# Electronics and Communication Engineering - Signals and Systems - Discussion

Discussion Forum : Signals and Systems - Section 1 (Q.No. 10)

10.

If £[

*f*(*t*)] = F(*s*), then £[*f*(*t*-*T*)] =Answer: Option

Explanation:

A linear system is one in which the relationship between input and output is linear.

All linear system possess the property of superposition *i.e., * if input *u*_{1} gives output *y*_{1} and input *u*_{2} gives output *y*_{2} then input *u*_{1} + *u*_{2} will give output *y*_{1} + *y*_{2}.

Superposition implies homogencity *i.e., * if input *u* gives output *y*, then input *ku* gives output *ky* where *k* is a rational number.

In general a system is linear if a transformation *T* satisfies the relation

T(a*u*_{1} + β*u*_{2}) = aT(*u*_{1}) + βT(*u*_{2})

where a and β are constant.

Discussion:

5 comments Page 1 of 1.
Bipin Kumar said:
9 years ago

This can also be solved using time shifting property of Laplace.

(1)

Swapna said:
7 years ago

A digital signal processing system is described by the expression y(n)=2x(n) + x(n-1) +2y(n-1) than the system is,

Stable IIR Filter.

Astable IIR filter.

Can anyone tell me the correct answer for this?

Stable IIR Filter.

Astable IIR filter.

Can anyone tell me the correct answer for this?

Pratima Maiti said:
5 years ago

The answer should be e^-(sT) F(s).

Jyoti said:
5 years ago

Yes, right @Pratima.

Kulwinder Kaur said:
5 years ago

Using time shifting property , the answer is;

f{t-k} = e^-ks F{s} //property.

f{t-T} = e^-sT F{s}.

f{t-k} = e^-ks F{s} //property.

f{t-T} = e^-sT F{s}.

(1)

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