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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]

## 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

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## 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

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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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