Semester 1

This course introduces the representation, classification and properties of continuous and
discrete time signals, continuous and discrete systems, sampling of continuous time signals,
realization structures of finite duration and infinite duration impulse response filters. This
introduces the basic concepts of signals and their different application to computer science
Indicative Content
UNIT I: REPRESENTATION OF SIGNALS
Continuous and discrete time signals: Classification of Signals – Periodic aperiodic even –
odd – energy and power signals – Deterministic and random signals – complex exponential
and sinusoidal signals – periodicity – properties of discrete time complex exponential unit
impulse – unit step impulse functions – Transformation in independent variable of signals:
time scaling, time shifting. Determination of Fourier series representation of continuous time
and discrete time periodic signals – Explanation of properties of continuous time and discrete
time Fourier series
UNIT II: ANALYSIS OF CONTINUOUS TIME SIGNALS AND SYSTEMS
Continuous time Fourier Transform and Laplace Transform analysis with examples –
properties of the Continuous time Fourier Transform and Laplace Transform basic properties,
Parseval’s relation, and convolution in time and frequency domains. Basic properties of
continuous time systems: Linearity, Causality, time invariance, stability, magnitude and Phase
representations of frequency response of LTI systems -Analysis and characterization of LTI
systems using Laplace transform: Computation of impulse response and transfer function
using Laplace transform.
UNIT III: SAMPLING THEOREM AND z-TRANSFORMS
Representation of continuous time signals by its sample - Sampling theorem – Reconstruction
of a Signal from its samples, aliasing – discrete time processing of continuous time signals,
sampling of band pass signals. Basic principles of z-transform - z-transform definition –
region of convergence – properties of ROC – Properties of z-transform – Poles and Zeros –
inverse z-transform using Contour integration - Residue Theorem, Power Series expansion
and Partial fraction expansion, Relationship between z-transform and Fourier transform.
UNIT IV: SYSTEMS
Computation of Impulse & response & Transfer function using Z Transform. DTFT Properties
and examples – LTI-DT systems -Characterization using difference equation – Block diagram
representation – Properties of convolution and the interconnection of LTI Systems – ality and
stability of LTI Systems. viewing differential / difference equations as systems that process
signals, the notions of input, output and internal signals, block diagrams (series, parallel and
feedback connections), properties of input-output models (causality, delay, stability, gain, shiftinvariance, linearity), transient and steady state behavior
UNIT V: LINEAR TIME-INVARIANT SYSTEMS
Continuous and discrete impulse response; convolution operation, transfer functions and
frequency response, time-domain interpretation of stable and unstable poles and zeros, statespace models (construction from high-order ODEs, canonical forms, state transformations and
stability), and the discretisation of models for systems of continuously indexed signals.
UNIT VI: SYSTEMS WITH FINITE AND INFINITE DURATION IMPULSE
RESPONSE
Systems with finite duration and infinite duration impulse response – recursive and nonrecursive discrete time system – realization structures – direct form – I, direct form – II,
Transpose, cascade and parallel forms.