convolution

1. I What type of convolution integral is this?

Convolution has the form (f\star g)(t) = \int_{-\infty}^{\infty}f(\tau)g(t-\tau)d\tau However, I for my own purposes I have invented a similar but different type of "convolution" which has the form (f\star g)(t) = \int_0^{\infty}f(\tau)g(t/\tau)d\tau So instead of shifting the function g(t)...
2. Trying to intuit the unit impulse response

1. Homework Statement Hi there, I've been trying to gain some intuition on how the convolution sum works, but as I dig deeper I am realizing that there is an issue with my intuition of signals and systems, in particular the unit impulse response. My issue is trying to understand how a unit...
3. Determine impulse response given input and output signals

1. Homework Statement Hello everyone, In the following problem I have to find the unknown impulse response g1(t) given the input and output signals, as shown below: (the answer is already there, at the moment I am trying to understand how to get there). 2. Homework Equations I have...

13. Convolution Integral Properties

1. Homework Statement Either by using the properties of convolution or directly from the definition, show that: If $$F(t)=\int^t_{-\infty} f (\tau) d \tau$$ then $$(F * g) (t) = \int^t_{-\infty} (f * g) (\tau) d \tau$$ 2. Homework Equations The convolution of $f$ with $g$ is given...
14. Is there a mistake in my calculation or in my reasoning?

1. Homework Statement y'' + 3y' + 2y = r(t), r(t) = u(t - 1) - u(t - 2), y(0) = y'(0) = 0. I need to solve this by convolution, which I know is commutative. The problem is that my calculation gives (f * g) =/= (g * f). Could someone please tell me where my mistake is? 2. Homework...
15. Fourier Transform and Convolution

Considering two functions of $t$, $f\left(t\right) = e^{3t}$ and $g\left(t\right) = e^{7t}$, which are to be convolved analytically will result to $f\left(t\right) \ast g\left(t\right) = \frac{1}{4}\left(e^{7t} - e^{3t}\right)$. According to a Convolution Theorem, the convolution of two...
16. Inverse Laplace Transform of a fractional F(s)

1. Homework Statement Having a little trouble solving this fractional inverse Laplace were the den. is a irreducible repeated factor 2. The attempt at a solution tryed at first with partial fractions but that didnt got me anywhere, i know i could use tables at the 2nd fraction i got...
17. Integration by sketching

I greatly appreciate this chance to submit a query. I have the following integral: $$\int_{1}^t 2sin(t-\tau)e^{-2(t-1)} d\tau$$ and it has been suggested to me that if I sketch the two constituent functions and multiply them, I can read the answer off the paper. So here are my sketches: go...
18. Step Validity with the Fourier Transform of Convolution

A convolution can be expressed in terms of Fourier Transform as thus, $\mathcal{F}\left\{f \ast g\right\} = \mathcal{F}\left\{f\right\} \cdot \mathcal{F}\left\{g\right\}$. Considering this equation: $g\left(x, y\right) = h\left(x, y\right) \ast f\left(x, y\right)$ Are these steps valid...
19. Use convolution integral to find step response of a system

1. Homework Statement An electrical network has the unit-impulse response :h(t)=3t⋅e-4t .If a unit voltage step is applied to the network, use the convolution integral to work out the value of the output after 0.25 seconds. 2. Homework Equations Convolution integral: y(t)=f(t)*h(t) Unit step...
20. Correlation between Iterative Methods and Convolution Codes

Hey guys so I have this Calc 3 project and the end is throwing me for a loop. I've done the encoding part, and i've coded the standard iterative methods, but I don't see how the two correlate so I can use the iterative methods to decode a "y stream" with the inputs specified...
21. Convolution Dirac impulse and periodic signal

Hi ☺️ i have to do a convolution with a periodic signal and a dirac impulse: x(t)=sen(πt)(u(t)−u(t−2)) h(t)=u(t−1)−u(t−3) The first is a periodic graph that intersect axis x in points 0 , 1 and 2 (ecc) The se ing is a rectangle ( Dirac impulse ) that intersect AxiS x in points 1 and 3. For...