definition - What is Convolution? - Mathematics Stack Exchange
2015年9月6日 · 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 product of the functions give? Why are is it being integrated on negative infinity to infinity? What is the physical significance of the convolution?
Can someone intuitively explain what the convolution integral is?
Intuition for Convolution. A convolution is the amount of an overlap area of one function f as it is shifted over another function g at a given time offset. Example using discrete valued functions. Let’s say we are transforming a certain function f(t) by passing it through a filter g(t) to get the output h(t): f(t) -> [ g(t) ] -> h(t)
Meaning of convolution? - Mathematics Stack Exchange
2010年10月26日 · 27. 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 could give me a good explanation. I can't seem to grasp other than the fact that it is just a particular integral of two functions.
analysis - History of convolution - Mathematics Stack Exchange
2015年7月4日 · 2. Let f, g ∈ L1(R), we may define the convolution of f and g as follows: f ∗ g(x) = ∫Rf(x − y)g(y)dy, (x ∈ R). It is well known that it can be defined on general locally compact group as well. It the operation convolution (I think) in analysis (perhaps, in other branch of mathematics as well) is like one of the most useful operation ...
Calculate convolution (integral) - Mathematics Stack Exchange
2018年1月31日 · If instead the right hand side of the interval intersects the domain of integration, we have $$ -.1\leq .7-x\leq .1 $$ then the convolution is the integral $$ 5\int_{-.1}^{.7-x}(x+t)\mathrm dt $$ and if the left hand side does, $-.1\leq .4-x\leq .1$, then the convolution is $$ 5\int_{.4-x}^{.1}(x+t)\mathrm dt $$ if we the left and right end ...
Why do we define the convolution? - Mathematics Stack Exchange
As a special case, the convolution of a function f(t) f (t) with the Dirac delta function gives f(0) f (0) (the response of the system at t = 0 t = 0). Because of the above, the input signal is thought of as "smearing" the impulse response on the time axis. Mathematically, it means that convolution of a given function f f with a smooth function ...
Definition of convolution? - Mathematics Stack Exchange
A shift-invariant linear operator T is completely determined by its impulse response T(δ) = f (where δ is the Dirac delta function). You can show that for any function g, T(g) = f ∗ g. This motivates the definition of convolution. – littleO. Mar 16, 2014 at 19:19. 1. The Cross-correlation does use x+y. – Navin.
Definition of Convolution - Mathematics Stack Exchange
When I read the notes, a convolution is defined as: (f ∗ g)(x) = ∫ + ∞ − ∞f(τ)g(x − τ)dτ. What is the difference if we define a convolution integral as follows: (f ∗ g)(x) = ∫ + ∞ − ∞f(τ)g(τ − x)dτ. Unless g is a even function, you are likely to get a different …
analysis - Convolution of functions defined on manifold
2015年3月14日 · As Olivier mentioned if you assume M M has a group structure and the measure induced by μ μ is a Haar measure then you can define the convolution of compactly supported functions by f ⋆ g(x) =∫M f(xy−1)g(y)dμ(y). f ⋆ g (x) = ∫ M f (x y − 1) g (y) d μ (y). if M M is compact then obviously all functions on it are compactly ...
Why is a convolution of an - Mathematics Stack Exchange
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