Important 2 marks Questions with Answers

Important 2mark Questions with Answers

UNIT 2: ANALYSIS OF CONTINUOUS TIME SIGNALS

1. Define Fourier series

Continuous time Fourier series is defined as

2. State Dirichlet conditions for Fourier series.

(i) The function x(t) should lie within the interval T₀

(ii) Function x(t) should be absolutely integrable.

(iii) Function x(t) should have finite number of maxima and minima within the interval T₀

(iv) Function x(t) should have finite number of discontinuities in the interval T₀.

3. What do the Fourier series co-efficients represent?

Fourier series co-efficient represents various frequency components present in  the signal.

4. What are the differences between Fourier series and Fourier transform.

5. What is the relationship between Laplace transform and Fourier transform.

Fourier transform is same as Laplace transform if S = jω

X(s) = X(jω)

6. Write the Fourier transform pair for x(t)

7. Find the Fourier transform of x(t) = e ^{– a t} u(t), a > 0

8. What is the Laplace transform of the function x(t) = u(t) – u(t-2)?

9. Find the laplace transform of the signal, u(t)

10. State the Initial and final value theorem of Laplace transform.

Initial value theorem

Initial value of x(t) is given as

Final value of x(t) is given as

11. State equation for trignometric Fourier series.

12. Find the Laplace transform of x(t) = t e ^{– a t} u(t), where a > 0

Differentiation in S domain property gives

13. Find the Laplace transform of signal u(t)

14. What is the Laplace transform of the function x(t) = u(t) - u(t-2)

15. Obtain the Fourier series co-efficients for

Discrete time Fourier series Fourier series

Comparing above equation with (1)

16. State the time scaling property of Laplace transform

Expansion in time domain is equivalent to compresion, in frequency domain.

17. Define the ROC of the Laplace transform.

The area in the S-plane where Laplace transform exists is called region of convergence.

18. Determine the Laplace transform of δ(t-5) and u(t-5)

19. Define Parseval's relation for continuous time periodic signal.

Total average power of the periodic signal x(t), is equal to the sum of the average powers of its phasor components i.e.,

20. Determine Laplace transform of x(t) = e ^{– a t} sin (ωt) a(t).

21. Determine the Fourier series coefficients for the signal cos πt.

The complex Exponential series representation of a periodic signal with fundamental T₀ is given by,

To evaluate the complex Fourier coefficients of cоs πt, we can Euler's formula.

22. Determine the LT of the signal δ(t-5) & u(t-5). [May '12]

Using time-shifting property LT, 

23. What is the FT of a DC signal of amplitude 1? [May'13]

24. Find the Fourier coefficients  [may'15] (R 13)

Expanding x(t) terms of complex exponentials,

Collecting terms we get,

Thus, the Fourier coefficient are,

25. Draw the spectrum of a CT rectangular pulse. [May'15]

The spectrum a CT rectangular pulse is a sinc function

26. Given  [May '15]

27. What is the inverse Fourier Transform of  [May'16]

28. Give the Laplace Transform of x(t) = 3e ^{– 2 t} u(t) - 2e ^{- t} u(t) with ROC.

29. Draw the single sided spectrum for x(t) = 7 + 10 cos [40 πt + π/2]. [Nov '11]

Expanding x(t) into complex sinusoid pairs,

The frequency pairs that define the two-sided line spectrum are  

30. State the convergence series representation of CT periodic signals. [Nov '14]

Most of the results presented for 2π - periodic functions extend easily to functions 2L- periodic functions. So we only discuss the case of 2π - periodic functions.

Definition. The function f(X) defined on [a, b], is said to be piecewise continuous if and only if, there exits a partition {X₁, X₂,...X_n} of [a, b] such that

(i) f(x) continuous on [a, b] except be for the points X_i,

(ii) The right-limit and lest-limit of f(X) at the points X_i exist.

31. Find the ROC of the LT of x(t) = u(t). [Nov' 14] (R 13)