there is plot of extracted waves .My doubt is whether these waves means cosine (or sine) functions from the summation terms of the Fourier series formula?
2.Whether these images(plot of Extracted waves ) are called as basis images(functions) in mathematics?
Note: Although above Fourier Formula is for 1D signal and video is of 2D image,please keep in mind Fourier series formula for 2D signal.
http://data:image/jpeg;base64,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
Here in the above formula there are summation terms of cosine and sine functions.I want to ask few queries regarding it.
1.In the given video at bottom middle there is plot of extracted waves .My doubt is whether these waves means cosine (or sine) functions from the summation terms of the Fourier series formula?
2.Whether these images(plot of Extracted waves ) are called as basis images(functions) in mathematics?
Note: Although above Fourier Formula is for 1D signal and video is of 2D image,please keep in mind Fourier series formula for 2D signal.