SIGNALS AND SYSTEMS QUESTION BANK

UNIT-I: INTRODUCTION
Syllabus

Definition of Signals and Systems, Classification of Signals, Classification of Systems, Operations on

signals: time-shifting, time-scaling, amplitude-shifting, amplitude-scaling. Problems on classification
and characteristics of Signals and Systems. Complex exponential and sinusoidal signals, Singularity
functions and related functions: impulse function, step function signum function and ramp function.
Analogy between vectors and signals, orthogonal signal space, Signal approximation using orthogonal
functions, Mean square error, closed or complete set of orthogonal functions, Orthogonality in
complex functions.
Related problems.
QUESTION BANK
PART-A

1. Define Signal.
2. Define system.
3. What are the major classifications of the signal?
4. Define discrete time signals and classify them.
5. Define continuous time signals and classify them.
6. Define discrete time unit step &unit impulse.
7. Define continuous time unit step and unit impulse.
8. Define unit ramp signal.
9. Define periodic signal and non-periodic signal.
10. Define even and odd signal ?
11. Define Energy and power signal.
12. Define unit pulse function.
13. Define continuous time complex exponential signal.
14. What is continuous time real exponential signal.
15. What is continuous time growing exponential signal?
State the BIBO criterion for stability.

PART-B

1. Prove the following:

(i) The power of the energy signal is zero over infinite time.
(ii) The energy of the power signal is infinite over infinite time.( Regular, Feb/March 2022, R20,
Set-1, 7M, E-Evaluate)
2.Define the error function while approximating signals and hence derive the
expression for condition for orthogonality between two waveforms f1(t) andf2(t).
(Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)
3 .Define a system. How are the systems classified? Define each one of them.
(Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)

4. Test the Causality and Stability of the following system

(i) y(n) = x(n) – x(–n–1) + x(n–1) (ii ) y(t) = 5 e–2t u(t).
(Regular, Feb/March 2022, R20, Set-1, 7M, C-Create)
 5. Determine whether the following signals are energy or power signals.
(i)x(t)=sin2ω0t (ii)x(t)=tu(t). (Reg/Sup, Jan 2023, R20, Set-1, 7M, E-Evaluate)

6. Distinguish between Causal and Non-casual systems with an example. (Reg/Sup, Jan 2023, R20,
Set-1, 7M, A-Analyze)
7. Explain about time shifting and scaling properties with an example. (Reg/Sup, Jan 2023, R20,
Set-1, 7M, E-Evaluate)
8.Discuss briefly Orthogonality in complex functions. (Reg/Sup, Jan 2023, R20, Set-1, 7M, C-
Create)
9. Define a signal? Give various classifications of signals and explain each classification. (Sup, July
2023, R20, Set-1, 7M, R-Remember)
10.Find the power and rms value of signal x(t)=20Cos(2πt). (Sup, July 2023, R20, Set-1, 7M, R-
Remember)
11. Distinguish between
i) Linear and nonlinear systems
ii) Time variant and Time invariant systems
iii) Stable and Unstable systems. (Sup, July 2023, R20, Set-1, 7M, A-Analyze)
12.Find whether the following signals are even or odd :
(i) e4t (ii) u(t + 2) − u(t − 2) (iii) u(−n + 2)u(n + 2) (Sup, July 2022, R20, Set-1, 7M,
R-Remember
13.Define orthogonal signal space and explain clearly its application in representing
a signal. (Sup, July 2022, R20, Set-1, 7M, R-Remember)
14.Distinguish between
i) Continuous-time and discrete-time systems
(ii) Static and dynamic systems
(iii) Causal and Non-Causal systems (Sup, July 2022, R20, Set-1, 7M, A-Analyze)
15. Verify whether x(t) = Ae–α(t . u (t)., α> 0 is an energy signal or not. (Sup, July 2022, R20, Set-1,
7M)

UNIT-II: FOURIER SERIES AND FOURIER TRANSFORM

Syllabus

Fourier series representation of continuous time periodic signals, properties of Fourier series,
Dirichlet’s conditions, Trigonometric Fourier series and Exponential Fourier series, Complex Fourier
spectrum. Deriving Fourier transform from Fourier series, Fourier transform of arbitrary signal,
Fourier transform of standard signals, Fourier transform of periodic signals, properties of Fourier
transforms, Fourier transforms involving impulse
function and Signum function. Introduction to Hilbert Transform.

