Help with Haar wavelet transform problems?

[ashah99]

Homework Statement

Plot the scaling space V1 given wavelet and scaling coefficients and vice versa.

Relevant Equations

The relevant equations are given with the problem statement snippet below.

Attempt: This is where I am having difficulties understanding and getting a start at a solution. I get a lot of definitions and yet no worked examples. The plot will be constant piece-wise functions, as I understand, but I am having trouble visualizing. Any guidance is much appreciated.

 

[lippyka]

It can be helpful to start by looking at some examples of constant piece-wise functions. A good place to start is with linear functions, which can be represented on a graph as a straight line. You can also graph functions that are composed of two or more linear pieces, for example an "S" or "Z" shape. These are called piece-wise linear functions. You can also have piece-wise nonlinear functions such as a quadratic or cubic function. In each case, the function is constant within a certain range and then changes abruptly at specific points. To visualize these functions, you can draw a graph with the x-axis representing the input values and the y-axis representing the output values. Then plot the points that make up the function, connecting them with a line to show the continuous function. This will help you to understand how the function behaves over different ranges of inputs. You can also experiment with different functions to get a better understanding of how they work. For example, try plotting a few functions with different shapes, slopes and locations on the graph to see how they compare. This will give you a better idea of how different piece-wise functions behave.