# 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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### Help in understanding a coding technique based on inverse mapping of a dynamical system

Based on paper titled : Simultaneous Arithmetic Coding and Encryption Using Chaotic Maps by Kwok-Wo Wong et. al The Authors use a non-linear dynamical system for generating keys to be used in ...
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### $\cos(2\pi f nT +2\pi N_n) =\ cos(2\pi f nT)$ and more, why?

I am studying signals and systems and this came up? Could someone explain why is $\cos(2\pi f nT +2\pi N_n)$ equal to $\ cos(2\pi f nT)$? The book says: "because $N_n$ is an integer" I am ...
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### Prove Differentiator is Linear and Time-Invariant

The differentiator gives an output equal to the derivative of its input. Show that the differentiator is a linear time invariant system. Consider the input $f(t)=\sin(t^2).$ Attempt For time-...
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### Quick Fourier Series help?

I was given a graph (shown above) and was asked to represent this as a Fourier Series. I was able to solve $a_0$ with no problem. However, when I was integrating for $a_n$ and $b_n$, I was having a ...
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### How to show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$

I am trying to solve the following exercise: Show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ (i.e. $x_n = w_1 x_{n-1} + w_2 x_{n-2}$). ...
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### Polar form of the Fourier transform of $\sin(t)$

I'm studying signal processing, and I came across the Fourier transform of sin(t). It ends up being a purely imaginary (dirac delta) impulse pair. But when considering the frequency domain ...
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### Finding convolution of two functions?

1. Continuous Functions $x_1(t)$ and $x_2(t)$ definitions' link How to evaluate $(x_1∗x_2)(t)$ at $t = −T, 0, +T$ in terms of $T$ 2. Discrete Functions $x_1[n]$ and $x_2[n]$ definitions' link ...
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### Help in plotting the Z-transform and Fourier Transform of the following Sequences.

I'm taking Digital Signal Processing class at the moment and while I believe I understand the theory behind the z-transform and fourier transform, in this case DFT and DTFT, I'm stuck as to how to ...
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### Determining if a function is linear, time invariant, both or not

I have the function $y(t)=t^2x(t-1)$ and I need to figure out if it is linear or not and time invariant or not. By the looks of it I guessed it to be not linear but the answer is linear but not time ...
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### Difficult problem involving a percentage of the period of a sinusoid

Im having difficulty intuitively understanding how to solve this problem: $x(t) = A\cos(\omega t + \phi)$ $A > 0$ $\phi\in(−\pi,\pi]$. $x(t) ≥ 2.4$ for $18$% of each period takes $0.123$ ...
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### Implementing Normalized Cross-Correlation using FFT - How to?

Is there any way to calculate the normalized cross correlation between 2 signals by using the FFT? (I managed to implement it already for standard cross correlation equation). Thanks in advance,
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### Is constant system a Causal System?

Is y(t) = 1 a causal system? From the definition of causal systems , a causal system is a system where the output depends on past and current inputs. Here the system doesn't depend on any input. So,...
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### Orthogonality of Two Signals.

My last question's link: Reconciling different definitions of orthogonality However, I failed to understand why they are equivalent. If $f$ and $g$ are real, \begin{align} \int_{<T>}f(t)g(t)~...
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### Reconciling different definitions of orthogonality

I want to establish about orthogonality in my mind. I knew the orthogonality of two functions $f$ and $g$ in interval T like the following: $$\int_{<T>}f(t)g^*(t)~dt=0 \tag{1}$$ where  g^*(...
I'm reading through a derivation in a book and am having trouble understanding a step. Here's a screenshot 3.46 is the equation in $(k,\omega)$ space. They're doing an inverse Fourier transform back ...