Signals Fourier

8/11/2019 Signals Fourier

1/5


2/5

c) 1.0d) 1.4

Q7. The fundamental frequency of the composite signal

x(t) = 2+ 3 cos ( 0.2 t ) + cos ( 0.25 t + /2 ) + 4 cos ( 0.3 t - ) is

a) 0.05 rad/secb) 0.1 rad/secc) 0.2 rad/secd) 0.25 rad/sec

Q8. The fundamental frequency of the composite signal

x(t) = 30 sin 100t + 10 cos 300t + 6 sin (500t + /4)

a) 100b) 300c) 500d) 1500

Q9. x(t) is a periodic signal and is given by x(t) = e -t ; for one period - 1 t 1 over oneperiod = 2 . The d.c. component of x(t) is given by

a) e e -1 b) 0.5(e + e -1)c) e 0.5e -1 d) 0.5(e e -1)

Q10. A half wave rectified sinusoidal waveform has a peak voltage of 10V. Its averagevalue and the peak value of the fundamental component are respectively given by :

a) 10/ , 10/ b) 20/ , 10/ c) 10/ , 5/ d) 20/ , 5


3/5

Q11. Consider the following statements related to fourier series of a periodic waveform

a) It expresses the given periodic waveform as a combination of d.c component,sineand cosine components of different harmonic frequencies

b) The amplitude spectrum is discrete

c)

The evaluation of fourier coefficients gets simplified if waveform symmetriespropertiesd) The amplitude spectrum is continuous

Q12. A square wave is defined by x(t) = A for 0 < t < T 0/2 and A for T 0/2 < t < T 0. It isperiodically extended outside the interval. What is the general coefficient a n in thefourier expansion of this wave

a) 0b)

c)

d)

Q13. A periodic signal which can be expanded in Fourier series is

a) Is power signalb) Is energy signalc) Neither energy nor power

d) Can be energy or power depending on nature

Q14. The Fourier series of a real periodic function has only

P) Cosine terms if it is evenQ) Sine terms if it is evenR) Cosine terms if it is oddS) 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


4/5

Q15. The trigonometric Fourier series of an even function does not even have the

a) Cosine termsb) Dc componentc) Sine terms

d)

Odd terms.

Q16. Match the following and choose the correct combination.

GROUP-1

E. Continuous and aperiodic signal

F. Continuous and periodic signal

G. Discrete and aperiodic signal

H. Discrete and periodic signal

GROUP-2

1. Fourier representation is continuous and aperiodic

2. Fourier representation is discrete and aperiodic

3. Fourier representation is continuous and periodic

4. Fourier representation is discrete and periodic

a). E-3,F-2,G-4,H-1

b) E-1,F-3,G-2,H-4

c) E-1,F-2,G-3,H-4

d) E-2,F-1,G-4,H-3

Q17. Choose the function f(t); - < t < +, for which a Fourier Series cannot be defined

a. 3 sin (25t)b. 4 cos(20t+3) +3 sin (10t)c. exp(-|t|)sin (25t)d. 1


5/5

Q18. Consider the function

f(x) = 2x, 0 < x < 1.

A. Find the Fourier cosine series of f(x) Hint: youre using the even half -range

expansion.

Q19. Let f(x) = |x| for 2 x 2, and let g(x) = 4|x| + 3 for 2 x 2. The Fourier

series for f is given by

Q20. Find the Fourier series for ,

Documents

Signals Fourier