PART-A
1. What are Dirichlet’s conditions for the convergence of Fourier series.
2. What is the significance of the Gibbs phenomenon.
3. What is the effect of symmetry on Fourier coefficients.
4. What is Parseval's theorem in the context of Fourier series.
5. What is the Fourier transform and how is it related to the Fourier series.
6. What are the properties of Fourier Transforms.
7. What is the definition of the Signum Function.
8. What is the Hilbert Transform.
9. What is the relationship between the Hilbert Transform and the Fourier Transform?
10. Write down the exponential form of the Fourier series representation of a Periodic
signal?
 11. Write down the trigonometric form of the fourier series representation of a periodic
signal?
PART-B
1.What is the Fourier transform of a rectangular pulse from t=-T/2tot=T/2. (Reg/Sup, Jan 2023,
R20, Set-1, 7M, R-Remember)
2.State and prove the time-convolution property of Fourier transform. (Reg/Sup, Jan 2023,
R20, Set-1, 7M)
3. Find the Fourier transforms of signalx(t)=e-A(t)sin(t). (Reg/Sup, Jan 2023, R20, Set-1, 7M, R-
Remember)
4. Show that the unit impulse function is the derivative of unit step function. (Reg/Sup, Jan
2023, R20, Set-1, 7M, R-Remember)
5. Derive the expression for Fourier Transform from Fourier Series. (Regular, Feb/March 2022,
R20, Set-1, 7M)
6. State and prove Differentiation and integration properties of Fourier Transform.( Regular,
Feb/March 2022, R20, Set-1, 7M)
7. State and prove Parseval’s relation of Fourier Transform. (Regular, Feb/March 2022, R20, Set-1,
7M)
8. Derive the relation between trigonometric and exponential Fourier series coefficients. (Regular,
Feb/March 2022, R20, Set-1, 7M, R-Remember)
9. Define Fourier transform. Explain the properties of Fourier transform. (Sup, July 2023, R20, Set-
1, 7M, R-Remember)
10. Find the trigonometric Fourier series expansion of a Half wave rectified cosine function with
fundamental time period of 2π. (Sup, July 2023, R20, Set-1, 7M, R-Remember)
 11.Find the Fourier transform of x(t)=u(2t),where u(t )is the unit step function. (Sup,
July 2023, R20, Set-1, 7M,R-Remember)
12.Explain Dirchlet’s conditions and its significance to obtain Fourier series
representation of any signal. (Sup,July 2023,R20,Set-1,7M,U-Understand)
13. Obtain the Fourier transform of the following functions. (i) Unit step
function,(ii) Unit impulse function. (Sup,July 2022,R20,Set-1,7M)
14. Find the complex exponential Fourier series coefficient of the signal
x(t) = sin3πt + 2cos4πt (Sup,July 2022,R20,Set-1,7M,R-Remember)
15.Explain the Fourier transform of signum function and also sketch. It s magnitude
and phase spectra. (Sup,July 2022,R20,Set-1,7M,U-Understand)
16.What is the Significance of Hilbert Transform? Explain in detail.
(Sup,July 2022,R20,Set-1,7M,R-Remember)

UNIT-III: ANALYSIS OF LINEAR SYSTEMS

Syllabus
Introduction, Linear system, impulse response, Response of a linear
system, Linear time invariant (LTI) system, Linear time
variant(LTV)system, Concept of convolution in time domain and
frequency domain, Graphical representation of convolution, Transfer
function of a LTI system, Related problems. Filter characteristics of
linear systems. Distortion less transmission through a system, Signal
band width, system band width, Ideal LPF, HPF and BPF characteristics,
Causality and Poly-Wiener criterion for physical realization, relationship
between bandwidth and rise time.

PART-A

1. Define Transfer function of the DT system.

2. Define impulse response of a DT system.
3. State the significance of difference equations.
4. Write the difference equation for Discrete time system.
5. Define frequency response of the DT system.
6. What is the condition for stable system.
7. What are the blocks used for block diagram representation.
8. State the significance of block diagram representation.
9. What are the properties of convolution?
10. State the Commutative properties of convolution?
11. State the Associative properties of convolution
12. State Distributive properties of convolution
13. Define causal system.
14. What is the impulse response of the system y(t)=x(t-t0).

