signal glossary

Here is the exhaustive “Master Glossary of Definitions” for ECE 2107. I have meticulously extracted both the exam-tested terms (from PYQs) and the foundational terms (from the syllabus, lecture notes, and textbooks) required to master this course.

1. Signals and Systems Fundamentals

Term	Definition	Year of Appearance
Signal	A physical quantity or function of one or more independent variables (like time) that carries information about the behavior or nature of a phenomenon.	2025, 2024, 2023, 2021, 2020, 2019, 2018, 2017, 2016, 2015
System	A physical device, process, or mathematical algorithm that manipulates or operates on an input signal to produce a desired output signal.	2025, 2024, 2023, 2019, 2018, 2016, 2015
Continuous-Time Signal	A signal that has a defined amplitude at every continuous, infinitesimally small instant of time.	Foundational (Syllabus)
Discrete-Time Signal	A sequence of values defined only at specific, discrete integer instances of time (usually representing sampled data).	Foundational (Syllabus)
Deterministic Signal	A signal whose future values can be completely and exactly predicted by a mathematical equation or formula.	2018
Random (Nondeterministic) Signal	A signal containing uncertainty or noise, whose future values cannot be predicted exactly but can only be described statistically.	2018
Even Signal	A signal exhibiting exact symmetry across the vertical axis, satisfying the mathematical condition $f(t)=f(-t)$.	2018
Odd Signal	A signal exhibiting anti-symmetry across the origin, satisfying the mathematical condition $f(t)=-f(-t)$.	2018
Energy Signal	A signal with a finite total energy ($0<E<\infty$) and zero average power over infinite time, typically representing a transient pulse.	2016, 2015
Power Signal	A signal with finite average power ($0<P<\infty$) and infinite total energy, typically representing periodic or infinite-duration signals.	2016, 2015
Unit Step Function ($u(t)$)	A fundamental singularity function that equals 1 for $t\ge 0$ and 0 for $t<0$, commonly used to mathematically represent a DC switch closing.	2022
Unit Impulse Function ($\delta (t)$)	Also known as the Dirac delta function, it has infinite amplitude at $t=0$, zero amplitude everywhere else, and a total integrated area of exactly 1.	2022
Ramp Function ($r(t)$)	A signal that grows linearly with time for $t\ge 0$ and is zero for $t<0$, mathematically represented as $t\cdot u(t)$.	2022
Signum Function (sgn(t))	A mathematical function that evaluates to +1 for positive time, -1 for negative time, and 0 at $t=0$.	2022, 2019
Memoryless System	A system whose output at any given instant depends strictly on the input at that exact same instant, with no reliance on past or future data.	2024, 2016
Causal System	A physically realizable system whose present output depends only on present and past inputs, never on future inputs.	2015
Linear System	A system that perfectly satisfies the mathematical principles of both superposition (additivity) and homogeneity (scaling).	2017
Time-Invariant System	A system whose behavioral characteristics do not change over time; delaying the input shifts the output by the exact same delay without altering its shape.	Foundational (Notes)
Recursive System	A system with feedback, where the current output depends on present/past inputs as well as past outputs.	2024, 2017, 2016
Invertible System	A system in which a unique input can be perfectly recovered from its corresponding output by applying an inverse system.	2016
System Stability (BIBO)	A condition where any Bounded Input applied to the system guarantees a Bounded Output, preventing infinite responses.	2021, 2016
Impulse Response ($h(t)$)	The specific output behavior of a Linear Time-Invariant (LTI) system when a unit impulse function $\delta (t)$ is applied as the input.	2018, 2016

2. Fourier Analysis (Series & Transform)

Term	Definition	Year of Appearance
Fourier Series	The mathematical expansion of a periodic signal into an infinite sum of harmonically related sinusoidal waves (sines and cosines) and a DC component.	2022, 2020, 2019, 2018, 2017
Orthogonality	A mathematical property where the integral of the product of two different signals over a set period is zero, indicating they share no common frequency information.	Foundational (Notes)
Fourier Transform	An integral operation that converts an aperiodic time-domain signal into a continuous frequency-domain spectrum, revealing all frequency components present.	2025, 2024, 2016, 2015
Fourier Transform Pair	A specific linkage between a unique time-domain function and its exact corresponding frequency-domain Fourier transform representation (e.g., $f(t)\leftrightarrow F(j\omega )$).	2019
Parseval’s Theorem	A theorem proving that the total energy of a signal computed in the time domain is exactly equal to its total energy computed across the frequency spectrum.	Foundational (PYQ related)
Gaussian Pulse	A noise-modeling pulse defined by the exponential $e^{-\pi t^2}$ that forms a bell curve and possesses the unique property of being its own Fourier transform.	Foundational (PYQ related)

