Syllabus for Signals and Systems Course EC 315
(Semester I Academic year 2014-15)
1.
Introduction to signals and systems, classification of
signals, Analog/digital, deterministic/ Stochastic, periodic/aperiodic,
Continuous time/Discrete time, one sided/two sided, energy, power contained in
the signals, basic definition of signals and systems, frequency, phase,
mathematical preliminaries (4)
2.
Continuous Time
Signals and Systems
a. Introduction to orthogonal representation of signals
b. Fourier Series analysis – Trigonometric form, Exponential form, Dirichlet Conditions, Magnitude and phase spectra, Series expansion for symmetric signals – Even symmetry, odd symmetry, Half wave symmetry
c. Continuous Time Fourier transform – Definition, Properties – Linearity, Time shift, Modulation, Multiplication, Convolution, differentiation in time and frequency, duality, Parseval’s relation, real signal, even signal, complex conjugate, time reversal, etc. Magnitude and phase spectra of some popular functions in communication such as Unit step, sin/cosine, Gaussian, etc.
d. Continuous time systems – representation, classification – linear, Time invariant, causal, stable, LTI systems and its representation, Convolution, impulse response, frequency response, Integro-differential equations and systems, Laplace Transform- Review, properties, Transfer function. (18)
a. Introduction to orthogonal representation of signals
b. Fourier Series analysis – Trigonometric form, Exponential form, Dirichlet Conditions, Magnitude and phase spectra, Series expansion for symmetric signals – Even symmetry, odd symmetry, Half wave symmetry
c. Continuous Time Fourier transform – Definition, Properties – Linearity, Time shift, Modulation, Multiplication, Convolution, differentiation in time and frequency, duality, Parseval’s relation, real signal, even signal, complex conjugate, time reversal, etc. Magnitude and phase spectra of some popular functions in communication such as Unit step, sin/cosine, Gaussian, etc.
d. Continuous time systems – representation, classification – linear, Time invariant, causal, stable, LTI systems and its representation, Convolution, impulse response, frequency response, Integro-differential equations and systems, Laplace Transform- Review, properties, Transfer function. (18)
3.
Discrete Time Signals and
Systems
a. Discrete Time Fourier transform – Definition, Properties – Linearity, Time shift, Modulation, Multiplication, Linear Convolution, differentiation in frequency, Parseval’s relation, real signal, even signal, complex conjugate, time reversal, etc. Basic DTFT pairs.
b. Discrete Fourier Transform/Series- Definition, Properties- Periodicity, Circular time shift, DFT of real, conjugate symmetric/anti-symmetric sequences, Evaluation methods- DFT matrices for N=2,3,4,5,and 8, Computational complexity, Circular Convolution, Parseval’s relation.
c. Discrete time systems – representation, classification – linear, Time invariant, causal, stable, memoryless, LTI systems and its representation, Linear Convolution of sequences, impulse response, frequency response, Difference equations and systems, Z – Transfrom- Review, properties, ROC, properties of ROC, Transfer function, poles and zeros (18)
a. Discrete Time Fourier transform – Definition, Properties – Linearity, Time shift, Modulation, Multiplication, Linear Convolution, differentiation in frequency, Parseval’s relation, real signal, even signal, complex conjugate, time reversal, etc. Basic DTFT pairs.
b. Discrete Fourier Transform/Series- Definition, Properties- Periodicity, Circular time shift, DFT of real, conjugate symmetric/anti-symmetric sequences, Evaluation methods- DFT matrices for N=2,3,4,5,and 8, Computational complexity, Circular Convolution, Parseval’s relation.
c. Discrete time systems – representation, classification – linear, Time invariant, causal, stable, memoryless, LTI systems and its representation, Linear Convolution of sequences, impulse response, frequency response, Difference equations and systems, Z – Transfrom- Review, properties, ROC, properties of ROC, Transfer function, poles and zeros (18)
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