Engineering reference for Indian students

Applied

Signals & Systems

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Continuous Time Signals
Continuous-time signals are classified by properties — periodic/aperiodic, even/odd, energy/power — and built from the elementary step, impulse and ramp; energy signals have finite ∫|x|² dt while power signals have finite average power.
$Periodic: x(t+T) = x(t); fundamental period T_{0}$
Laplace Transform
The Laplace transform maps a time function into the s-domain, turning differentiation into multiplication by s; it solves linear differential equations algebraically and yields the transfer function of LTI systems.
Fourier Series and Transform
The Fourier series represents a periodic signal as a sum of harmonics (a discrete line spectrum), while the Fourier transform extends this to aperiodic signals (a continuous spectrum), revealing frequency content.
Sampling Theorem
A bandlimited signal can be reconstructed exactly from its samples if the sampling rate exceeds twice its highest frequency (Nyquist rate); sampling too slowly causes aliasing, folding high frequencies into the baseband.
LTI System Response
An LTI system is completely described by its impulse response h(t); the output is the convolution of input and impulse response, which becomes simple multiplication in the Laplace or Fourier domain.
$Group delay \tau_{g} = -d∠\frac{H}{d\omega}$