# Tagged Questions

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### Finding the period of complex exponential function

I am having some trouble finding the period of the following discrete signal: $x[n]=e^{jn2\pi/3}+e^{jn3\pi/4}$
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### Differential Equation has a unique solution periodic

Let $A(t)$ continuous and periodic of period $S$ in $\mathbb{R}$. Suppose $x' = Ax$ has $\varphi \equiv 0$ as the only periodic solution of period $S$. Show that there exists $\delta> 0$ such that ...
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### Addition of two cosine waves with different periods

I was just wondering if anyone knows how to add two different cosine equations together with different periods to form one equation. Is there a way to do this and get a real answer or is it just all ...
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### Definite Integral of Periodic Function Multiplied by another Function

For one part of a problem I am working on, I am trying to show that $y'(t) \geq 1$ for all $t \geq 0$ when $y'= 1- \int^t_0 g(s)y(s) ds$ When $g(t)$ is periodic, $g(t) <0$ for all $t$, and ...
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### Help with the system of 13 equations

Homework from electronics class, but since it looks like a math problem to me i decided to look for help here. I am given this composite periodic signal that has 6 harmonics: ...
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### An inequality on $C^1$ periodic functions

Suppose $f \in C^1(\mathbb{R})$ and $f(x + 1) = f(x) \ \forall x \in \mathbb{R}$. Show that $$||f||_{\infty} \leq \int_0^1|f| + \int_0^1|f'|.$$ I have tried using techniques in Fourier Analysis such ...
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### Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers.

I have an assignment question that says "Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers." I'm told that $\sin 2\theta = 2 \sin\theta \cos\theta$ but I don't know how ...
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### Fourier Series problem

Suppose you are given the following information about a continuous-time periodic signal, $x(t)$, with period $6$ and its Fourier series coefficients $(a_k)$, (1)-(4). Using the synthesis equation, ...
Given $f:\mathbb R\to \mathbb R^+$ continuous and periodic of period $T\geq 0$, I am asked to prove that $$\int_0^T\frac{f(x)}{f(x+\alpha)}\mathrm dx\geq T,\; \forall \alpha\in\mathbb R.$$ How does ...