# Questions tagged [signal-processing]

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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### Let $q\in\mathbb{Z}$. What is the smallest period of $\sin(2t)−\sin(qt)$?

Question: Let $q\in\mathbb{Z}$. What is the smallest period of $\sin(2t)−\sin(qt)$? My attempt: the period of $\sin(t)$ is $2\pi$, so the period of $\sin(2t)$ is $\pi$ and the period of $\sin(qt)$ is ...
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### Energy of a signal simplification

I'm learning about signals from the textbook Signals and Systems Second Edition, by Oppenheim and Willsky in order to learn more about Fourier Analysis and I'm having difficulty with the Energy ...
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### What is the cubic expectation (third-order moment) of a complex gaussian vector (say, E[$aa^{T}a$])?

For a real gaussian vector, an explicit formula for the cubic expectation can be found in Matrix Reference Manual (search 'Cubic Expectations' in this link for detail), i.e., say $a$ is a complex ...
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### Time instant when signal reaches positive peak [closed]

I need to calcualte at what time a waveform x(t) reaches its positive peak where x(t) = 0.5cos(500t + 130). Please note that ...
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### Error in solution of 3-45 in Solution Manual of Signals and Systems Oppenheim 2nd edition

Hello I was solving the question 3-45 of the book Signals and Systems 2nd edition and I assume there is an error in the solution manual, kindly if someone confirm that am I right? or the solution ...
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### Chained Kalman Filters

I have read the term “chaining Kalman filters” and I wanted to know precisely what the chained form of a Kalman filter is. I’ve seen also the term dual Kalman filter framed as a different concept ...
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### Why these operations calculates group delay?

In textbook, group delay is defined as negative derivative of phase (in frequency domain). And in discrete signal, derivative can be approximately calculated as differentiation. But when I browse some ...
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### Understanding Quasi-Stationary Processes

Assume an Ergodic Process. A random process $s[n]$ (this notation refers to a sequence but is popular in the field of signal processing) is said to be quasi-stationary provided that it satisfies the ...
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### Spectral analysis of signal that is observed for a finite time ("philosophical" question)

We want to estimate the spectral density of a certain real signal $x(t)$, where time $t$ runs indefinitely over the real line (let's say that $x(t)$ may be the realization of a continuous stationary ...
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### Difference between techniques of period calculations? Continuous time vs discrete time?

For calculating period of continuous time signal,we simply divide 2pi by omega and get period value But in case of discrete time signal, procedure is not straight forward like continuous time, ...
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### Hot to get $e^{iwT} = 1$, $T = \frac{2\pi}{w}$?

Can someone please explain how to get to the above conclusion for T from the equation provided? I understand: $e^{iwT} = 1$ Can be written as: $\cos(wT) + i\sin(wT) = 1$ But I’m at a loss as how to ...
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### Approximation of a function using a correlated function

Suppose we have two functions: $f_1(x)$ and $f_2(x)$ that are highly correlated, but with the exact correlation unknown. Both functions are sampled; $f_1$ with a large number of samples such that a ...
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### Problem integrating with Dirac-delta functions

I'm currently studying signal and system, and the homework requires to find the impulse response of the system $$y(t)=\int_{-\infty}^t(t-\tau+2)x(\tau)d\tau$$ I want to plug in $x(\tau)=\delta(\tau)$: ...
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### Identifying a raised sinusoid with uniformly spaced samples

You are given a model for an input signal of the form $y(t) = a \cos(\omega t) + b \sin(\omega t) + c$ where the constants $a,b,c$, and $\omega$ are unknown. You want to identify these unknowns from ...