PART-B

1. Obtain the conditions for distortion less transmission through a system. (Reg/Sup, Jan
2023, R20, Set-1, 7M)
 2. Discuss the concept of convolution in time domain and frequencydomain. (Reg/Sup, Jan
2023, R20, Set-1, 7M)
3. Write about filter characteristics of linear systems. (Reg/Sup, Jan 2023, R20, Set-1, 7M)
4. Find the convolution of two signals x(t)=u(t-1)–u(t+1) and h(t)=e-atu(t), a>0. (Reg/Sup,
Jan 2023, R20, Set-1, 7M, R-Remember)
5.What is an LTI system? Explain its properties. Derive an expression for the transfer
function of an LTI system.( Regular, Feb/March 2022, R20, Set-1, 7M, R-
Remember)
6.Explain the concept of Paley-Wiener criterion for physical realizability using relevant
expressions. (Regular, Feb/March 2022, R20, Set-1, 7M, E-Evaluate)
7.Explain the filter characteristics of ideal LPF, HPF and BPF using their magnitude and
phase responses. (Regular, Feb/March 2022, R20, Set-1, 7M, E-Evaluate)
8.Obtain conditions for the distortion less transmission through a system. Regular,
Feb/March 2022, R20, Set-1, 7M)
9. Explain the filter characteristics of ideal LPF,HPF and BPF using their magnitude and
phase responses. (Sup, July 2023, R20, Set-1, 7M, E-Evaluate)

10. Obtain the impulse response of an LTI system defined by dy(t)/dt+2y(t)=x(t).

Also obtain the response of this system when excited by e–2tu(t). (Sup, July 2023, R20,
Set-1, 7M)
11. What is the impulse response of two LTI systems connected in parallel? State the
convolution Integral for CT LTI systems? (Sup, July 2023, R20, Set-1, 7M, R-
Remember)
12. Explain the characteristics of ideal LPF and HPF. (Sup, July 2023, R20, Set-1, 7M,
E-Evaluate)
13.Prove that the Transmission of a pulse through a Low Pass Filter causes the
dispersion of the pulse. (Sup,July 2022,R20,Set-1,7M,E-Evaluate)
14.Derive the relation between bandwidth and rise time. (Sup,July 2022,R20,Set-1,7M)
15.State and prove the sampling theorem for low pass signals. (Sup,July 2022,R20,Set-
1,7M)
16.Explain the detection of periodic signals in the presence of noise by cross-
correlation. (Sup,July 2022,R20,Set-1,7M,U-Understand)

UNIT–IV
Syllabus
CORRELATION: Auto-correlation and cross-correlation of functions,
properties of correlation function, Energy density spectrum, Parseval’s
theorem, Power density spectrum, Relation between Convolution and
correlation, Detection of periodic signals in the presence of noise by
correlation, Extraction of signal from noise by filtering.
SAMPLINGTHEOREM: Graphical and analytical proof for Band
Limited Signals, impulse sampling, Natural and Flat top Sampling,
Reconstruction of signal from its samples, effect of under sampling –
Aliasing, Introduction to B and Pass sampling, Related problems.
 PART-A

1. What is meant by sampling.

2. State Sampling theorem.
3. What is meant by aliasing.
4. What are the effects aliasing.
5. How the aliasing process is eliminated.
6. .Define Nyquist rate and Nyquist interval.
7. Define sampling of band pass signals.
8. What is the difference between correlation and covariance.
9. What is auto -correlation.
10. What is cross-correlation.
11. What is the relationship between the power density spectrum and the autocorrelation
function?
PART-B
1.Find the Nyquist rate andNyquist interval or the signals
(a) rect(300t)
(b) 10sin40ᴨtcos300ᴨt(Reg/Sup, Jan 2023, R20, Set-1, 7M, R-Remember)

2.Explain the difference between Impulse, Natural and Top Sampling. (Reg/Sup, Jan 2023,
R20, Set-1, 7M, U-Understand)
3. Define power density spectrum and its properties. (Reg/Sup, Jan 2023, R20, Set-1, 7M,
R-Remember)
4. Interpret about the sampling of band pass signals. (Reg/Sup, Jan 2023, R20, Set-1, 7M,
E-Evaluate)
5. State and explain the sampling theorem for band pass signals.( Regular, Feb/March
2022, R20, Set-1, 7M)I
6. Explain the method of detection of periodic signals in the presence of noise by
correlation. (Regular, Feb/March 2022, R20, Set-1, 7M, U-Understand)

7. Find the Cross correlation between triangular and gate function as shown in below.

(Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)

8. Derive the relationship between autocorrelation and energy spectral density of

an energy signal.
(Regular, Feb/March 2022, R20, Set-1, 7M)
9. Explain briefly detection of periodic signals in the presence of noise by correlation. (Sup,
July 2023, R20, Set-1, 7M,U-Understand)

