Signals and Systems Notes Gate 2026

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

             - 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 Notes

👉 For Signals Systems

   Download(download)

👉 Reference Books: 

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

  Download(download)

✅ Conclusion

Signals and Systems is a core scoring subject in GATE 2026. Focus on Fourier and Laplace Transforms, Z-transform, DTFT/DFT, and LTI systems, as these areas contribute to most questions. Mastering both theory and problem-solving ensures high accuracy in the exam.