Basic Signal Processing 2022 scheme notes VTU University 4th SEM Electronic Communication and Engineering | BEC402 notes

Scheme & Syllabus Copy of Basic Signal Processing 2022 scheme notes

Basic Signal Processing 2022 scheme BEC402 notes and syllabus copy

Module 1: Vector Spaces

• Topics:
  • Vector Spaces and Null Subspaces
  • Rank and Row Reduced Form
  • Independence, Basis, and Dimension
  • Dimensions of the Four Subspaces
  • Rank-Nullity Theorem
  • Linear Transformations
• Orthogonality:
  • Orthogonal Vectors and Subspaces
  • Projections and Least Squares
  • Orthogonal Bases and Gram-Schmidt Orthogonalization Procedure (Refer Chapters 2 and 3 of Text 1)

Module 2: Eigenvalues and Eigenvectors

• Topics:
  • Review of Eigenvalues and Diagonalization of a Matrix
  • Special Matrices (Positive Definite, Symmetric) and Their Properties
  • Singular Value Decomposition (Refer Chapter 5, Text 1)

Module 3: Introduction and Classification of Signals

• Topics:
  • Definition of Signal and Systems with Examples
  • Elementary Signals/Functions:
    • Exponential, Sinusoidal, Step, Impulse, and Ramp Functions
  • Basic Operations on Signals:
    • Amplitude Scaling, Addition, Multiplication
    • Time Scaling, Time Shift, and Time Reversal
  • Expression of Triangular, Rectangular, and Other Waveforms in Terms of Elementary Signals
• System Classification and Properties:
  • Linear-Nonlinear
  • Time Variant-Invariant
  • Causal-Noncausal
  • Static-Dynamic
  • Stable-Unstable
  • Invertible (Text 2) [Only for Discrete Signals & Systems]

Module 4: Time Domain Representation of LTI Systems

• Topics:
  • Impulse Response and Convolution Sum
  • Computation of Convolution Sum Using Graphical Method:
    • Unit Step and Unit Step
    • Unit Step and Exponential
    • Exponential and Exponential
    • Unit Step and Rectangular
    • Rectangular and Rectangular
  • LTI System Properties in Terms of Impulse Response:
    • System Interconnection
    • Memoryless, Causal, Stable, Invertible
    • Deconvolution and Step Response (Text 2) [Only for Discrete Signals & Systems]

Module 5: The Z-Transforms

• Topics:
  • Z-Transform and Properties of the Region of Convergence
  • Properties of the Z-Transform
  • Inverse Z-Transform by Partial Fraction
  • Causality and Stability
  • Transform Analysis of LTI Systems