# 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 ...
1 vote
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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 $$S_1 = \sum_{i=1}^{10} A_i \... 1 vote 0 answers 93 views ### Non-coherent FSK and Orthogonality and square-law detectors This is a basic figure that explains how Non-Coherent FSK actually works. The incoming signal  r (t)=\sqrt{2 P}{Cos}(2 \pi t (\text{fc}+\text{fi})+\text{n(t)} where P denotes the signal power in ... 1 vote 1 answer 111 views ### How to prove a train of sinc pulses in digital communicaton system are orthogonal to each other? Consider a train of sinc pulses:$$\phi_n(t)= \frac{\sin(\omega_M(t-nT_s))}{\omega_M(t-nT_s)}\quad; n=0,\pm1,\pm2,\dots$$\quadwhere,\quad T_s=\frac{\pi}{\omega_M} Now ,in order to show sinc ... 2 votes 1 answer 49 views ### About the orthogonality of columns in Zadoff-Chu matrix As we know that Zadoff-Chu matrix is similar to Walsh-Hadamard matrix where every columns in those matrices is orthogonal with the any other column. For Walsh-Hadmard matrix, the orthogonality is ... 1 vote 1 answer 57 views ### How \Delta f=\frac{1}{2T} satifies the orthogonality condition? Let$$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 ... 3 votes 1 answer 411 views ### 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] \... 0 votes 0 answers 27 views ### 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 ... 4 votes 2 answers 140 views ### 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 ... 5 votes 1 answer 138 views ### 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 ... -1 votes 1 answer 99 views ### 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}>... 1 vote 0 answers 51 views ### 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 ... 0 votes 1 answer 54 views ### 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}... 1 vote 3 answers 2k views ### 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 ... 1 vote 0 answers 20 views ### 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 \... 1 vote 1 answer 59 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 ... 4 votes 1 answer 346 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/... 0 votes 0 answers 256 views ### 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 ... 0 votes 1 answer 32 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 ... 1 vote 1 answer 157 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{...
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\...