At the end of this course, the student should be able to: 1. Understand and apply the concepts about linear time-invariant (LTI) systems 2. understand and apply Fourier Series representation of periodic continuous-time signals 3. understand and apply Fourier Transform representation of periodic and aperiodic continuous-time signals 4. Apply Laplace transforms to analyze LTI Systems
Course Content: 1. Signals (continuous-time): Signal classification (analog-digital, energy-power, even-odd, periodic-aperiodic, deterministic-random etc.), standard signals (unit step, unit impulse, ramp, exponential, sinusoids), transformations of the independent variable (4 classes) 2. Systems (continuous-time): System classification (memory, causal, stable, linear, time-invariant, invertible etc.), Impulse response of an LTI system, convolution integral, graphical convolution, system properties from impulse response, complex exponential as eigenfunction of LTI systems, interconnection of LTI systems (6 classes) 3. Discrete-time signals and systems: Emphasize similarities and differences with continuous-time counterpart (3 classes) 4. Continuous-time Fourier series: Periodic signals and their properties, exponential and trigonometric FS representation of periodic signals, convergence, FS of standard periodic signals, salient properties of Fourier series, FS and LTI systems, some applications of FS (eg. filtering) (6 classes) 5. Continuous-time Fourier transform: Development of Fourier representation of aperiodic signals, convergence, FT of standard signals, FT of periodic signals, properties of FT, some applications of FT (eg. modulation) (6 classes) 6. Laplace Transform: Bilateral Laplace transform, region of convergence, properties of Laplace transform, standard Laplace transform pairs, transfer function of LTI system, characterising LTI system properties from transfer function, algebra of transfer functions and block diagram representations, Unilateral Laplace transform – brief introduction and application to simple initial value problems (8 classes) 7. Sampling (Bridge continuous and discrete): Sampling theorem and signal reconstruction, notion of aliasing with examples, Sampling in frequency domain (5 classes)
Signals and Systems: Oppenheim, Willsky and Nawab (2nd Edn).
Reference Books:Principles of Linear Systems and Signals: B.P. Lathi (2nd Edn)