This set of Signals & Systems Questions and Answers for Campus interviews focuses on “Convolution : Impulse Response Representation for LTI Systems – 2”.

1. The convolution sum is given by _____ equation.

View Answer

Explanation: By the definition of convolution sum we can write the equation as

x[n]*h[n] = ∑

^{∞}

_{k=-∞}x[k]h[n-k].

2. When the sequences x1 [n] = u [n] and x2 [n] = u [n-3], the output of LTI system is given as _____

a) y[n] = n-2, n>3

b) y[n] = n-2, n≥3

c) y[n] = n+2, n>3

d) y[n] = n-2, n≤3

View Answer

Explanation: The output y[n] =∑

^{∞}

_{k=-∞}u(k)u(n-k-3), by solving the above summation either by graphically or by direct summation we get .

3. The impulse response h (t) of an LTI system is given by e^{-2t}.u(t) . What is the step response?

a) y(t) = ^{1}⁄_{2} (1 – e^{-2t}) u (t)

b) y(t) = ^{1}⁄_{2} (1 – e^{-2t})

c) y(t) = (1- e^{-2t}) u (t)

d) y(t) = ^{1}⁄_{2} (e^{-2t}) u (t)

View Answer

Explanation: Given x (t) = u (t) and h (t) = e

^{-2t}.u(t). By using convolution integral

We get output y (t) as y(t) =

^{1}⁄

_{2}(1 – e

^{-2t}) u (t).

4. Is (t)*h(t) = h(t)*x(t)?

a) True

b) False

View Answer

Explanation: By the properties of convolution we say that x(t)*h(t) = h(t)*x(t)

It can be proved using the convolution integral

.

5. Compute u (t) convolved with itself?

a) y(t)=t.u(t)

b) y(t)=u(t)

c) y(t)=t^{2}.u(t)

d) y(t)=t.u(t-1)

View Answer

Explanation: By taking x (t) = u (t) and h (t) = u (t) and substituting in the integral

On solving the given integral we get y (t) = t u (t).

6. Convolve the signals e^{-2t} u(t), e^{-3t} u(t). Determine the output?

a) y(t) = (e^{-2t} – e^{-3t})u(t)

b) y(t) = (e^{-2t} – e^{-3t})

c) y(t) = (e^{-3t} – e^{-2t})u(t)

d) y(t) = (e^{-t} – e^{-3t})u(t)

View Answer

Explanation: By solving the convolution integral

, we get output asy(t) = (e

^{-2t}– e

^{-3t})u(t).

7. Convolve graphically.

a)

b)

c)

d)

View Answer

Explanation: Step 1: sketch x (τ) and h (-τ)

Step 2: Obtain the product x (τ) h (t-τ) and the area under this product will give y (0)

Step 3: sketch h (1-τ) and compute y (1) and so on

Step 4: similarly sketch h (-1-τ) and compute y (-1) and so on.

Hence we get the output as .

8. Convolve graphically the below given signals, and determine the correct sequence?

a) Y (-1) = 0, y (1) = 2, y (3) = 2

b) Y (-1) = 2, y (1) = 2, y (3) = 2

c) Y (-1) = 0, y (1) = 0, y (3) = 2

d) Y (-1) = 0, y (1) = 3, y (3) = 2

View Answer

Explanation: Step 1: sketch x (τ) and h (-τ)

Step 2: Obtain the product x (τ) h (t-τ) and the area under this product will give y (0)

Step 3: sketch h (1-τ) and compute y (1) and so on

Step 4: similarly sketch h (-1-τ) and compute y (-1) and so on.

By following above steps we get the output as

9. Convolve given x (t) with itself and choose the correct output.

a)

b)

c)

d)

View Answer

Explanation: Step 1: sketch x (τ) and h (-τ)

Step 2: Obtain the product x (τ) h (t-τ) and the area under this product will give y (0)

Step 3: sketch h (1-τ) and compute y (1) and so on

Step 4: similarly sketch h (-1-τ) and compute y (-1) and so on.

By computing the above steps we get output y (t).

10. Find the convolution of x1[n] = {1, 2, 3, 4} and x2[n] = {2, 1, 2, 1}.

a) Y[n] = {14, 10, 14, 10}

b) Y [n] = {14, 16, 14, 16}

c) Y [n] = {14, 16,-14,-16}

d) Y [n] = {14,-16,-14, 16}

View Answer

Explanation: By using convolution sum we get x1[n]*x2[n] = {14, 16, 14, 16}. This can be verified using tabular method of convolution.

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