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SIGNALS AND SYSTEMS
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DI04041031
Code: DI04041031
Credits: 4
Semester 4
Nano
Signals and Systems
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Follow on Instagram for UpdatesSignals and Systems Syllabus — Unit-wise Content
The official GTU curriculum for Signals and Systems (subject code DI04041031) as prescribed for Nano · Semester 4 divides the course into 5 units, covering 107 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (DI04041031)Unit 1 Introduction to signals and Systems
- 1.1. Basic concepts of signals
- 1.1.1. Continuous time (CT) and Discrete time (DT)
- 1.1.2. Multichannel and multidimensional signals
- 1.1.3. Periodic and non-periodic signals
- 1.1.4. Deterministic and random signals
- 1.1.5. Energy and power signals
- 1.1.6. Even and odd signals
- 1.2. Standard Test Signals
- 1.2.1. Impulse signal
- 1.2.2. Step signal
- 1.2.3. Ramp signal
- 1.2.4. Parabolic signal
- 1.2.5. Sinusoidal signal
- 1.3. Basic operations on signals
- 1.3.1. Time shifting operation
- 1.3.2. Time reversal (inversion)
- 1.3.3. Signal Addition
- 1.3.4. Signal Multiplication
- 1.3.5. Time scaling operation
- 1.3.6. Amplitude scaling operation
- 1.4. Introduction to Systems
- 1.5. Classification of systems
- 1.5.1. Continuous Time system (CT) &Discrete Time system (DT)
- 1.5.2. Static system& Dynamic system
- 1.5.3. Linear system & Nonlinear system
- 1.5.4. Causal system & non-causal system
- 1.5.5. Time invariant system & Time variant system
- 1.5.6. Stable system & Unstable system
- 9. 20 GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma Engineering Level: Diploma Branch: Automation and Robotics Subject Code : DI04041031 Subject Name : Signals and Systems w.e.f. 2025-26 http://syllabus.gtu.ac.in/ Page 3 of 8
Unit 2 Discrete time LTI systems
- 2.1. Introduction to Linear-Time-Invariant (LTI) Systems
- 2.2. Characterization of Linear-Time-Invariant (LTI) Systems
- 2.3. The Continuous-Time Unit-Impulse Response and the Convolution Integral
- 2.4. Convolution Sum for Discrete-Time LTI Systems
- 2.5. Properties of Linear-Time-Invariant (LTI) Systems
- 2.5.1. Commutative Property
- 2.5.2. Distributive Property
- 2.5.3. Associative Property
- 2.5.4. Static and Dynamic LTI Systems
- 2.5.5. Invertibility of LTI Systems
- 2.5.6. Causality for LTI Systems
- 2.5.7. Stability for LTI Systems
- 2.6. Unit-Step Response of an LTI System
- 2.7. Basic Building Blocks of Continuous-Time and Discrete-Time Systems
Unit 3 Frequency Analysis of Discrete Time Fourier Transform(DTF T)
- 3.2. The Discrete-Time Fourier Transform: Representation of Aperiodic Signals
- 3.3. Properties of DTFT
- 3.3.2. Time-Shifting Property
- 3.3.3. Frequency-Shifting Property
- 3.3.5. Multiplication by n: Frequency Differentiation
- 3.3.6. Time Reversal
- 3.4. Discrete time LTI systems characterized by Linear constant-co-efficient difference equation
Unit 4 Discrete Fourier Transform (DFT) and its Application
- 4.2. Frequency Domain Sampling: The Discrete Fourier Transform
- 4.2.1. Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals
- 4.2.2. Derivation of an Interpolation Formula for X(ω)
- 10. 20 GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma Engineering Level: Diploma Branch: Automation and Robotics Subject Code : DI04041031 Subject Name : Signals and Systems w.e.f. 2025-26 http://syllabus.gtu.ac.in/ Page 4 of 8
- 4.3. The Discrete Fourier Transform (DFT)
- 4.4. The Inverse Discrete Fourier Transform (DFT)
- 4.4. The DFT as a Linear Transformation
- 4.5. Comparison of DTFT and DFT
- 4.6. Discrete Fourier Transform (DFT) of Standard Signals
- 4.7. Detailed Explanation of Cyclic Property of Twiddle Factor
- 4.8. Properties of Discrete Fourier Transform (DFT)
- 4.8.3. Circular Symmetries of a Sequence
- 4.8.4. Symmetry Properties of DFT
- 4.8.5. Duality Property
- 4.8.6. Multiplication of Two DFTs and Circular Convolution
- 4.9. Frequency Analysis of Signals Using the DFT
- 4.9.1. Linear Convolution Using DFT
- 4.9.2. Steps to Calculate Linear Filtering Using DFT
Unit 5 Z-Transform
- 5.1. Introduction to The z-Transform
- 5.2. Region of Convergence (ROC)
- 5.3. Properties of z-Transform
- 5.4.1. Linearity Property
- 5.4.2. Time Reversal
- 5.4.3. Time Shifting Property
- 5.4.5. Differentiation Property
