CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## University of Mumbai Semester 4 (SE Second Year) Signals and Systems Revised Syllabus

University of Mumbai Semester 4 (SE Second Year) Signals and Systems and their Unit wise marks distribution

### Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Introduction to Signals and Systems | - |

200 | System Analysis | - |

300 | Fourier Analysis of Continuous Time Signals | - |

400 | Module 4 | - |

500 | Module 5 | - |

600 | Module 6 | - |

Total | - |

## Syllabus

100 Introduction to Signals and Systems

- Definition of signals and systems
- Communication and control systems as examples
- Classification of signals: Continuous time and discrete time, even, odd, periodic and non periodic, deterministic and non deterministic, energy and power.
- Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration (accumulator for DT), time scaling, time shifting and folding, precedence rule.
- Elementary signals: exponential, sine, step, impulse and its properties, ramp, rectangular, triangular, signum, sinc functions.
- Systems: Definition, Classification: linear and non linear, time variant and invariant, causal and noncausal, static and dynamic, stable and unstable, invertible.

200 System Analysis

- System modeling: Input output relation, impulse response, block diagram, integro-differential equation.
- Definition of impulse response
- Convolution integral
- Convolution sum
- Computation of convolution integral using graphical method and analytical method.
- Properties of convolution
- System interconnection
- System properties in terms of impulse response
- Step response in terms of impulse response.

300 Fourier Analysis of Continuous Time Signals

- Orthogonal functions
- Representation of signals in terms of weighted orthogonal basis functions
- Coefficient calculation on the basis of minimum square error.
- Fourier series: Representation of Fourier series in terms of sine, cosine, exponential functions.
- The complex Fourier spectrum, Properties of Fourier series, Power Density Spectrum.
- Convergence of Fourier series
- Gibbs phenomenon
- Fourier transform and its properties.
- Fourier transform of singular functions.
- Energy density spectrum.

400 Module 4

l

401 Fourier Series of Discrete Time Signal

- Harmonically related complex exponential
- Determination of discrete time Fourier series – Properties
- Discrete time Fourier transform – Properties
- Fourier Transform of periodic signals

500 Module 5

501 Laplace Transform

- Double sided Laplace transforms.
- Region of Convergence, properties, Unilateral Laplace Transform, properties, applications of Laplace transform to the solution of differential equations.
- Relationship between Laplace and Fourier transform.

600 Module 6

601 Z-transformation

- Definition
- Region of Convergence, properties and inverse of z transform.
- Long division method
- Partial fraction expansion method
- Residue method – one-sided Z-transform –properties – initial value & final value theorem - solution of LCCDE with initial conditions – zero input response and zero state response - system function – poles and zeros – basic concept of BIBO stability.
- Analysis of discrete time systems using Z−transform. Relationship between Laplace and Z transform.

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