BE Biomedical Engineering Semester 4 (SE Second Year)University of Mumbai
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Signals and Systems Semester 4 (SE Second Year) BE Biomedical Engineering University of Mumbai Topics and Syllabus

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CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

Topics with syllabus and resources

100.00 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.
200.00 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.
300.00 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.
400.00 Module 4

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401.00 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
500.00 Module 5
501.00 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.
600.00 Module 6
601.00 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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