Questions tagged [orthogonal-signals]

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How to construct signal-geometric framework

Consider the signal set $\left\{s_i(t) = t^{\frac{1}{i+1}}\right\}_{i=1}^4$ defined over the interval $\left[−1, 1\right]$. Represent these signals within a signal geometric framework. In this ...
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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 ...
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Finding set of orthogonal basis functions for composite signals

I've been given a list of 5 composite signals, where each is composed of 10 sinusoids of different frequencies. For instance, the first composite signal $S_1$ is given by $$ S_1 = \sum_{i=1}^{10} A_i \...
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Non-coherent FSK and Orthogonality and square-law detectors

This is a basic figure that explains how Non-Coherent FSK actually works. The incoming signal $ r (t)=\sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)}$ where P denotes the signal power in ...
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How to prove a train of sinc pulses in digital communicaton system are orthogonal to each other?

Consider a train of sinc pulses: $$\phi_n(t)= \frac{\sin(\omega_M(t-nT_s))}{\omega_M(t-nT_s)}\quad; n=0,\pm1,\pm2,\dots$$ $\quad$where,$\quad T_s=\frac{\pi}{\omega_M}$ Now ,in order to show sinc ...
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About the orthogonality of columns in Zadoff-Chu matrix

As we know that Zadoff-Chu matrix is similar to Walsh-Hadamard matrix where every columns in those matrices is orthogonal with the any other column. For Walsh-Hadmard matrix, the orthogonality is ...
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How $\Delta f=\frac{1}{2T}$ satifies the orthogonality condition?

Let $$s_{ml}(t)=\sqrt{\frac{2E}{T}}\exp(j2\pi\Delta fmt)$$ where $T$ is the time-period of signal $\Delta f$ is the frequency spacing The text says that two signals $s_{ml}(t)$ and $s_{nl}(t)$ are ...
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Processes: Orthogonal, Uncorrelated, Statistically Independent

How are they all related? You can define them as: Orthogonal Processes: $E[XY] = 0$ Uncorrelated Processes: $E[XY] = E[(X - \mu_x)(Y - \mu_y)] = 0$ Statistically Independent Processes: $E[XY] = E[X] \...
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How can we generate an orthogonal sinusodial signal to any other signal?

I have three signals which are \begin{align} A&=\cos\left(2\pi ft + \frac \pi2\right)\\ B&=\cos\left(2\pi ft\right)\\ C&=\cos\left(2\pi ft + \frac {5\pi}4\right) \end{align} What i need ...
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Orthogonal Codes for Band Limited Channel

In this question orthogonal family and pulse shaping filter the user asked about possible loss of orthogonality of orthogonal codes due to the use of raised cosine pulse shaping and I showed as an ...
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On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
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Orthogonality of filter impulse response to its even shift

I meet this problem but still do not know how to solve it. Could you guy give me some guides? Upsampling by 2 ($U_2$) followed by filtering by $g$, with operator $G$ And given: $<g_n,g_{n-2k}>...
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Detect orthogonal sequence with fading

For a set of $N$ orthogonal sequences $\textbf{A}^i = \{a_1^i,a_2^i,...,a_M^i\}, i =1 ..N$, the detection of these sequences can be done by calculating the inner product (dot product) of receive ...
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Refinement equation and orthogonal wavelets basis

I have a wavelet function space defined by, $ \phi(x) = \sqrt(2) \sum_n h_{\phi}(n) \phi(2x-n) $ . given the Fourier transform of the function is: $\hat{\phi}(\omega) = \frac{1}{\sqrt(2)} \hat{h}...
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How can I know if these two signal are orthogonal to each other

So the question is to determine if this statement is true or false. The question can be seen below. I know that two signals are orthogonal if their inner product is equal to 0. I know how this ...
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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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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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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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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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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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2 votes
1 answer
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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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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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4 votes
1 answer
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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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2 votes
1 answer
158 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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12 votes
7 answers
38k 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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3 answers
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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 ...
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