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Signals and Systems - Analysis of Continuous Time Signals - Important Short Questions and Answers: Analysis of Continuous Time Signals

**1.** **What are the Dirichlet’s conditions of
Fourier series?**

(i).The
function x(t) should be single valued within the interval T_{0}

(ii). The
function x(t) should have atmost a finite number of discontinuities in the
interval T_{0}

(iii).
The function x(t) should have finite number of maxima and minima in the
interval T_{0}

(iv). The
function should have absolutely integrable.

**2.** **State any two properties of continuous time
Fourier transform.**

**Convolution (Time) Property:**

It states
that,

x
(t)*y(t) **↔ ^{(FT)}**X
(jΩ)Y(jΩ)

**Modulation Property (or) Frequency Shifting:**

It states
that,

**3. Find the
laplace transform of the signal**

**4. What are the difference between Fourier series
and Fourier transform? **

**Fourier Series**

1.
Fourier series is calculated for periodic signals.

2.
Expands the signals in time domain.

3. Three
types of Fourier series such as trigonometric, Polar and Complex Exponential

**Fourier Transform**

1.
Fourier Transform is calculated for non-periodic as well as periodic signals.

2.
Represents the signal in frequency Domain

3.
Fourier transform has no such types.

**5.** **State initial and final value theorem of
Laplace transform.**

**6. Define the Fourier transform pair for continuous
time signal. (Or) Give synthesis and
analysis equations of CT Fourier Transform. **

**7.** **Find inverse Fourier transform of X(ω)=2πδ
(ω).**

**8. State the
time scaling property of Laplace Transform.**

**9.** **What is the Fourier Transform of a DC
signal of amplitude 1?**

**10. Define region of convergence of the Laplace
Transform.**

**11. State the relationship between fourier
transform and laplace transform.**

• The
laplace transform is same as fourier transform when s =jω

**12.
****State any
two properties of ROC of laplace transform X(s) of a signal x(t).**

__Properties
of ROC:__

·
No poles lie in ROC.

·
ROC of the causal signal is right hand sided. It is
of the form Re(s)>a.

·
ROC of the non causal signal is left hand sided. It
is of the form Re(s) < a.

·
The system is stable if its ROC includes jω**
**axis of
s-plane.

**13. Determine fourier series coefficients for
signal cos **

**14. Give analysis and synthesis equations of
fourier transform.**

**15. Obtain the fourier transform of X(f) = e**-at**u(t)**** , a > 0**

**16. What is the condition to be satisfied for the
existence of fourier transform for CT periodic signals? **

The function
x(t) should be absolutely integrable for the existence of fourier
transform.

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