2015年9月6日 · 3 The definition of convolution is known as the integral of the product of two functions $$ (f*g) (t)\int_ {-\infty}^ {\infty} f (t -\tau)g (\tau)\,\mathrm d\tau$$ But what does the …

2024年9月12日 · I am merely looking for the result of the convolution of a function and a delta function. I know there is some sort of identity but I can't seem to find it. $\int_ {-\infty}^ {\infty} f …

2022年10月25日 · My final question is: what is the intuition behind convolution? what is its relation with the inner product? I would appreciate it if you include the examples I gave above and …

Since the Fourier Transform of the product of two functions is the same as the convolution of their Fourier Transforms, and the Fourier Transform is an isometry on $L^2$, all we need find is an …

I am currently learning about the concept of convolution between two functions in my university course. The course notes are vague about what convolution is, so I was wondering if anyone …

I'm having a hard time understanding how the convolution integral works (for Laplace transforms of two functions multiplied together) and was hoping someone could clear the topic up or link …

2020年1月5日 · I am learning how to calculate convolution of basic signals, such as rectangular ones. Specifically, the definition of such a signal is: $$ \operatorname {rect}_T (t)= \begin …

If $f,g$ are both nonnegative proving commutativity of convolution can be done without a tedious change of variable. Indeed, let $X$ be a random variable with density $f$ and let $Y$ be a …

2015年7月4日 · It the operation convolution (I think) in analysis (perhaps, in other branch of mathematics as well) is like one of the most useful operation (perhaps after the four …

But in general, convolution of functions is almost a ring (there's no exact identity element). The linear space of compactly supported distributions forms an actual ring under convolution, and …