Hello,

Haar is the simplest wavelet family. It has only 2 taps. The other families contain 8 taps but with different characteristics (orthogonal, bi-orthogonal etc.). It depends on data which family is suited well. Generally research test the families with their test data different ways before selecting the suitable one.

Here is a best wavelet tutorial link where you find your answer (Part 3 and Part 4);

http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html

Thanks.

Hi Roy,

Basic simplest form of wavelet is Haar which is having two coefficients, a single vanishing moment and linear phase characteristics (perfect reconstruction). We could use this mother wavelet for an application which needs these qualities. Specifically, it would be an optimal choice for finding the location of edges. Haar/db1/sym1/biort1.1 are the same one. Other variants like db4 differs with its number of coefficients.

Hope these points would be useful.

Every wavelet is implemented through their wavelet filters(low pass and high pass).Haar is simple and the filter is having 2 coefficients in both Low pass and high pass. Harr wavelet is symmetric so that linear phase can be achieved.It is having one vanishing movement.other mentioned wavelets like Daubechies,Coiflet etc., are having more vanishing moments,not symmetric and more coefficients  both in low pass and high pass side. 

I do agree with Sudhakar Radhakrishnan. Harr wavelet is the most suitable one for wavelet analysis from our experience

Haar wavelets are "nice" in time domain (compactly supported, small support, only 2 taps), but not in frequency domain. Daubechies wavelets , sometimes called  have larger supports than that of Haar.  There are a plenty of them depending on the number of vanishing moments. 

You should read the following basic literature. These books are what I do recommend my students:

DAUBECHIES, I., 1992. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics.

BURRUS, C.S., R.A. GOPINATH and H. GUO, 1998. Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice Hall.

Haar-Wavelets are only suitable for elementary work. Usually more complex wavelets are necessary. We are working on wavelets since 12 years now and Haar-WT is really something for work on textbook level. Which kind of type you apply is strongly dependent on the application. We apply WT in image processing (document authentication) and Haar ist not applicable here, but others.

WT usage depends on the structure, topolology, etc. of your signal. This is what counts - not the simplicity of the WT.

excellent explanation Mr. Aydin Imani. I agree with you. Haar wavelet is used to detect sudden changes. The others are used to smooth the images and for texture analysis.

The basic and the simplest one is Haar wavelet, whereas daubechies , coiflet offered more efficiency in term of image parameterization and classsification.

The haar wavelet can be applied for image taken in conrolled environement, but when the image presents some noise, daubechies is well suitable;

I can add that Daubechies wavelet can be correctly applied for speech caracterization and achieved good results.

I compared these wavelets for EEG signal analysis. Haar ,Daubechies, coiflet, and symlet wavelets. According to my results for non-stationary signals instead of these wavelets biorthogonal is best for decomposing the signal.

Symlet8 contains more vanishing moment ie the filter contains 8 by 8 coefficients. In convolution process, the filter coefficients make gradual changes in intensity values it effects smoothness.

Dear Prabhakar T,

Try to read this paper there is a comparative study of four wavelet mother function which are Daubechies, Bior, coiflet, and symlet (i.e., db4, sym7, coif3, and

bior3.9)

Electroencephalogram Signals Denoising using Various Mother Wavelet Functions: A Comparative Analysis

https://dl.acm.org/citation.cfm?id=3132313

Regards.

Zaid

The main difference between these wavelet functions is due to the vanashing moments, because this property indicates that the discrete wavelet transform can be used as a differential operator. Which is very useful in the analysis of singularities. In many applications, the Haar wavelet function is very attractive because it guarantees low redundancy in the algorithm that is used. In the case that you want to apply the wavelet shrinkage algorithm to one-dimensional functions, you should look for the wavelet function that most correlates with the function being analyzed, in order to extract the information you want. I hope my answer is useful.