- 5.4.6. Convolution Property
- 5.4.7. Correlation Property
- 5.5. Introduction to The Inverse z-Transform
- 5.6. Methods for Inverse z-Transform
- 5.6.1. Long Division Method
- 5.6.2. Partial Fraction Expansion Method
- 5.6.3. Residue Method
- 8. 20 Total 45 100 GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma Engineering Level: Diploma Branch: Automation and Robotics Subject Code : DI04041031 Subject Name : Signals and Systems w.e.f. 2025-26 http://syllabus.gtu.ac.in/ Page 5 of 8 SUGGESTED PRACTICAL EXERCISES The following practical outcomes (PrOs) that are the sub-components of the COs. Some of the PrOs marked ‘*’ are compulsory, as they are crucial for that particular CO. These PrOs need to be attained at least at the ‘Precision Level’ of Dave’s Taxonomy related to ‘Psychomotor Domain’. Approx. Hrs. required
- 1. Study the simulation software for simulation of signals and system. 2Hrs
- 2. Classify CT/DT signals as energy/power, periodic/aperiodic, and even/odd based on mathematical definitions. 2Hrs
- 3. Generate standard test signals (impulse, step, ramp, parabolic, sinusoidal) using analytical or simulation tools. 2Hrs
- 4. Perform basic signal operations such as time shifting, scaling, and time reversal and observe their effects on signal shape. 4Hrs
- 5. Classify systems as linear/nonlinear, causal/non-causal, stable/unstable, and time-invariant/time-variant using given input-output relationships. 2Hrs
- 6. Compute the response of CT LTI systems using convolution integral. 2Hrs
- 7. Compute the response of DT LTI systems using convolution sum. 2Hrs
- 8. Verify LTI system properties such as linearity, time invariance, commutativity, associativity, and distributivity. 4Hrs
- 9. Determine the unit step response and derive system output using impulse response relationships. 2Hrs
- 10. Compute the DTFT of a discrete-time sequence and interpret its magnitude and phase spectrum. 4Hrs
- 11. Verify DTFT properties such as time-shifting, frequency-shifting, scaling, and time reversal using example signals. 4Hrs
- 12. Compute DFT and IDFT of sequences and interpret spectral components. 2Hrs
- 13. Verify DFT properties including periodicity, linearity, symmetry, and perform circular convolution. 4Hrs
- 14. Perform linear convolution using the DFT method. 2Hrs
- 15. Perform frequency-domain analysis of signals using DFT to extract magnitude and phase information. 2Hrs
- 16. Compute z-transform of standard signals and identify their regions of convergence (ROC). 2Hrs
- 17. Verify key properties of z-transform such as linearity, shifting, scaling, convolution, and differentiation. 4Hrs GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma Engineering Level: Diploma Branch: Automation and Robotics Subject Code : DI04041031 Subject Name : Signals and Systems w.e.f. 2025-26 http://syllabus.gtu.ac.in/ Page 6 of 8 Approx. Hrs. required
- 18. Compute the inverse z-transform using Partial Fraction Expansion methods. 2Hrs Total 48 Note i. More Practical Exercises can be designed and offered by the respective course teacher to develop the industry relevant skills/outcomes to match the COs. The above table is only a suggestive list. ii. The following are some sample ‘Process’ and ‘Product’ related skills (more may be added/deleted depending on the course) that occur in the above listed Practical Exercises of this course required which are embedded in the COs and ultimately the competency.. Sr. No. Sample Performance Indicators for the PrOs Weightage in %
- 1. Ability to Apply Theoretical Concepts 20
- 2. Accuracy of Computation / Simulation 20
- 3. Use of Tools and Techniques 20
- 4. Record observations correctly 20
- 5. Interpret the result and conclude 20 Total 100 MAJOR EQUIPMENT/ INSTRUMENTS AND SOFTWARE REQUIRED These major equipment/instruments and Software required to develop PrOs are given below with broad specifications to facilitate procurement of them by the administrators/management of the institutes. This will ensure conduction of practical in all institutions across the state in proper way so that the desired skills are developed in students. S. No. Equipment Name with Broad Specifications PrO. No. 1 PC / Laptop with Required Software Minimum recommended specs:
- 8. GB RAM i3 processor or above Windows / Linux / macOS 1,3,4,6 to18
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