1 $Which of the following signals can be represented by a Fourier Series?$

A.

Any continuous time signal

B.

Energy signals only

C.

Periodic power signals

D.

Aperiodic energy signals

2 $The condition for a signal to be periodic with period is:$

A.

for all

B.

for only

C.

D.

3 $In the trigonometric Fourier series representation, the term represents:$

A.

Fundamental frequency component

B.

Average (DC) value of the signal

C.

RMS value of the signal

D.

Phase angle

4 $The fundamental angular frequency is related to the time period by:$

A.

B.

C.

D.

5 $Which of the following is the correct synthesis equation for the Exponential Fourier Series?$

A.

B.

C.

D.

6 $The set of functions form an:$

A.

Inconsistent set

B.

Orthogonal set

C.

Exponential set

D.

Aperiodic set

7 $For the Exponential Fourier Series coefficient, what is the value of ?$

A.

B.

The RMS value

C.

The average value of

D.

8 $If a periodic signal is even, i.e.,, its Trigonometric Fourier Series contains:$

A.

Sine terms only

B.

Cosine terms and a DC term

C.

Sine terms and a DC term

D.

Odd harmonics only

9 $If a periodic signal is odd, i.e.,, which coefficients are zero?$

A.

only

B.

only

C.

and

D.

and

10 $The relationship between the exponential Fourier coefficient and trigonometric coefficients (for) is:$

A.

B.

C.

D.

11 $The Dirichlet conditions provide sufficient conditions for:$

A.

The periodicity of a signal

B.

The convergence of the Fourier Series

C.

The linearity of a system

D.

The stability of a system

12 $Which of the following is NOT a Dirichlet condition?$

A.

must be absolutely integrable over one period

B.

must have a finite number of maxima and minima in one period

C.

must differ from zero for all

D.

must have a finite number of discontinuities in one period

13 $At a point of discontinuity, the Fourier series of converges to:$

A.

B.

C.

D.

14 $The Gibbs phenomenon refers to:$

A.

The divergence of Fourier series for non-periodic signals

B.

Oscillatory behavior and overshoot near discontinuities in a truncated Fourier series

C.

The decay of coefficients for smooth signals

D.

The phase shift in the frequency spectrum

15 $For a real-valued signal, the exponential Fourier series coefficients satisfy the conjugate symmetry property:$

A.

B.

C.

D.

16 $A signal has half-wave symmetry if:$

A.

B.

C.

D.

17 $A signal with half-wave symmetry contains only:$

A.

Even harmonics

B.

Odd harmonics

C.

DC component and even harmonics

D.

Cosine terms only

18 $Parseval's relation for the Exponential Fourier Series states that the average power is:$

A.

B.

C.

D.

19 $If, then the coefficients of the time-shifted signal are:$

A.

B.

C.

D.

20 $If, then the coefficients of the time-reversed signal are:$

A.

B.

C.

D.

21 $The Fourier series coefficients of the derivative of a periodic signal are related to (coefficients of) by:$

A.

B.

C.

D.

22 $For the integration property to hold (i.e., coefficients become), what condition must the signal satisfy?$

A.

It must be even

B.

It must be odd

C.

Its average value must be zero

D.

It must be discontinuous

23 $Multiplication of two periodic signals and in the time domain corresponds to what operation on their Fourier series coefficients?$

A.

Multiplication

B.

Addition

C.

Discrete Convolution

D.

Differentiation

24 $The plot of versus frequency (or index) is known as the:$

A.

Phase spectrum

B.

Magnitude spectrum

C.

Power density

D.

Phase plot

25 $For a real-valued signal, the magnitude spectrum is:$

A.

An odd function of

B.

An even function of

C.

Always zero

D.

Non-symmetric

26 $For a real-valued signal, the phase spectrum is:$

A.

An odd function of

B.

An even function of

C.

Constant

D.

Always positive

27 $The Fourier series of an Impulse Train consists of:$

A.

Constants (all are equal)

B.

Decaying exponentials

C.

Sine waves only

D.

Zero coefficients

28 $If a signal is real and even, its exponential Fourier coefficients are:$

A.

