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A theorem stating that a continuous signal can be completely represented in its samples and fully reconstructed if it was sampled at twice the highest frequency component.

A mathematical transform oftentimes used in the analysis and design of digital filters that maps the discrete time signal into a complex frequency domain.

A mathematical operation used to determine the output of an LTI system given the input signal and the system's impulse response.

An algorithm to compute the Discrete Fourier Transform (DFT) efficiently, by reducing the number of computations from $O(N^2)$ to $O(N log N)$.

The process of mapping a large set of input values to a (countable) smaller set – such as rounding values to some unit of precision.

The effect that causes different signals to become indistinguishable from each other when sampled, often due to a violation of the Nyquist theorem.

A type of signal processing filter designed to have a frequency response that is as flat as possible in the passband.

A filter with a steeper roll-off and more passband ripple or stopband ripple than a Butterworth filter.

A transform that maps a finite list of equally spaced samples of a function into a list of coefficients of a finite combination of complex sinusoids.

The output of a linear time-invariant (LTI) system when presented with a unit impulse input.

A type of filter whose impulse response settles to zero in finite time as opposed to Infinite Impulse Response (IIR) filters.

A filter whose impulse response is non-zero over an infinite length of time, typically implemented using feedback.

Another name for the Nyquist theorem, which describes the minimum rate at which a signal can be sampled without introducing errors.

The number of samples of a signal that are taken per second to represent the signal digitally.

A mathematical method used in signal processing to convert an analog filter design to a digital filter design.

A linear operator that takes a signal and produces a signal with a phase shift of -90 degrees for all frequency components.

A filter that automatically adjusts its parameters according to an optimization algorithm designed to minimize a predefined cost function.

A function used to taper the end of a segment of signal data before digital signal processing is performed to reduce edge effects.

The spreading of signal energy across multiple frequency bins in the result of digital signal processing, which usually occurs with discrete signals.

The difference between the true analog value and quantized digital value, due to the discrete levels in digital representations.

The analysis of signals with respect to both time and frequency in order to understand features of the signal that change over time.

The response of a system to various frequencies of a signal’s phase shift introduced by the system.

The relationship between the amplitude of the output signal of a system compared to the input signal as a function of frequency.

A measure used in science and engineering to quantify how much a signal has been corrupted by noise.

A mathematical function that equals zero everywhere except at zero where it is infinitely high, with the integral over the entire real line equals one.

A system or device that selectively passes certain frequencies and attenuates others of a digital signal.

A mathematical method used in regression analysis to determine the best-fitting curve by minimizing the sum of the squares of the offsets.

An optimal linear filter designed to maximize the signal-to-noise ratio for a known signal template.

A mathematical representation of the relation between the input and output of a linear time-invariant system.