doubt on the W-suffix-0(W0)

[sanjayras...@gmail.com]

Hi,

I have a question about what is happening in this video at 00:06:39 -

http://www.youtube.com/watch?v=vFqfjYXNM2k#t=399s.

what Wo means in the above discussion? so far, we have discussed about Vo ,where does this Wo suddenly comes from? it is said in the lecture that Wo is linear combination of psi translated in time. I understand it like, the approximation function of the actual function in unit time interval, whereas Vo as, space which contains functions to express the additional information when the actual function is resolved in a unit time interval. As suffix changes with 'W' ,the approximation of the actual function goes close or far to resembling the actual function.similarly as suffix changes with 'V' the extra information increases or decreases with the suffix. were my understanding correct or if i need to correct them?.

Thanks!

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Reference Key - ag9zfm5wdGVsbW9vYzIwMTNyIgsSFVN0dWRlbnRRdWVzdGlvbkVudGl0eRiAgIDAv-yICgyiAQ1uc19ub2MxNl9lYzA1

[shivama...@gmail.com]

On Sunday, April 10, 2016 at 9:41:56 PM UTC+5:30, sanjayras...@gmail.com wrote:
> Hi,
>
>
> I have a question about what is happening in this video at 00:06:39 -
>
>
>
>
> http://www.youtube.com/watch?v=vFqfjYXNM2k#t=399s.
>
>
>
> what Wo means in the above discussion?
> so far, we have discussed about Vo ,where does this Wo suddenly comes from?
>
> it is said in the lecture that Wo is linear combination of psi translated in time.
> I understand it like, the approximation function of the actual function in unit time interval, whereas Vo as, space which contains functions to express the additional information when the actual function is resolved in a unit time interval.
>
> As suffix changes with 'W' ,the approximation of the actual function goes close or far to resembling the actual function.similarly as suffix changes with 'V' the extra information increases or decreases with the suffix.
> were my understanding correct or if i need to correct them?.
>
>
>
> Thanks!
>
>
>
>
>

> Reference Key - ag9zfm5wdGVsbW9vYzIwMTNyIgsSFVN0dWRlbnRRdWVzdGlvbkVudGl0eRiAgIDAv-yICgyiAQ1uc19ub2MxNl9lYzA1

Dear sanjay,

Before coming to the answer of your question it is mandatory for you to realize that there is a huge difference between a "function" and a "subspace". W_0 is a subspace(for more information regarding what is a subspace Kindly refer to the solution of assignment 2). So, it makes no sense to say that W_0(which is a subspace) is a linear combination of dilated and translated version of "psi(t)", the wavelet function.
I hope that by now you are comfortable with the establishment of the ladder of subspaces. Also I'm assuming that you must know that one can(for example) have a better approximation of a signal in the space V_1 as compared to V_0 so It is intuitively clear that we are adding some extra information to our signal approximation while going from V_0 to V_1. This extra information is captured by functions in W_0 subspace.

I hope you are satisfied with this answer. Sorry for replying so late. If you have any further questions we'll be happy to help you out.

Thanks and regards,
TA