Real and Even

B.

Purely Imaginary and Odd

C.

Complex

D.

Real and Odd

29 $If a signal is real and odd, its exponential Fourier coefficients are:$

A.

Real and Even

B.

Purely Imaginary and Odd

C.

Purely Imaginary and Even

D.

Complex

30 $The frequency spectrum of a continuous time periodic signal is:$

A.

Continuous and periodic

B.

Continuous and aperiodic

C.

Discrete and aperiodic

D.

Discrete and periodic

31 $What happens to the Fourier coefficients if the signal is time-scaled to where ?$

A.

The coefficients change to

B.

The coefficients remain the same, but the fundamental frequency becomes

C.

The coefficients are squared

D.

The coefficients become zero

32 $Which signal has Fourier coefficients that decay as ?$

A.

A smooth continuous signal

B.

A signal with jump discontinuities (e.g., Square wave)

C.

A signal with discontinuous first derivative (e.g., Triangular wave)

D.

Impulse train

33 $Which signal has Fourier coefficients that decay as ?$

A.

Square wave

B.

Triangular wave (Continuous but discontinuous slope)

C.

Impulse train

D.

Sine wave

34 $When simulating the frequency spectrum of a periodic signal using software, the spacing between spectral lines is determined by:$

A.

The sampling frequency

B.

The fundamental frequency

C.

The amplitude of the signal

D.

The phase of the signal

35 $In a software simulation, calculating Fourier Series coefficients often involves numerical integration. Which method effectively implements this for discrete data?$

A.

Laplace Transform

B.

Fast Fourier Transform (FFT)

C.

Z-Transform

D.

Convolution

36 $The Power Spectral Density (PSD) of a periodic signal describes:$

A.

How energy is distributed with frequency

B.

How power is distributed with frequency

C.

The total energy of the signal

D.

The phase shift at each frequency

37 $If, the exponential Fourier coefficients are:$

A.

, others 0

B.

C.

, others 0

D.

38 $If, the exponential Fourier coefficients are:$

A.

B.

C.

D.

39 $What is the Fourier Series representation of a constant signal ?$

A.

for

B.

for all

C.

D.

It does not exist

40 $The linearity property of Fourier Series implies that if, then its coefficients are:$

A.

B.

C.

D.

41 $Frequency shifting: If the coefficients are shifted to, the time domain signal becomes:$

A.

B.

C.

D.

42 $The Fourier series expansion of a periodic square wave with zero DC value contains:$

A.

All harmonics

B.

Odd harmonics of sine (or cosine) terms

C.

Even harmonics only

D.

Only the fundamental component

43 $If a periodic signal is decomposed into even and odd parts, then generates:$

A.

Re

B.

Im

C.

D.

Zero coefficients

44 $The total power of a periodic signal is 10 W. If the DC component power is 2 W, what is the power contained in the AC components?$

A.

12 W

B.

8 W

C.

5 W

D.

100 W

45 $Why is the exponential form of Fourier series often preferred over the trigonometric form in software simulation and analysis?$

A.

It avoids complex numbers

B.

Mathematical compactness and ease of manipulation

C.

It only deals with positive frequencies

D.

It has no convergence issues

46 $For a periodic signal, if, the Fourier Series becomes:$

A.

Fourier Transform

B.

Laplace Transform

C.

Z-Transform

D.

Discrete Fourier Series

47 $Which mathematical tool is used to prove the orthogonality of the basis functions in Fourier Series?$

A.

Integration over one period

B.

Differentiation

C.

Convolution

D.

Limit as

48 $If a periodic signal is time-shifted, which aspect of its spectrum changes?$

A.

Magnitude spectrum only

B.

Phase spectrum only

C.

Both magnitude and phase

D.

Neither magnitude nor phase

49 $In the context of software simulation, 'Aliasing' would occur if:$

A.

The signal is not periodic

B.

The sampling rate is too low compared to the highest frequency harmonic

C.

The Fourier series is truncated

D.

The signal has no DC component

50 $The RMS value of a periodic signal can be calculated from the Fourier coefficients as:$

A.

B.

C.

D.

Unit 3 - Practice Quiz