# Tagged Questions

Questions on the (continuous or discrete) convolution of two functions. It can also be used for questions about convolution of distributions (in the Schartz's sense) or measures.

23 views

### 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 ...
81 views

### Convolution of two Uniform random variables

We have $X \sim \mathrm{Unif}[0,2]$ and $Y \sim \mathrm{Unif}[3,4]$. The random variables $X,Y$ are independent. We define a random variable $Z = X + Y$ and want to find the PDF of $Z$ using ...
27 views

30 views

142 views

### Solving forced undamped vibration using Laplace transforms

I'm heaving trouble solving the following undamped forced vibration problem using Laplace transforms: $$\ddot{q}(t) + \omega_n^2 q(t) = \cos(\omega t).$$ I will show what I have done so far, and I'd ...
26 views

### Any way to simplify this integral?

$$\int_{-\infty}^{\infty}e^{-y\left(x\right)}\left(\log\int_{-\infty}^{\infty}e^{-y\left(z\right)}N\left(x-z,v\right)dz\right)dx$$ where $y(x)\equiv\sum_{i=1}^{n}c_{i}x^{i}$, $n$ is even and ...
31 views

### Support of convolution in pde

Let $f$ be an square-integrable function on a bounded domain U. Moreover $\eta(x) = C e^{-\frac {1}{1-x^2}}$ on $[-1,1]$ and 0 elsewhere. C is taken in such a way that the integral over eta is ...
143 views

231 views

### Calculation of the convolution of Cauchy density function $\int_{-\infty}^{\infty}\frac{ab}{\pi^2}\frac{1}{y^2+a^2}\frac{1}{(x-y)^2+b^2}dy$

I tried to calculate the following integral, which is the convolution of Cauchy density function: $$\int_{-\infty}^{\infty}\frac{ab}{\pi^2}\frac{1}{y^2+a^2}\frac{1}{(x-y)^2+b^2}dy$$ I tried to use ...
39 views

### Inverse Laplace Transform of $F(s) = \frac{3s+8}{(s^2+2s+20)^2}$

Having a little trouble solving this fractional inverse Laplace were the den. is a irreducible repeated factor $$F(s) = \frac{3s+8}{(s^2+2s+20)^2}$$ tried to apply partial fractions to it and i just ...
147 views

### Gaussian smoothing kernel with different sigma values

I am not a mathematician by training, so excuse my lack of vocabulary or the imprecision in my question. I have a 1D distribution that I need to convolute, using a Gaussian kernel. However, all the ...
75 views

### Find the CDF of the sum of the inverse square of n random normal numbers

Question If I have n independent random normal numbers denoted $X_i$ each with mean $\mu_i$ and variance $\sigma_i$ (for $i = 1 ... n$). For each $X_i$ I have a weighting factor $w_i$. What is the ...
28 views

### Convolution basic

I am stuck with this question. Need some help. Solve for $y(t)$: $$\frac{d^2y}{dt^2} + 3\frac{dy}{dt} + 2y = 2*x(t)$$ Given, $x(t) = \cos(tu(t))$, where $u(t)$ is unit step function, and with ...
67 views

### Does infinite repeated convolution with the same normal distribution converge?

According to Wikipedia, This result is known as Cramér's decomposition theorem, and is equivalent to saying that the convolution of two distributions is normal if and only if both are normal. ...