ENEX 255Bachelor in Electronics, Communication and Information Engineering · Semester 41 Paper Available
Signals and Systems
Past examination question papers and complete curriculum syllabus for Signals and Systems (ENEX 255), Bachelor in Electronics, Communication and Information Engineering Semester 4 under Institute of Engineering (IOE), Tribhuvan University.
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Most Frequently Asked Questions
Top recurring IOE board exam questions for Signals and Systems with verified mark schemes, formula notation, and recurrence frequency.
Showing 30 of 30 top repeated questions
Signal and its Types
5 Questions
#1Repeated 4 Times[8 Marks]Signal and its Types
Define energy signal and power signal with mathematical expressions and examples. Determine whether the signal $x(t) = e^{-at}u(t)$ for $a > 0$ (or $x(t) = 5\cos(t)$) is an energy signal, power signal, or neither, and calculate its total energy or average power.
Appeared in:2081 Chaitra2079 Jestha2078 Chaitra2077 Chaitra
#2Repeated 3 Times[6 Marks]Signal and its Types
Explain System Properties: Linearity, Time-Invariance, Memory, Causality, and Invertibility. Test whether the following systems satisfy linearity and time-invariance: (a) $y(t) = x(2t)$, (b) $y(t) = t x(t)$, (c) $y[n] = x^2[n]$.
Appeared in:2081 Chaitra2078 Chaitra2075 Bhadra
#3Repeated 2 Times[4 Marks]Signal and its Types
Show that any arbitrary continuous or discrete time signal can be decomposed into an even component and an odd component ($x(t) = x_e(t) + x_o(t)$). Find and sketch the even and odd components of a given signal.
Appeared in:2076 Baisakh2075 Bhadra
#4Repeated 2 Times[6 Marks]Signal and its Types
Explain time shifting, time scaling, and time reversal (reflection) operations on continuous-time and discrete-time signals with neat graphical illustrations.
Appeared in:2081 Chaitra2076 Baisakh
#5Repeated 2 Times[4 Marks]Signal and its Types
Derive the necessary condition for a discrete-time complex exponential signal $x[n] = e^{j\omega_0 n}$ to be periodic. What is its fundamental period $N$?
Appeared in:2079 Jestha2076 Baisakh
Fourier Transform
11 Questions
#1Repeated 4 Times[6 Marks]Fourier Transform
State and prove Parseval's relation for: (a) Continuous-Time Fourier Series, and (b) Discrete-Time Fourier Series (DTFS).
Appeared in:2079 Jestha2078 Chaitra2076 Baisakh2076 Bhadra
#2Repeated 4 Times[6 Marks]Fourier Transform
Find the Continuous-Time Fourier Transform (CTFT) of the signal $x(t) = e^{-at}u(t)$ for $a > 0$. Plot its magnitude and phase spectrum.
Appeared in:2081 Chaitra2079 Chaitra2078 Chaitra2076 Bhadra
#3Repeated 3 Times[6 Marks]Fourier Transform
State and prove the Convolution property of the Continuous-Time Fourier Transform: $\mathcal{F}\{x_1(t) * x_2(t)\} = X_1(j\omega) X_2(j\omega)$.
Appeared in:2081 Chaitra2079 Chaitra2076 Bhadra
#4Repeated 3 Times[8 Marks]Fourier Transform
Derive the synthesis and analysis equations of the Discrete-Time Fourier Transform (DTFT). State and prove the Linearity, Time-Shifting, and Frequency-Shifting properties of DTFT.
Appeared in:2081 Chaitra2077 Chaitra2076 Baisakh
#5Repeated 3 Times[8 Marks]Fourier Transform
State and prove the Dirichlet Conditions for the existence and convergence of Fourier Series. Determine the Continuous-Time Fourier Series (CTFS) exponential coefficients $c_n$ for a periodic symmetric square wave and plot its line spectrum.
Appeared in:2081 Chaitra2078 Chaitra2076 Baisakh
#6Repeated 3 Times[8 Marks]Fourier Transform
State and prove key properties of the Continuous-Time Fourier Transform (CTFT): Time-Shifting, Frequency-Shifting (Modulation), Time-Scaling, and Duality Property. Compute the Fourier transform of a Gaussian pulse $x(t) = e^{-a t^2}$.
Appeared in:2081 Chaitra2079 Jestha2075 Bhadra
#7Repeated 3 Times[8 Marks]Fourier Transform
State and prove Parseval's Theorem for Continuous-Time Energy and Power Signals. For signal $x(t) = e^{-a t} u(t)$ ($a > 0$), calculate the total energy in the time domain and verify using frequency domain energy spectral density $|X(\omega)|^2$.
Appeared in:2081 Chaitra2078 Chaitra2074 Bhadra
#8Repeated 3 Times[8 Marks]Fourier Transform
Define the Discrete-Time Fourier Transform (DTFT). State its properties and compute the frequency response $H(e^{j\Omega})$ and magnitude response $|H(e^{j\Omega})|$ of an LTI system described by difference equation $y[n] - 0.5 y[n-1] = x[n]$.
