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This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of which fall under the umbrella of local transforms.

I wonder, might there be other global transforms besides projection onto a family of orthogonal complex exponentials as with the DFT?

(I am aware of the DST and DCT, however I am looking for applicable non-sinusoidal bases).


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The Hadamard transform is an example. It uses Walsh functions as its basis. – Jason R Feb 4 '13 at 19:09
Thanks @JasonR I had forgotten about those. – Mohammad Feb 4 '13 at 19:17
For the sake of opening up discussion on this, can you define what "global" and "local" mean in the context of a transform? – user2718 Feb 5 '13 at 14:43
@BruceZenone Global in this context would mean a transformation that acts on the entire length of the signal. In other words, the entire signal is projected upon a set of bases functions. (DFT). In contrast, local transformations would be where only parts of the signal are projected upon basis functions. (DWT). – Mohammad Feb 5 '13 at 15:05

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