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ss15_B01-1 (DT Signals by Impulses)

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SS2-6: Representation of DT Signals

x[n] = ... + x[1] delta[n+1] + x[0] delta[n] + x[-1] delta[n-1] + ...

(a) True or (b) False

(b) False


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ss15_B01-2 (DT Unit Impulse Response & Convolution Sum)

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SS2-12: Convolution of x[n] & h[n]

If a system is linear 
and its impulse response for delta[n-k] is h_k[n],
then for any input x[n],
the output y[n] = x[n]*h_k[n].

(a) True or (b) False

(b) False


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ss15_B01-3 (Ex 2.1-2.2)


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ss15_B01-4 (Ex 2.3-2.5)

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ss15_B02-1 (CT LTI Systems)


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ss15_B02-2 (CT Impulse Response & Convolution Integral) 

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SS2-34: LTI and Convolution

For an CT LTI system denoted by h(t), and
any input signal x(t) and its corresponding output y(t),
which of the following statements is/are true?

(a) x(t) = \int_{-\infty}^{+\infty} { \delta(\tau)} { x(t-\tau)} d \tau
(b) h(t) = \int_{-\infty}^{+\infty} { h(\tau)} { \delta(t-\tau)} d \tau
(c) y(t) = \int_{-\infty}^{+\infty} { h(\tau)} { x(t-\tau)} d \tau


(a), (b), (c)

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ss15_B02-4 (Convolution Sum and Integral) 

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SS2-41: Signals and Systems

For x(t), y(t), h(t) used to describe the input, output and system,
the variable t in x(t) and y(t) denote absolute (world ) time
and variable t in h(t) denotes the relative time, 
i.e., the influence/affecting time instance of the input x(t) on the system.
(a) True or (b) False

(a) True


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ss15_B03-2 (Properties - Commutative Distributive)


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SS2-45: Commutative

Which one(s) is(are) True?

(a) \sum_{r=-\infty}^{+\infty} h[r] x[n-r] = \sum_{r=+\infty}^{-\infty}  x[n-r] h[-r] 
(b) \sum_{r=-\infty}^{+\infty} h[r] x[n-r] = \sum_{r=+\infty}^{-\infty}  x[n-r] h[r] 
(c) \int_{+\infty}^{-\infty} x(\sigma-t) h(-\sigma) (d \sigma) = \int_{-\infty}^{+\infty} x(t-\sigma) h(\sigma) d \sigma
(d) \int_{+\infty}^{-\infty} x(t-\sigma) h(\sigma) (-d \sigma) = \int_{-\infty}^{+\infty} x(t-\sigma) h(\sigma) d \sigma


(b)
(d)


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SS2-46: Commutative Distributive Associative

Which one(s) is(are) True?

(a) x(t)*( h_1(t) + h_2(t) ) = x(t)*h_1(t) + x(t)*h_2(t)
(b) (x_1[n] + x_2[n] )*h_1[n]  = x_1[n]*h[n] + x_2[n]*h[n]
(c) x(t)*( h(t)*y(t) ) = ( x(t)*(h(t) )*y(t))

(a) (b) (c)


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ss15_B03-3 (Properties - Associative Memory Invertible)


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ss15_B03-5 (Properties - Causality)


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ss15_B03-6 (Stability Ex-2.13 Impulse Step Responses) 


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SS2-51-57-60: Memory Causal Stable

For an LTI system by h[n] = (0.8)^n u[n+3],
then the system is:

(a) memoryless
(b) causal
(c) stable



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ss15_B04-1 (Linear Const Coeff Diff Eqn)

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SS2-81: Output Input Impulse Response

When x(t) = \delta(t) and y(t) = f(t),
then, when x(t) = g(t), then y(t) = ? 

y(t) = f(t) * g(t)



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ss15_B05-1 (Singularity Functions Ex-2.16)


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SS2-72: Unit Doublets

Which one(s) is(are) true?

(a) y(t) = x(t)*u_1(t): y(t) is the derivative of x(t).
(b) y(t) = x(t)*u_{-1}(t): y(t) is the integral of x(t).
(c) x(t) = x(t)*u_0(t).
(d) u_{-2}(t) = u(t) * u(t).

a, b, c, d


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