Convolution with an delta function

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Homework Help Overview

The discussion revolves around the convolution of an arbitrary function f(t) with a comb function, which consists of a series of delta functions spaced at intervals of T. Participants are exploring whether the result of this convolution yields an array of copies of f(t) or discrete points at specific intervals.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are considering the implications of the domain of f(t) on the convolution result. There is a reference to the sampling property of the delta function, suggesting a connection to how f(t) behaves under convolution with delta functions.

Discussion Status

The conversation is ongoing, with some participants seeking clarity on the outcome of the convolution. There is a sense of inquiry, as individuals express uncertainty and prompt others to engage in figuring out the answer.

Contextual Notes

There is an indication that the solution may vary based on the specific characteristics of f(t), which remains unspecified in the discussion.

spaghetti3451
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Homework Statement



Convolve an arbitary function f(t) with comb(t) [a sum of delta functions that run from -infinity to infinity with spikes at t = nT]. Is the convolution an array of copies of f(t) or is it a set of discrete points such that f(t) is returned at every t = nT?

Homework Equations





The Attempt at a Solution



The solution depends on the domain of f(t).
 
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[tex]f(t)*\delta(t-t_0) = \int\limits_{-\infty}^{\infty} \delta(\tau-t_0) f(t-\tau) \,d\tau=f(t-t_0)[/tex]
via sampling property of the impulse
 
So what's the answer?
 
failexam said:
So what's the answer?

That is what *you* are required to figure out.
 

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