3. Laplace Transform & Circuit Analysis

Term	Definition	Year of Appearance
Laplace Transform	An integral transform that maps a real time-domain function into a complex $s$-domain ($s=\sigma +j\omega$), highly useful for analyzing damped or unstable systems.	2019, 2017, 2016, 2015
Poles (s-domain)	The complex frequencies (values of $s$) that cause the denominator of a transfer function to equal zero, making the function approach infinity.	2023, 2022, 2018, 2017
Zeros (s-domain)	The complex frequencies (values of $s$) that cause the numerator of a transfer function to equal zero, forcing the output of the system to zero.	2023, 2022, 2018, 2017
Transfer Function	The mathematical ratio of the Laplace transform of the output signal to the Laplace transform of the input signal, assuming all initial conditions are zero.	2019
Initial Value Theorem	A Laplace domain theorem used to mathematically determine the instantaneous value of a signal immediately after a switch closes ($t\to 0^{+}$).	2023, 2019, 2016
Final Value Theorem	A Laplace domain theorem used to evaluate the steady-state, long-term DC behavior of a system as time approaches infinity ($t\to \infty$).	2023, 2019, 2016
Absolute Stability	A system condition dictated by the $s$-plane where absolutely all poles of the transfer function lie strictly in the left-hand half of the complex plane.	Foundational (Notes)
Marginal Stability	A borderline system condition where poles exist directly on the imaginary $j\omega$-axis (without multiplicity), causing a sustained, non-decaying oscillation.	Foundational (Notes)

4. Z-Transform & Discrete System Analysis

Term	Definition	Year of Appearance
Z-Transform	The discrete-time counterpart to the Laplace transform that maps a discrete sequence into the complex $z$-plane to simplify difference equations.	2022, 2018, 2016
Region of Convergence (ROC)	The specific bounded area in the complex $s$-plane or $z$-plane where the mathematical integral or summation of the transform strictly converges to a finite value.	2024, 2021, 2020, 2019, 2018, 2017, 2015
Auto-correlation	A signal processing technique that mathematically compares a signal against a delayed version of itself to detect hidden periodic patterns or noise.	2015
Cross-correlation	A mathematical operation measuring the exact degree of similarity between two entirely different signals as one is shifted relative to the other.	2015
Transfer Function (z-domain)	The ratio of the Z-transform of the discrete output sequence to the Z-transform of the discrete input sequence.	2022, 2021, 2015

5. DFT & Fast Fourier Transform (FFT)

Term	Definition	Year of Appearance
FFT Algorithm	The Fast Fourier Transform is a highly optimized mathematical algorithm that computes the Discrete Fourier Transform (DFT) while drastically reducing computational complexity from $O(N^2)$ to $O(N{\log }_{2}N)$.	2025, 2024, 2023
DIT-FFT	Decimation-In-Time FFT, an algorithm that recursively breaks the time-domain input sequence into smaller even and odd indexed subsequences to compute the spectrum.	2025
DIF-FFT	Decimation-In-Frequency FFT, an algorithm that recursively partitions the frequency-domain output into smaller components to achieve rapid calculation.	Foundational (PYQ related)

6. Sampling, Filters & Network Theory

Term	Definition	Year of Appearance
Sampling Theorem	Also known as the Shannon-Nyquist theorem; it asserts that an analog signal must be sampled at a rate strictly greater than twice its highest frequency component to prevent data loss.	2024, 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2015
Aliasing Effect	A destructive frequency-folding distortion that occurs when a continuous signal is under-sampled, causing high frequencies to masquerade as false low frequencies.	2021, 2019, 2018, 2016, 2015
Over-sampling	The engineering practice of sampling an analog signal at a frequency drastically higher than the absolute minimum Nyquist rate to ease filter design.	2018, 2016, 2015
Nyquist Rate Sampling	The absolute minimum critical boundary sampling frequency ($f_s=2f_{max}$) allowed to perfectly reconstruct an analog signal.	2018, 2016, 2015
Up-sampler	A discrete-time signal processing block that artificially increases a signal’s sampling rate by inserting zero-valued samples between existing data points.	2022, 2021
Down-sampler	A discrete-time signal processing block that reduces a signal’s sampling rate by actively discarding a specified integer number of samples.	2022, 2021
Filtering	The signal processing action of deliberately passing certain desired frequency components of a signal while suppressing or blocking others.	2023
Network Theory	The analytical study and mathematical modeling of interconnected electrical components to solve for unknown voltages and currents.	2025, 2022
Two-Port Network	A conceptual electrical circuit modeled as a “black box” possessing exactly one input port (pair of terminals) and one output port.	2024

7. State-Space Representation

Term	Definition	Year of Appearance
State of a System	The absolute minimal amount of current information required, which, alongside future inputs, can mathematically predict the entire future behavior of the system.	2019, 2017, 2016
State Variables	The minimal set of independent dynamic variables (such as energy stored in an inductor or capacitor) used to formulate the state vector of an interconnected system.	Foundational (Notes)
State Space	An $n$-dimensional mathematical hyperspace where the coordinate axes represent the system’s state variables, used to visualize dynamic progression over time.	Foundational (Notes)

missed

Here is the deep-check analysis. While the previous Master Glossary captured the explicit “Define X” questions, a forensic scan of the “Distinguish between”, “Write short notes on”, and specific filter/network design questions reveals several critical, highly-testable terms that were structurally hiding in plain sight.

