convolution

Question 1

what is the delta of dirac used for?

Answer 1

The delta function 𝛿(t-t) may be employed to extract a value out from a time history at time t = tau

( Any function x(t) multiplied by the function 𝛿(t-t) and then integrated, is equal to x(t)
evaluated at time t = tau )

Question 2

property of the fourier transform of the function delta

Answer 2

it is =1 if t=0 and It is =0 everywhere else

Question 3

talk about signal of sequence of impulses

Answer 3

A function x(t) can be seen as the sum of an infinite number of delta functions, each
delayed and weighted

Question 4

what is an invariant system (or constant coefficient system)

Answer 4

a system is invariant if h(t,tau) (=weighting function) is a function of tau only, meaning it is just depending on the delay between the stimulus and the response

Question 5

what is the kronecker delta

Answer 5

When we move from the continuous domain to the discrete domain, the Delta of Dirac
can be seen as the Kronecker delta
(=1 if n=0; =0 in the other cases)

Question 6

the convolution integral can be applied to…

Answer 6

-linear systems
-constant coefficient systems ( h(t,tau)=h(tau) )
-physically existing systems (response is null before the stimulus is applied)

Question 7

what does the convolution theorem tells us

Answer 7

that moltiplication in frequency is expressed as convolution in time (and viceversa)

Question 8

how we can give a physical meaning to the convolution

Answer 8

assuming that x is the input to the system and h is the unit impulse response of our system and using the superimposition principle

Question 9

frequency response function in frequency is translated in time domain in…

Answer 9

the unit impulse response