This set of Signals & Systems Questions and Answers for Aptitude test focuses on “Properties of the Impulse Response Representation for LTI Systems”.

[NOTE:’*’ is reffered as convolution operation]

a) y(t) = x(t) *(h1(t) + h2(t))

b) y(t) = x(t) + (h1(t) + h2(t))

c) y(t) = x(t) * (h1(t) h2(t))

d) y(t) = (x(t) * h1(t)) + h2(t)

View Answer

Explanation: The equivalent impulse response of two systems connected in parallel is the sum of individual impulse responses. It is represented as

y(t) = x(t) * h1(t) + x(t) * h2(t) = x(t) * (h1(t) + h2(t)).

2. When two LTI systems with impulse responses ha (t) and hb (t) are cascaded then equivalent response is given by ______

a) h(t) = ha(t) + hb(t)

b) h(t) = ha(t) – hb(t)

c) h(t) = ha(t) hb(t)

d) h(t) = ha(t) * hb(t)

View Answer

Explanation: The equivalent impulse response of two systems connected in series (cascaded) is given by convolution of individual impulse responses.

3. What is this property of impulse response is called ___________

h1(t) * h2(t) = h2(t) * h1(t)

a) Associative property

b) Commutative property

c) Distributive property

d) Closure law

View Answer

Explanation: Impulse response exhibits commutative property and it is given mathematically by the equation

h1(t) * h2(t) = h2(t) * h1(t).

4. The overall impulse response of the system is given by ______

a) h(t) = (h1(t) + h2(t) * h3(t)) – h4(t)

b) y(t) = x(t) * (h1(t) + h2(t)*h3(t)) – h4(t)

c) h(t) = (h1(t) + h2(t) * h3(t)) + h4(t) * x(t)

d) h(t) = (h1(t) h2(t) * h3(t)) – h4(t)

View Answer

Explanation: In the above given system h1 (t) and h2 (t) are connected in parallel hence it is

h1 (t) +h2 (t) which is cascaded to h3 (t) and its equivalent is connected in parallel with h4 (t). Hence the equivalent impulse response is given by h(t) = (h1(t) + h2(t) * h3(t)) – h4(t).

a) h[n] = (h1[n]-h2[n])*h3[n]+h5[n]*h4[n]

b) h[n] = (((h1[n]-h2[n])*h3[n])+h5[n])*h4[n]

c) h[n] = (((h1[n]-h2[n])*h3[n])-h5[n])*h4[n]

d) h[n] = (((h1[n]-h2[n])*-h3[n])-h5[n])*h4[n]

View Answer

Explanation: Here in the above system h1 [n] and h2 [n] are connected in parallel and given by h1 [n] – h2 [n], this is cascaded with h3 [n] and given by (h1 [n] – h2 [n]) * h3 [n], this is again connected in parallel with h5 [n] and its equivalent is cascaded with h4 [n]. The equivalent response is given by h[n] = (((h1[n]-h2[n])*h3[n])-h5[n])*h4[n].

6. The condition for memory-less system is given by _____

a) h[k] = cδ[k]

b) h[k] = cδ[n-k]

c) h[k] = ch[k]δ[k]

d) h[k] = ch[n-k]δ[k]

View Answer

Explanation: The LTI discrete-time system is said to be memory-less if and only if it satisfies the condition h[k]=cδ[k]. All memory-less LTI systems perform scalar multiplication on the input.

7. The causal continuous system with impulse response should satisfy ____ equation.

a) h(t)=0,t<0

b) h(t)=0,t>0

c) h(t)≠0,t<0

d) h(t)≠0,t≤0

View Answer

Explanation: To the continuous system to be causal, the impulse response should satisfy the equation h(t)=0,t<0 and convolution integral is given by y(t)=∫

_{0}

^{∞}h(τ)x(t-τ)dτ.

8. Causal systems are ______

a) Anticipative

b) Non anticipative

c) For certain cases anticipative

d) For certain cases anticipative and non anticipative

View Answer

Explanation: Causal systems are non anticipative. They cannot generate an output before the input is applied. Which indicates the impulse response is zero for negative time.

View Answer

Explanation: If the condition ∑

^{∞}

_{k=-∞}|h[k]|<∞ is satisfied by an LTI system then it is said to be stable and for continuous time signal the condition is given by integral

∫

^{∞}

_{-∞}|h(τ)|dτ<∞.

10. The impulse response of discrete-time signal is given by h [n] = u [n+3]. Whether the system is causal or not?

a) Causal

b) Non-causal

c) Insufficient information

d) The system cannot be classified

View Answer

Explanation: The given impulse response h [n] = u [n+3] is not causal because of the term u [n+3] which implies it is non zero for n= -1, -2, -3.

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