discrete-time wavelet transform vs discrete wavelet transform vs integer wavelet transform

Hi,

I am very confused about the names of discrete wavelet transform and I
don't know what to do.

In the book "Wavelets and subband coding" and in the book "Introduction
to data compression"
says that the discrete-time wavelet transform is a wavelet series that
uses continuous function but the corresponing transform is discrete.
The discrete wavelet transform is the one that everything is
discrete.in the book "Data compression the complete reference" the
writer inserts another transform the integer wavelet transform. Is the
integer wavelet transform the same with the discrete wavelet transform?
I've seen also and the name fast wavelet transform. I am very confused.
In the website "A Really Friendly Guide to wavelets" I think that the
writer with the phrase "discrete wavelet transform" means the
discrete-time wavelet transform. WHICH IS FINALLY THE DISCRETE WAVELET
TRANSFORM????? PLEASE HELP!

leonadavinci@gmail.com wrote:

> Hi,
> 
> I am very confused about the names of discrete wavelet transform and I
> don't know what to do.
> 
> In the book "Wavelets and subband coding" and in the book "Introduction
> to data compression"
> says that the discrete-time wavelet transform is a wavelet series that
> uses continuous function but the corresponing transform is discrete.
> The discrete wavelet transform is the one that everything is
> discrete.in the book "Data compression the complete reference" the
> writer inserts another transform the integer wavelet transform. Is the
> integer wavelet transform the same with the discrete wavelet transform?
> I've seen also and the name fast wavelet transform. I am very confused.
> In the website "A Really Friendly Guide to wavelets" I think that the
> writer with the phrase "discrete wavelet transform" means the
> discrete-time wavelet transform. WHICH IS FINALLY THE DISCRETE WAVELET
> TRANSFORM????? PLEASE HELP!

I think the discrete-time wt is used to mean wavelet transform of continuous
signals with discrete sampling. I.e you calculate the inner product
(integral) at discrete points in time and scale. 

In discrete wavelet transform you only calculate the inner products of the
continuous signal and the scaling function at one scale and for discrete
points in time. From there on you use discrete dyadic filter bank to
calculate the rest of the decomposition (i.e approx and detail coefficients
for the rest of the scales). This is also referred to as Fast Wavelet
Transform.

-- 
Jani Huhtanen
Tampere University of Technology, Pori

Jani Huhtanen wrote:
> leonadavinci@gmail.com wrote:
>
> > Hi,
> >
> > I am very confused about the names of discrete wavelet transform and I
> > don't know what to do.
> >
> > In the book "Wavelets and subband coding" and in the book "Introduction
> > to data compression"
> > says that the discrete-time wavelet transform is a wavelet series that
> > uses continuous function but the corresponing transform is discrete.
> > The discrete wavelet transform is the one that everything is
> > discrete.in the book "Data compression the complete reference" the
> > writer inserts another transform the integer wavelet transform. Is the
> > integer wavelet transform the same with the discrete wavelet transform?
> > I've seen also and the name fast wavelet transform. I am very confused.
> > In the website "A Really Friendly Guide to wavelets" I think that the
> > writer with the phrase "discrete wavelet transform" means the
> > discrete-time wavelet transform. WHICH IS FINALLY THE DISCRETE WAVELET
> > TRANSFORM????? PLEASE HELP!
>
> I think the discrete-time wt is used to mean wavelet transform of continuous
> signals with discrete sampling. I.e you calculate the inner product
> (integral) at discrete points in time and scale.
>
> In discrete wavelet transform you only calculate the inner products of the
> continuous signal and the scaling function at one scale and for discrete
> points in time. From there on you use discrete dyadic filter bank to
> calculate the rest of the decomposition (i.e approx and detail coefficients
> for the rest of the scales). This is also referred to as Fast Wavelet
> Transform.
>
> --
> Jani Huhtanen
> Tampere University of Technology, Pori

Is there any good book that explain these things?

leonadavinci@gmail.com wrote:

> 
> Jani Huhtanen wrote:
>> leonadavinci@gmail.com wrote:
/* snip */
> 
> Is there any good book that explain these things?

I learned basics of wavelets from "Wavelets and Filter Banks by Gilbert
Strang, Truong Nguyen" 
http://www.amazon.com/gp/product/0961408871/102-4667879-7500913?v=glance&n=283155

It explains these things quite well, but requires also some work from the
reader. But there should be better books out there (I hope). I suggest you
take a trip to your local/uni library.

-- 
Jani Huhtanen
Tampere University of Technology, Pori