Questions tagged [orthogonal-signals]

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Expectation of power spectrum for nonorthogonal wavelets

I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum"). Let $x_n$ denote the signal, sampled at increments $\...
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32 views

Is it possible to spread signal using sum of more than one orthogonal code

I was wondering if we can spread the signal using more than one spreading code. Assume we have the Walsh code used to spread the transmitted signal, the Walsh code is, for example, gotten based on ...
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91 views

When Two Sampled Sinusoidal Are Orthogonal?

If two analog sinusoidal are orthogonal with duration T, their minimum frequency difference should be 1/2T in case of no phase offset between them. And if there is phase offset, the difference is 1/...
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CDMA-DSSS with orthogonal codes and BPSK modulation: proper way to demodulate

I am having problems when demodulating the signal: If I demodulate the sequence chip by chip and then operate only with binary information the "integrate and dump" (correlator) sometimes will provide ...
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1answer
25 views

Are there analogues to orthogonal transformations in non-orientable surfaces?

I am working on extremely large, symmetric matrices of counts, and attempting to identify patterns/shapes within them. Wavelets are a popular tool in image processing, and have some nice statistical ...
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1answer
70 views

Temporal Orthogonality

I'm studying Digital Communication and I couldn't understand the relationship between temporal orthogonality and sampling theorem. Definition of the Temporal Orthogonality is as follows: $$\mathrm{...
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1answer
190 views

struggling to understand why Fourier basis is orthogonal

Studying DSP on my own time on Coursera. Was given a proof to why the Fourier basis is orthogonal, but I can't figure it out. Here is how it is proof goes. Consider the Fourier basis $$ \left\...
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1answer
52 views

Does Hamming encoding preserve orthogonality?

The question I have is this-- if I have two binary vectors, i.e. $x_1, x_2 \in \mathbb F_2^k$ that are orthogonal, i.e. $x_1^T x_2 = 0$, and let's say I Hamming encode each of them separately with an $...
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770 views

Orthogonal basis of signal space and the projection of white noise

I am trying to make the relation between linear modulation and nonlinear one by using orthonormal expansion. The purpose is to understand what is orthonormal set in each case and to understand the ...
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1answer
91 views

Absolute maximum number of possible PN sequences for given length

I previously asked if it was possible to use encryption-grade randomness as a CDMA spreading sequence and learned that the codes must be orthogonal, not necessarily random. I've tried different ways ...
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19k views

When are two signals orthogonal?

The classical definition of orthogonality in linear algebra is that two vectors are orthogonal, if their inner product is zero. I thought this definition might be applied to signals as well, but then ...
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365 views

Proving orthogonality

How to prove a cosine signal with irrational period and another cosine signal with a rational period are orthogonal? For example, $\cos(4t)$ and $\cos(4\pi t)$ sum is aperiodic. Hence it is said that ...