Convolution Integral properties

Thread starter benfrankballi
Start date Sep 29, 2011
Tags

Convolution Integral Properties

AI Thread Summary

The discussion focuses on proving the equations y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t) within the context of linear time-invariant (LTI) systems. It references the convolution integral y(t) = x(t) * h(t) as a foundational concept. Participants suggest that the proof may be more appropriate for the Fourier Transform area rather than the Differential Equation forum. The conversation emphasizes the need for clarity in applying convolution properties to differentiate the output signal. Overall, the discussion highlights the relationship between convolution and differentiation in signal processing.

Sep 29, 2011

benfrankballi

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t)

I know that in an LTI system y(t) = x(t) * h(t) = \int x(\tau) * h(t-\tau) from \infty to -\infty

But how would I go about trying to prove the first two equations?

Engineering news on Phys.org

Sep 29, 2011

yungman

Go to Differential Equation forum here to ask, this really belong to Fourier Transform area.

Thread 'When 50,000 volts go through a wire at 5,000,000 FPS - The Slow Mo Guy'

View full post »

Thread 'Weird near-field phenomenon I get in my EM simulation'

I recently made a basic simulation of wire antennas and I am not sure if the near field in my simulation is modeled correctly. One of the things that worry me is the fact that sometimes I see in my simulation "movements" in the near field that seems to be faster than the speed of wave propagation I defined (the speed of light in the simulation). Specifically I see "nodes" of low amplitude in the E field that are quickly "emitted" from the antenna and then slow down as they approach the far...

View full post »

Thread 'EMF (Electromagnetic Field) & EHS (Electromagnetic Hyper Sensitivity)'

Hello dear reader, a brief introduction: Some 4 years ago someone started developing health related issues, apparently due to exposure to RF & ELF related frequencies and/or fields (Magnetic). This is currently becoming known as EHS. (Electromagnetic hypersensitivity is a claimed sensitivity to electromagnetic fields, to which adverse symptoms are attributed.) She experiences a deep burning sensation throughout her entire body, leaving her in pain and exhausted after a pulse has occurred...

View full post »