While studying about Wavelet Transform, I'm confused as why this is called a [1 -1] Filter , Here is what i'm talking about.
In this hypothetical example the student does fairly well the first half of the term then neglects his or her studies for the last half. Thus the exam scores for the term were 80%, 80%, 80%, 80%, 0%, 0%, 0%, and 0%* We can tell the average of all the scores (40%) and when the scores “tanked” after the 4th exam just by looking. Knowing the answer in advance, however, is a good way to learn and to verify the wavelet transforms. Then we can use them with confidence on real-world data where we can’t simply “eyeball” the final values.
We will now walk through the CWT process step by step using the simplest of the wavelet filters on this example. We begin by comparing the humble Haar wavelet filter, [1 –1], with the data as shown
80 80 80 80 0 0 0 0
If We now keep subtracting each value from the next value we will eventually get,
[0, 0, 0, 80, 0, 0, 0]
Now If I want to stretch the Filter to three points i.e If the filter is stretched from [1 –1] to [1 0 –1].
How will I calculate these points as I did in case of two point Filter where i simply subtract each value from the next value ?