Appeared in:2081 Chaitra2077 Chaitra2074 Bhadra
#9Repeated 3 Times[6 Marks]Fourier Transform
Explain the relationship and mapping between Continuous-Time Fourier Transform (CTFT), Laplace Transform, Discrete-Time Fourier Transform (DTFT), and Z-Transform.
Appeared in:2081 Chaitra2077 Chaitra2076 Baisakh
#10Repeated 2 Times[6 Marks]Fourier Transform
State and prove the Duality property and Time-Scaling property of the Continuous-Time Fourier Transform.
Appeared in:2081 Chaitra2077 Chaitra
#11Repeated 1 Times[6 Marks]Fourier Transform
Compute the 4-point Discrete Fourier Transform (DFT) for the sequence $x[n] = \{3, -2, 1, 4\}$ using the twiddle factor matrix $W_N^{kn}$.
Appeared in:2079 Jestha
Linear Time Invariant (LTI) System
12 Questions
#1Repeated 4 Times[8 Marks]Linear Time Invariant (LTI) System
Define an LTI system and explain fundamental system properties: Linearity, Time-Invariance, Causality, Memory, and BIBO Stability. State the condition for an LTI system to be causal and stable in terms of impulse response.
Appeared in:2081 Chaitra2079 Chaitra2078 Chaitra2076 Baisakh
#2Repeated 3 Times[6 Marks]Linear Time Invariant (LTI) System
Derive the Convolution Integral for a continuous-time Linear Time-Invariant (LTI) system: $y(t) = \int_{-\infty}^\infty x(\tau)h(t-\tau)d\tau$.
Appeared in:2081 Chaitra2077 Chaitra2075 Bhadra
#3Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Derive the Convolution Sum for a discrete-time LTI system: $y[n] = \sum_{k=-\infty}^\infty x[k]h[n-k]$. Find and plot the convolution sum of sequences $x[n] = \{1, 3, 4, 3, 1\}$ and $h[n] = \{2, 2, -2\}$ (or $x[n] = \{3, 1, 5\}$ and $h[n] = \{1, 4, -2, 3\}$).
Appeared in:2081 Chaitra2079 Chaitra2076 Baisakh
#4Repeated 3 Times[7 Marks]Linear Time Invariant (LTI) System
Derive formula to calculate the impulse response of an Ideal Low-Pass Filter in continuous/discrete time. Prove, with necessary mathematical derivations, that an ideal low-pass filter is non-causal and physically unrealizable.
Appeared in:2079 Jestha2077 Chaitra2076 Baisakh
#5Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Define the Continuous-Time Convolution Integral $y(t) = \int_{-\infty}^{\infty} x(\tau) h(t - \tau) d\tau$. Compute the analytical and graphical convolution of two rectangular pulses $x(t) = u(t) - u(t - 2)$ and $h(t) = u(t) - u(t - 3)$.
Appeared in:2081 Chaitra2079 Jestha2077 Chaitra
#6Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Explain Ideal Lowpass Filter and Paley-Wiener Criterion for filter physical realizability. Prove that an ideal brick-wall lowpass filter is non-causal and exhibits the Gibbs phenomenon in its step response.
Appeared in:2081 Chaitra2077 Chaitra2075 Bhadra
#7Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Define the Bilateral Laplace Transform and Region of Convergence (ROC). Derive properties of ROC for causal, anti-causal, and two-sided signals. Determine the Laplace transform and ROC of $x(t) = e^{-2t} u(t) + e^{-3t} u(-t)$.
Appeared in:2081 Chaitra2078 Chaitra2077 Chaitra
#8Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Solve the differential equation $\frac{d^2 y}{dt^2} + 5\frac{dy}{dt} + 6y(t) = \frac{dx}{dt} + x(t)$ for unit step input $x(t) = u(t)$ with initial conditions $y(0^-) = 1, y'(0^-) = 2$ using the unilateral Laplace transform, separating Zero-Input and Zero-State responses.
Appeared in:2081 Chaitra2079 Jestha2075 Bhadra
#9Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Define the Discrete-Time Convolution Sum $y[n] = \sum_{k=-\infty}^{\infty} x[k] h[n - k]$. Compute the convolution of $x[n] = (0.5)^n u[n]$ and $h[n] = u[n] - u[n - 4]$.
Appeared in:2081 Chaitra2078 Chaitra2076 Baisakh
#10Repeated 3 Times[8 Marks]Linear Time Invariant (LTI) System
Determine the System Function $H(z)$, pole-zero constellation, impulse response $h[n]$, and BIBO stability for a discrete LTI system given by $y[n] - \frac{3}{4} y[n-1] + \frac{1}{8} y[n-2] = x[n] + 2 x[n-1]$.
