# Questions tagged [orthornormal]

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### How to find the orthonormal basis for these three signals

I've been given these signals: $$S1(t) = 1$$ $$S2(t) = t$$ $$S3(t) = t^2$$ I have to find 3 basis functions using Gram - Schmidt algorithm on the interval $|t| \le 1$. Now, I know the procedure and ...
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### Other Examples of Complete Orthonormal Systems

I am interested in other examples of finite and complete orthogonal basis. I am not confident in my use of the term “complete”, so what I mean specifically is a set of basis vectors that can be used ...
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### What's a Normalized function?

I'm studing Representations of Random Processes and the book talks about Orthonormal functions, but doesn't make it clear what is it. I was able to realize that a set of functions are orthonormal if ...
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### Geometric representation of a signal using basis functions

I'm trying to solve the following problem where I need to express $x(t)$ in terms of the given $φ_i(t)$ functions. (It is proven that the $φ_i(t)$ functions are orthonormal).: Here's what I tried: In ...
64 views

### Pros/Cons to using Spectral and Diffusive Graph Wavelets

As I understand, there are two major methods of constructing wavelets on graphs. Spectral wavelets, from David K Hammond et. al, and diffusive wavelets from Coifman and Maggioni. I can't quite parse ...
1 vote
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### Partitioning the energy of a signal between its components

In physics, the total energy of a system is the summed energy of its component subsystems, and energy must be conserved, ie, adding the energy of the components gives the total energy. In signal ...
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### Relationship of input-outputs in Hartley transformation based on few elements in a vector

This question is related also to that question HERE, but with further details and another issue I need to solve. Assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is ...
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### How to find orthonormal basis function in the following digital communication problem?

I'm trying to express the following set of signals on orthonormal basis functions. These signals are to be transmitted using a 4-ary modulation scheme.How do i write ψ1(t)and ψ2(t) for the same. Also ...