Consider a signal defined by

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

Its Fourier Transform is

Workspace

Report

The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is

Workspace

Report

The value of the integral

**A. **

**B. **

**C. ** 24/13

**D. ** 12/13

**Answer : ****Option B**

**Explaination / Solution: **

over the contour |z| = 1, taken in the anti-clockwise direction, would be

Workspace

Report

Suppose x_{1}(t) and x_{2}(t) have the Fourier transforms as shown below

**A. ** x1(t) and x2(t) are complex and x1(t) x2(t) is also complex with nonzero imaginary part

**B. ** x1(t) and x2(t) are real and x1(t) x2(t) is also real

**C. ** x1(t) and x2(t) are complex but x1(t) x2(t) is real

**D. ** x1(t) and x2(t) are imaginary but x1(t) x2(t) is real

**Answer : ****Option C**

**Explaination / Solution: **

Which one of the following statements is TRUE?

Workspace

Report

The impulse response h(t) of a linear time invariant continuous time system is
described by where u(-t) denotes the unit
step function, and α and β are real constants. This system is stable if

**A. ** α is positive and β is positive

**B. ** α is negative and β is negative

**C. ** α is negative and β is negative

**D. ** α is negative and β is positive

**Answer : ****Option D**

**Explaination / Solution: **

This system is stable only when bounded input has bounded output For stability αt < 0 for t > 0 that implies α < 0 and βt > 0 for t > 0 that implies β > 0. Thus, α is negative and β is positive.

Workspace

Report

Let f(x) be a real, periodic function satisfying f(−x) = −f(x). The general form of its Fourier series representation would be

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option B**

**Explaination / Solution: **

Workspace

Report

A discrete time linear shift - invariant system has an impulse response h[n] with h[0] = 1,h[1] =- 1,h[2] = 2, and zero otherwise The system is given an input sequence x[n] with x[0] = x[2] = 1, and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are respectively

**A. ** 5, 2

**B. ** 6, 2

**C. ** 6, 1

**D. ** 5, 3

**Answer : ****Option D**

**Explaination / Solution: **

Workspace

Report

Let z(t) = x(t) * y(t), where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).
**A. ** c.x(ct) * y(ct)

**B. ** x(ct) * Y(ct)

**C. ** c.x(t) * y(ct)

**D. ** c.x(ct) * y(t)

**Answer : ****Option A**

**Explaination / Solution: **

Workspace

Report

The Fourier series of a real periodic function has only (P) cosine terms if it is even (Q) sine terms if it is even (R) cosine terms if it is odd (S) sine terms if it is odd Which of the above statements are correct ?

**A. ** P and S

**B. ** P and R

**C. ** Q and S

**D. ** Q and R

**Answer : ****Option A**

**Explaination / Solution: **

The Fourier series of a real periodic function has only cosine terms if it is even and sine terms if it is odd.

The Fourier series of a real periodic function has only cosine terms if it is even and sine terms if it is odd.

Workspace

Report

For a periodic signal the
fundamental frequency in radians/s is

**A. ** 100

**B. ** 300

**C. ** 500

**D. ** 1500

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

Workspace

Report