Appeared in:2081 Chaitra2079 Jestha2078 Chaitra
#11Repeated 3 Times[6 Marks]Linear Time Invariant (LTI) System
Define Group Delay $\tau_g(\omega) = -\frac{d\theta(\omega)}{d\omega}$ and Phase Delay $\tau_p(\omega) = -\frac{\theta(\omega)}{\omega}$. Explain how non-linear phase response causes dispersion and waveform distortion in broadband communication channels.
Appeared in:2081 Chaitra2079 Jestha2074 Bhadra
#12Repeated 2 Times[8 Marks]Linear Time Invariant (LTI) System
For a system characterized by a linear constant coefficient difference equation, determine the frequency response $H(e^{j\omega})$ and impulse response $h[n]$. Plot the magnitude and phase response.
Appeared in:2079 Jestha2077 Chaitra
Sampling
2 Questions
#1Repeated 5 Times[8 Marks]Sampling
State and prove the Nyquist-Shannon Sampling Theorem using frequency-domain analysis. Define Nyquist rate and Nyquist interval. What is aliasing and how is it prevented? Determine the Nyquist rate for $x(t) = \cos(200\pi t) + \sin(400\pi t)$.
Appeared in:2081 Chaitra2079 Chaitra2078 Chaitra2076 Baisakh2076 Bhadra
#2Repeated 3 Times[8 Marks]Sampling
Explain the Sampling Theorem for low-pass and band-pass signals. What is Aliasing? Explain Flat-top sampling and the derivation of aperture distortion with equalizer reconstruction.
Chapter-wise Units & Micro-Syllabus Topics (6 Units)
1. Signal and its Types
1.1Introduction to signal and signal processing
1.2Classification of signal based on dimension
1.3Classification of one-dimensional signal (CT and DT) and properties
1.4Fundamental signals: Delta function, unit step, ramp, rectangular pulse, signum function
1.5Relationship between unit step and delta function
1.6Signal classification based on causality
1.7Classification of signals based on periodicity (CT and DT)
1.8Transformation of the independent variable
1.9Energy and power signals
1.10Even and odd signals
1.11System, types of systems: Linear and non-linear, causal and non-causal, time-invariant and time-variant
2. Fourier Series
2.1Introduction to Fourier series
2.2Fourier series representation of continuous time periodic signal
2.3Properties of continuous time Fourier series: Linearity, time shifting, time scaling, time reversal, convolution, multiplication, frequency shifting, conjugate symmetry, Parseval’s relation
2.4Fourier series representation of discrete time periodic signal
2.5Properties of discrete time Fourier series: Linearity, time shifting, time scaling, time reversal, convolution, modulation, conjugate symmetry, Parseval’s relation
2.6Applications of Fourier series
3. Fourier Transform
3.1Introduction to Fourier transform
3.2Continuous time Fourier transform
3.3Properties of continuous time Fourier transform: Linearity, time shifting, frequency shifting, time scaling, time reversal, convolution, multiplication, duality, conjugation, Parseval’s relation
3.4Discrete time Fourier transform
3.5Properties of discrete time Fourier transform: Linearity, time shifting, frequency shifting, time reversal, convolution, modulation, conjugation, Parseval’s relation
3.6Fourier transform for periodic signals
3.7Applications of Fourier transform
4. Linear Time Invariant (LTI) System
4.1Linear time invariant (LTI) system
4.2Convolution integral properties of LTI system
4.3Representation of discrete-time signals in terms of impulses
4.4Convolution sum
4.5Representation of continuous-time signals in terms of impulses
4.6Convolution integral
5. Sampling
5.1Introduction to sampling
5.2Sampling theorem
5.4Signal reconstruction from sampled version
5.5Aliasing
5.6Band limited signals
6. Frequency Response of Continuous and Discrete Time Systems
6.1Frequency response of continuous time systems
6.2Transfer function of continuous time system
6.3Impulse response of ideal low-pass, band-pass and high-pass filter
6.4Response of ideal low pass filter to a step function input
6.5Frequency and Impulse response of RC filter
6.6Frequency response of discrete time systems: Transfer function
6.7Impulse response of low-pass, band-pass and high-pass filter
Examination Scheme & Marks Distribution
Evaluation Structure
Final Board Theory Exam: 60 Marks (Pass mark: 24)
Internal Assessment: 40 Marks (Pass mark: 16)
Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)
* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.
Exam Preparation Guidelines
Review the available past examination paper to understand question styling, typical derivation topics, and marks allocation.
Practice drawing labeled circuit schematics, deriving transfer functions, and showing systematic mathematical steps.
Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.
Frequently Asked Questions (Signals and Systems)
Q: How can I download Signals and Systems past question papers?
You can preview or download the Signals and Systems question papers (PDF) directly using the built-in viewer on this page with zero redirects or paywalls.
Q: What is the pass mark for Signals and Systems?
The general current scheme is a 60-mark final theory exam and a 40-mark internal assessment, with pass marks of 24 and 16. Verify the course-specific syllabus above.
Q: Where can I find the complete syllabus for this subject?
The available chapter-wise syllabus and topic breakdown is indexed in the Syllabus section above, with links to the curriculum PDF source.