Signals and Systems Notes for GATE 2026 (Handwritten)

Understanding Signals and Systems is essential for mastering communication, control, and digital signal processing — key areas in ECE, EE, and IN GATE papers. These handwritten notes offer a complete, structured guide to concepts, mathematical foundations, and applications of signals and systems.

From basic signal types to advanced transforms like Fourier, Laplace, and Z-Transform, these notes help build a strong conceptual and problem-solving base. Designed for GATE 2026 aspirants, they include definitions, derivations, and solved examples to make complex topics simple and intuitive

Topics Covered

1. Introduction

Why Study Signals & Systems
Elementary Signals: Unit impulse, step, ramp, sinusoidal, exponential
Signal Classification: Continuous/discrete, periodic/aperiodic, deterministic/random
System Classification: Linear, time-invariant, causal, stable, memoryless

2. Linear Time-Invariant (LTI) Systems

Continuous and Discrete Convolution
Properties of LTI systems (linearity, time invariance, causality, stability)
Step Response and Impulse Response

3. Fourier Series

Analogy between Vectors & Signals
Trigonometric Fourier Series
Exponential/Complex Fourier Series
Properties of Fourier Series
Applications: Spectrum analysis of periodic signals, square wave decomposition.

4. Fourier Transform

Introduction and definition
Properties of Fourier Transform
Distortionless Transmission
Hilbert Transform
Correlation functions
Sampling Theorem (Nyquist rate, aliasing)

5. Laplace Transform

Region of Convergence (ROC)
Properties of Laplace Transform
Causality and Stability
Applications in circuit analysis and control systems

6. Discrete-Time Fourier Transform (DTFT)

Convergence of DTFT
Oversampling and Sampling Rate Conversion
Frequency-domain analysis of discrete signals

7. Z-Transform

Introduction to Z-Transform
Properties of Z-Transform
Causality and Stability
Realization of Digital Systems
Applications: Discrete-time system design, DSP algorithms.

8. Discrete-Time Fourier Series

Representation of periodic discrete-time signals
Properties and applications in digital signal analysis

9. Digital Filter Design

IIR Filter Design
- Approximation of Derivatives
- Impulse Invariance Method
- Bilinear Transformation
- Matched Z-Transformation

Filter Types: Butterworth, Chebyshev, Elliptic (Cauer), Bessel
FIR Filter Design
- Direct design methods
- Windowing method

10. DFT & FFT

Introduction to DFT
Linear Convolution using DFT
Fast Fourier Transform (FFT) algorithms

11. Discrete-Time Processing of Continuous-Time Signals

Periodic Sampling
Frequency-domain representation of sampling
Reconstruction of bandlimited signals from samples
Discrete-time processing of continuous-time signals

📂 Download

Complete Notes of Signals and Systems 👇👇

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👉 For Previous year Paper of ECE Gate 👇

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Reference Books:

1. Signals And Systems by Alan V.Oppenheim, Alan S.Willsky, with S. Hamid Nawab 👇

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Conclusion

These **Signals and Systems handwritten notes** for **GATE 2026** are carefully designed to cover every topic from basic principles to advanced frequency-domain analysis. They will strengthen your theoretical understanding and improve your problem-solving accuracy in GATE exams.

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