1. What are the Dirichlet’s conditions of
Fourier series?
(i).The
function x(t) should be single valued within the interval T0
(ii). The
function x(t) should have atmost a finite number of discontinuities in the
interval T0
(iii).
The function x(t) should have finite number of maxima and minima in the
interval T0
(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-atu(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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