Take the 2-minute tour ×
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It's 100% free, no registration required.

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).

Thanks!

share|improve this question
4  
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
1  
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
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.