Signals and Systems
Continuous and discrete signals, convolution, Fourier transform, and Z-transforms.
Syllabus Units (4)
- Unit 1
Signal Classifications, Mathematical Operations & System Properties
Continuous and discrete signal types, elementary waveforms (Dirac impulse, unit step, ramp, complex exponential, sinc), independent variable transformations (time shifting, time scaling, time reversal), orthogonal even and odd signal decomposition, signal energy and power calculations, and rigorous classification of systems across linearity, time invariance, causality, BIBO stability, memory, and invertibility.
Read note - Unit 2
LTI Systems, Continuous & Discrete Convolution & Impulse Response
Linear Time-Invariant systems characterization, impulse response h(t) and h[n], continuous-time convolution integral, discrete-time convolution sum, graphical flip-and-shift method, system properties via impulse response (causality, BIBO stability, memory), step response derivation, and cascade and parallel interconnected systems.
Read note - Unit 3
Continuous & Discrete Fourier Analysis: Series, Transforms & Frequency Response
Harmonic decomposition, trigonometric and exponential Continuous-Time Fourier Series (CTFS), Dirichlet conditions, Gibbs phenomenon, Continuous-Time Fourier Transform (CTFT), time-frequency duality, Parseval energy theorem, Discrete-Time Fourier Series (DTFS), Discrete-Time Fourier Transform (DTFT) 2π-periodicity, and LTI frequency response H(jω) with active filtering.
Read note - Unit 4
Bilateral Laplace Transform, Z-Transform, Transfer Functions & Stability Analysis
Bilateral and unilateral Laplace transforms, s-plane Region of Convergence (ROC) properties, inverse Laplace via partial fractions, bilateral Z-transform, z-plane unit circle and annular ROC topology, inverse Z-transform, system transfer functions H(s) and H(z), conformal mapping z = e^(s Ts), and continuous/discrete LTI causality and BIBO stability.
Read note