ECE 21113 Signal Processing Theory - Lecture 1 Vocabulary

Vocabulary practice flashcards covering basic concepts, classifications, sampling, and quantization principles in Digital Signal Processing Theory (ECE 21113).

Digital Signal Processing

A field of engineering and applied mathematics dealing with signals originating from the real world—such as seismic vibrations, visual images, and sound waves—by processing them using digital systems.

Signal

A description of how one parameter is related to another parameter, or any physical quantity that varies with time, space, or other independent variables.

System

A physical device or process that performs an operation on an input signal to produce an output signal.

Time Domain

A signal representation where time is the independent variable plotted on the horizontal axis.

Frequency Domain

A signal representation where frequency is the independent variable plotted on the horizontal axis.

Spatial Domain

A signal representation where spatial position or coordinate is the independent variable on the horizontal axis.

Composite Signal

A real-world signal composed of many individual frequency components of differing amplitudes combined together.

Bandlimited Signal

A signal whose non-zero frequency components reside within a bounded range, typically located at the lower end of the frequency spectrum.

Analog System

A system where a signal value is specified for every continuous value of the independent variable at both input and output.

Digital System

A system where a signal value is specified only for discrete intervals of the independent variable at both input and output.

Continuous-Time Signal

A signal described by functions of a continuous independent variable, such as time $t$.

Discrete-Time Signal

A signal defined only at specific values of the independent variable, such as integer sample points $n$ in time.

Continuous-Valued Signal

A signal whose amplitude takes on all possible values over a finite or infinite continuous range.

Discrete-Valued Signal

A signal whose amplitude takes on values from a discrete, finite set of numbers.

Multichannel Signal

A signal generated by multiple sources and represented in vector or array form, such as multi-lead EEG signals.

Multidimensional Signal

A signal that is a function of two or more independent variables, such as image spatial coordinates $I(x, y)$.

Deterministic Signal

A signal that can be uniquely defined and described by an explicit mathematical expression, such as $v(t) = \sin(10\pi t)$.

Random Signal

A signal that cannot be expressed by a clear mathematical formula and is instead described statistically by its probability density function (PDF).

Symmetric Signal

Also known as an even signal; a signal that satisfies $x(t) = x(-t)$ or $x[n] = x[-n]$, remaining identical after time reversal.

Antisymmetric Signal

Also known as an odd signal; a signal that satisfies $-x(-t) = x(t)$ or $-x[-n] = x[n]$ with $x(0) = 0$, remaining identical after combined time and amplitude reversal.

Periodic Signal

A signal that repeats itself at regular intervals, satisfying $x(t) = x(t \pm nT_0)$ in continuous time or $x[n] = x[n \pm mN]$ in discrete time.

Energy Signal

A signal characterized by having a finite total energy $0 < E < \infty$ and zero average power $P = 0$.

Power Signal

A signal characterized by having infinite total energy $E = \infty$ and finite non-zero average power $0 < P < \infty$.

Sampling Theorem

A foundational theorem stating that to avoid aliasing when reconstructing an analog signal, the sampling rate $F_s$ must be at least twice the maximum frequency component $F_{\text{max}}$ of the signal ($F_s \ge 2F_{\text{max}}$).

Folding Frequency

The frequency $F_{\text{fold}} = \frac{F_s}{2}$, representing the maximum frequency component that can be uniquely reconstructed at a given sampling frequency $F_s$.

Aliasing

A distortion effect occurring when a signal is sampled below its Nyquist rate, causing frequency components higher than $\frac{F_s}{2}$ to appear as lower-frequency aliases.

Analog-to-Digital Converter

A system block consisting of a sampler, quantizer, and coder that converts a continuous-time analog input signal $x_a(t)$ into a digital binary sequence.

Quantization

The process of mapping a continuous-valued discrete-time signal (DT-CV) to a discrete-valued discrete-time signal (DT-DV) by assigning sample amplitudes to discrete levels.

Quantization Step

Also referred to as resolution $\Delta$; the distance between two consecutive quantization levels, defined as $\Delta = \frac{x_{\text{max}} - x_{\text{min}}}{L - 1}$.

Truncation

A quantization method that discards excess fractional digits by assigning each sample amplitude to the quantization level directly below it.

Rounding

A quantization method that eliminates excess fractional digits by mapping each sample amplitude to the nearest available quantization level.

Signal-to-Quantization Noise Ratio

A metric evaluating the fidelity of a quantized signal, calculated in decibels as $\text{SQNR}_{\text{dB}} = 10 \log_{10}\left(\frac{P_x}{P_q}\right)$, where $P_x$ is the signal power and $P_q$ is the quantization error power.