# Tagged Questions

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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### Why is the convolution output in terms of 't' not $\tau$?

The convolution integral is defined as: $$y(t) = (h * x)(t) = \int^{+\infty}_{-\infty} h(\tau). x(t-\tau)\ d\tau$$ where $h(t)$ and $x(t)$ are functions in terms of time. Why is $y$ in terms of '$t$...
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### Do decaying exponential signals have finite energy?

"A signal that decays exponentially has finite energy, so, it is also an energy signal." http://www.songho.ca/dsp/signal/signals.html I don't quite get how that can be true. Energy of a ...
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### Is there a name for this “simplified” Volterra series?

Consider a nonlinear, time-invariant system of the following form: $g(t) = \left[h_1(t) \ast f(t)^1\right] + \left[h_2(t) \ast f(t)^2\right] + \left[h_3(t) \ast f(t)^3\right] + ...$ where $\ast$ ...
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### Time period of Sinusoidal Signal

I have confusion in calculating the Time period of different signals. 1) $x(t) =3cos(4t + \pi/3)$ solution: 2$\pi$/4 = $\pi$/2 (It is periodic) 3) $x(t) =cos(t-\pi/9) +9sin(2\pi t + \pi/12)$ Solution: ...
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### How to calculate the cross-correlation of a halfwave?

I'm trying working on a vehicle modle and testing it with steering maneuvres standardised by the ISO. When it comes to data analysis the ISO standard says the following: 6.4 Time lag and Sine Time ...
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### Sampling theorem - signal reconstruction

Hi and thank you for your help. I got stuck for the last days with this chapter in this book https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html. What I do not understand is http://www....
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### Can someone explain the steps to the solution in detail please

I've got this question here. I already have the solution but I have no idea how the solution came up. Can someone share any steps in detail for dummies to understand the logic behind it. Any video any ...
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### How to know for sure this is a low-pass filter

Given the transfer function $$H(z) = \frac{1}{4}(1+z^{-1}+z^{-2}+z^{-3})$$ I understand I have to switch $z$ to $e^{j\Omega}$, $0\le\Omega\le\pi$, in order to find out how it interacts with ...
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### Constructing a 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: $\mbox{dct(eye($n,n$))}$ where dct is the ...
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### Best sources on complete transforms (classic orthonormal transforms) and overcomplete transforms in signal processing

In the introduction section of a thesis I read a little about classic orthonormal transforms such as Fourier, discrete cosine and wavelet transforms and their application in signal processing. Then ...
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### Isomorphisms of normed vector spaces

I'm having difficulty with the following question: Show that, for $\mathbb{F} \in \{\mathbb{R}, \mathbb{C}\}$ and for an infinite discrete time-domain $\mathbb{T}$, $\exists$ an isomorphism of normed ...
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### Is the sum of all cross-correlation samples representative of target existence likelihood?

Answers to this question take the peak in the cross correlation as the measure to the likelihood of the trigger signal exist in the received signal - this is pretty much text book. My question is ...
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### Effect of sampling frequency on Discrete Fourier Transform?

I don't get it. I have the following form of the DFT: $$Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1$$ But this assumes that the sampling ...
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### Minimum number of zeros of this Laplace transform

I've come across this question in my Signals and Systems class but I can't seem to understand what the answer might be. Here is the entire question: Consider a signal x(t) which has its Laplace ...
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### Result of sampling of function with too small fs and reconstruction with square function

everybody I have an exam in signal processing tomorrow and doing past exams to prepare myself however I'm on stuck on a particular problem. It is stated as: Considering an ideal sampling with f_s = ...
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### secret formula for the “sin” wave with variable rising/falling edge

My math is pretty much forgotten. I was wondering if someone can take a look at this and share what's the formula for creating something like this. https://drive.google.com/file/d/...
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### Find Discrete Time Fourier coefficients of $(-1)^n x[n]$

Given that $x[n]$ is an N-periodic sequence with Fourier coefficients $a_k$, I want to find the Fourier coefficients of $$(-1)^n x[n]$$ for the situation in which $N$ is odd. I'm also interested in ...
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### Lost power with apodizing mask

I previously asked a similar question on the signal processing community, but I think may be more easily solved from a mathematical perspective. I start out with an image, $I$. To be able to process ...
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### Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
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### Derivative of unit step function

The ramp function is given by r(t)=tu(t) If we differentiate ramp ,we get unit step function. That is, u(t)=1 So the derivative of unit step function is definitely 0 since u(t) is constant over the ...
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### Amplitude vs. Amplitude Spectrum?

I feel like I keep getting confused about amplitudes when talking about signal processing. Maybe someone can help clear my confusion. Lets say I have a simple sinusoid $f(t)=Asin(\omega_0 t)$ The ...