Here are the missed definitions and foundational concepts, categorized perfectly to patch the remaining gaps in your A+ arsenal.

1. Signals and Systems Fundamentals

Term	Definition	Year of Appearance
FIR (Finite Impulse Response) System	A discrete-time system whose impulse response settles to zero in finite time, inherently stable as it lacks feedback loops.	2018, 2015
IIR (Infinite Impulse Response) System	A discrete-time system whose impulse response continues indefinitely, typically constructed using recursive feedback loops.	2018, 2015
Time-Variant System	A system whose characteristics and behavior change over time, meaning a delayed input does not produce an identically delayed output.	2025, 2022
Anti-causal System	A non-physically realizable system whose current output depends only on future values of the input signal.	2025, 2020

2. Fourier Analysis (Series & Transform)

Term	Definition	Year of Appearance
Dirichlet Conditions	The strict mathematical prerequisites (single-valued, finite maxima/minima, finite discontinuities, and absolute integrability) a signal must satisfy to have a valid Fourier series.	2022, 2018, 2017
Symmetry Conditions (Fourier)	Waveform properties (Even, Odd, Half-wave symmetry) that force specific Fourier coefficients ($a_n$, $b_n$, or $a_0$) to exactly zero, drastically reducing calculation time.	2020, 2019
Energy Spectral Density (ESD)	A mathematical function describing how the total energy of an aperiodic energy signal is distributed continuously across various frequencies.	Foundational (Syllabus)
Power Spectral Density (PSD)	A mathematical function that shows how the average power of a periodic or random signal is distributed across its discrete frequency components.	Foundational (Syllabus)
Rayleigh’s Energy Theorem	The specific adaptation of Parseval’s theorem for aperiodic signals, proving that total time-domain energy equals the integral of the squared magnitude of the Fourier Transform.	Foundational (Notes)
Modulation Property (Frequency Shifting)	A theorem stating that multiplying a time-domain signal by a complex exponential shifts its entire frequency spectrum, forming the basis of telecommunications.	Foundational (Notes)

3. Laplace Transform & Circuit Analysis

Term	Definition	Year of Appearance
Routh-Hurwitz Criterion	An analytical mathematical procedure used to determine if a system is stable (poles in the left-half s-plane) without explicitly factoring high-order denominator polynomials.	Foundational (Notes)

4. Z-Transform & Discrete System Analysis

Term	Definition	Year of Appearance
One-Sided (Unilateral) Z-Transform	A Z-transform evaluated strictly from $n=0$ to $\infty$, making it uniquely capable of solving difference equations that have non-zero initial conditions.	2020
Two-Sided (Bilateral) Z-Transform	A Z-transform evaluated from $n=-\infty$ to $\infty$, which requires a rigorously defined Region of Convergence (ROC) to be inverted without ambiguity.	2020
Rational Z-Transform	A Z-transform that can be expressed as a ratio of two polynomials in $z$, from which the system’s poles and zeros are directly extracted.	2021

5. Sampling, Filters & Network Theory

Term	Definition	Year of Appearance
Ideal Sampling (Impulse Sampling)	A theoretical sampling method where the continuous analog signal is multiplied by a train of perfect, zero-width Dirac delta impulses.	2017
Natural Sampling	A practical sampling method where the analog signal is multiplied by a train of rectangular pulses, causing the top of each pulse to perfectly contour the shape of the analog wave.	2017
Flat-top Sampling	A practical sampling method (Sample-and-Hold) where the amplitude of the sampled pulse is held strictly constant for the duration of the pulse width, creating a staircase waveform.	2017
Anti-aliasing Filter	A strict analog low-pass filter placed before the A/D converter to block any frequencies above the Nyquist limit ($f_{max}<f_s/2$), preventing frequency folding.	2021, 2015
Butterworth Filter	An analog filter designed specifically to have an amplitude response that is “maximally flat” in the passband with absolutely no ripples, at the cost of a slower transition band roll-off.	Foundational (PYQ Related)
Elliptic Filter	An analog filter characterized by equalized ripple behavior in both the passband and the stopband, offering the sharpest possible transition (steepest roll-off) for a given filter order.	Foundational (PYQ Related)
Z-Parameters (Open-Circuit Impedance)	Network parameters that express the port voltages as a linear combination of port currents, calculated by selectively open-circuiting the input and output ports.	2022
Y-Parameters (Short-Circuit Admittance)	Network parameters that express the port currents as a linear combination of port voltages, calculated by selectively short-circuiting the input and output ports.	2025, 2022
ABCD-Parameters (Transmission)	Network parameters that directly relate the sending-end voltage/current to the receiving-end voltage/current, mathematically optimized for cascading multiple two-port networks.	2025, 2024, 2022