Projecting a Function on the Vector Space V₃ using the Haar Wavelets

This example is very similar to the first example, which projected a function onto a Fourier Space. We use the same function but a different interval. Once again, all the Maple code for this example is not present.

We start with the following function and graph.

Next, we define the inner product.

Now, we use the ODT to define our new function f.

Next, we can graph the function f on the interval [0,1].

> plot(f(t), t=0..1, axes=boxed);

Comparing h(t) to the projection of h(t) onto V₃ is shown below.

> plot({f(t),h(t)}, t=0..1, axes=boxed, color=[red, brown], thickness=3);

[G1]

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[G1]