10.Explain the relation between convolution and correlation. (Sup, July 2023, R20, Set-
 1, 7M, U-Understand)
11. Prove that auto correlation function and energy/power spectral density function
forms Fourier Transform pair. (Sup, July 2023, R20, Set-1, 7M,E-Evaluate)
12. Determine the auto correlation function and energy spectral density function of
x(t)=e–atu(t). (Sup, July 2023, R20, Set-1, 7M, E-Evaluate)
13.State and prove the sampling theorem for low pass signals. (Sup,July 2022,R20,Set-
1,7M)
14.Explain the detection of periodic signals in the presence of noise by cross-
correlation. (Sup,July 2022,R20,Set-1,7M,U-Understand)
15. Compare various sampling methods. (Sup,July 2022,R20,Set-1,7M,E-Evaluate)
16. Verify Parseval’s theorem for the energy of the signal x(t) = e–3tu(t). (Sup,July
2022,R20,Set-1,7M)

UNIT- V
Syllabus

LAPLACE TRANSFORMS: Introduction, Concept of region of

convergence (ROC) for Laplace transforms, constraints on ROC for
various classes of signals, Properties of L.T’s, Inverse Laplace
transform, Relation between L.T’s, and F.T. of a signal. Laplace
transform of certain signals using waveform synthesis.
Z–TRANSFORMS: Concept of Z-Transform of a discrete sequence.
Region of convergence in Z- Transform, constraints on ROC for various
classes of signals, Inverse Z- transform, properties of Z-transforms.
Distinction between Laplace, Fourier and Z transforms.

PART-A

1. Determine the transposed structure for the system given by difference equation
y(n)=(1/2)y(n-1)-(1/4)y(n-2)+x(n)+x(n-1)
b) Realize H(s)=s(s+2)/(s+1)(s+3)(s+4) in cascade form
2. A difference equation of a discrete time system is given below:
y(n)-3/4 y(n-1) +1/8 y(n-1) = x(n) +1/2 x(n-1)
3.draw direct form I and direct form II.
4.Realize the following structure in direct form II and direct form I
H(s) = s+1/s2 + 3s+5
5.Define Z transform.
6. What are the two types of Z transform? Define unilateral Z transform.
7. What is region of Convergence.
8. What are the Properties of ROC.
9. What is the time shifting property of Z transform.
10. What is the differentiation property in Z domain.
11. State convolution property of Z transform.
12. State the methods to find inverse Z transform.
13. State multiplication property in relation to Z transform.
14. State parseval’s relation for Z transform.
 15. What is the relationship between Z transform and Fourier transform.

PART-B

1.Define Laplace transform of signal x(t) and its region of

convergence(Reg/Sup, Jan 2023, R20, Set-1, 7M, R-Remember)
2.Find the Laplace transform of the following signal and its ROC. x(t) =
e -5t [u(t) - u(t-5)] (Reg/Sup, Jan 2023, R20, Set-1, 7M, R-Remember)
3.Distinguish between one-sided and two-sided z-transforms and its
ROC. (Reg/Sup, Jan 2023, R20, Set-1, 7M, A-Analyze)
4.Find the inverse z-transform of x(z)=z/(z+2)(z-3) when the ROC is
i) ROC:|z|<2 ii)ROC:2<|z|<3 (Reg/Sup, Jan 2023, R20,
Set-1, 7M, R-Remember).
5. Find the Laplace transform of the following signals:
(i) Impulse function (ii)unitstep function and iii) ASin(w0t)u(t)
(Sup, July 2023, R20, Set-1, 7M, R-Remember)
6.State the properties of ROC of Laplace Transform.
(Sup, July 2023, R20, Set-1, 7M)
7.State and prove the following properties of Ztransform:
(i) Time shifting, and
(ii) Differentiation in z-domain
(Sup, July 2023, R20, Set-1, 7M)
8.Distinguish between Fourier transform, Laplace transform and
z transforms. (Sup, July 2023, R20, Set-1, 7M, A-Analyze)
9. Find the Laplace Transform of the following:
(i) te–at u(t) and (ii) Cos(ω0t) u(t)
(Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)
10. What are the methods by which inverse z-transform can be found out? Explain any
one method. (Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)
11.State and prove time shifting and time convolution properties of z- transform.
(Regular, Feb/March 2022, R20, Set-1, 7M)

12. Find out the Laplace transform of the signal shown in below figure

(Regular, Feb/March 2022, R20, Set-1, 7M, R-Remember)

 13.State and prove time convolution property of Laplace Transform. (Sup,July
2022,R20,Set-1,7M)
14.Find the Z transform of x[n] = an+1 u[n+1]. (Sup,July 2022,R20,Set-1,7M,R-
Remember)
15.Obtain the Laplace transform of x(t) = e-at cos (ωo t) u (-t) and indicate its ROC.
(Sup,July 2022,R20,Set-1,7M)
16.Find the Z Transform of x[n] = nan–1 u[n]. (Sup,July 2022,R20,Set-1,7M,R-
Remember)