EC-7.1 Signals: Continuous, Discrete, and the Operations on Them
You can say what kind of signal you are holding — continuous or discrete, periodic or not, energy or power — and shift, scale, reverse or split one without losing your place.
Before:EC-4. Transforms, Complex Variables and Numerical MethodsUnlocks:S4-1. Analog CircuitsS4-3. Control SystemsS4-5. Probability Theory & Stochastic ProcessesS5-3. Digital Signal ProcessingPE2-3. Biomedical Instrumentation and Signal ProcessingEC-9. Microcontrollers and Embedded Systems
Almost every later subject here opens by assuming this vocabulary and then never teaching it. Communications talks about a band-limited signal, control talks about a step input, digital signal processing talks about a sequence, and all three assume you already know what those are and how to manipulate them. Meeting the vocabulary once, on its own, means none of those courses has to spend its first week on it, and it means a reader who arrives from a different subject is not quietly locked out.
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Continuous-time and discrete-time signals, and what actually separates them
A continuous-time signal has a value at every instant; a discrete-time one has values only at counted positions. The distinction is about the independent variable, not about whether the values themselves are rounded, and confusing the two causes trouble later.
NPTEL: Principles of Signals and Systems · CoursePeriodic and aperiodic signals, and the period of a sum
A signal is periodic when it repeats after a fixed interval, and the sum of two periodic signals is periodic only when their periods have a common multiple. That last condition is the reason some sums of sinusoids never repeat at all.
Energy signals and power signals, and why a signal is one or the other
A signal with finite total energy has zero average power, and one with finite nonzero average power has infinite energy. Knowing which kind you have decides which measures of size are meaningful and which are useless.
NPTEL: Signals and Systems (IIT Kanpur) · CourseShifting, scaling and reversing the independent variable
Delaying, stretching and reflecting a signal are all changes to its argument rather than to its values. Doing several at once is where mistakes happen, so the order in which you apply them has to be worked out and not guessed.
MIT RES.6-007: Signals and Systems · CourseEven and odd parts, and why every signal has both
Any signal splits uniquely into a symmetric part and an antisymmetric part, each built from the signal and its own reflection. This split reappears in the Fourier work, where it decides whether a transform is real or imaginary.
The standard signals: step, impulse, ramp and the exponential
A handful of signals are used everywhere as test inputs and as building blocks, and the relationships between them matter as much as the definitions. The step is the running total of the impulse, and the ramp is the running total of the step.
NPTEL: Signals and Systems (IISER Bhopal) · Course
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