S(caps)ignals and Systems is one of the core subjects for GATE 2026 (ECE) and forms the foundation for advanced topics like Communication Systems, Digital Signal Processing (DSP), and Control Systems. A strong grip on this subject ensures better accuracy in solving both theoretical and numerical problems.
This article provides chapter-wise GATE-focused notes covering the complete syllabus: from the basics of signals to Fourier, Laplace, Z-transform, Digital Filters, and practical applications.
(toc)Table of Content
1. Introduction
- Why Study Signals & Systems?
- Essential for understanding communication, DSP, and control.
- Elementary Signals: Unit impulse, step, ramp, sinusoidal, and exponential signals.
- Classification of Signals: Continuous-time, discrete-time, periodic, aperiodic, deterministic, random.
- Systems & Classification: Linear, time-invariant, causal, stable, dynamic, memoryless.
2. LTI (Linear Time-Invariant) 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
- 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
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