Lecture

Discrete-time signals: Fundamentals and Applications

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Description

This lecture introduces the concept of discrete-time signals, tracing back to ancient flood data representations and modern scientific experiments. It covers the analysis and synthesis of sequences, synchronization of audio and video, cooling laws, capacitor discharging, finite and infinite-length signals, periodic and finite-support signals, elementary operators, and energy and power calculations.

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Related concepts (25)

Discrete time and continuous time

In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next.

Signal

In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.

Quantization (signal processing)

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.

Capacitor types

Capacitors are manufactured in many styles, forms, dimensions, and from a large variety of materials. They all contain at least two electrical conductors, called plates, separated by an insulating layer (dielectric). Capacitors are widely used as parts of electrical circuits in many common electrical devices. Capacitors, together with resistors and inductors, belong to the group of passive components in electronic equipment.

Finite impulse response

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying). The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly samples (from first nonzero element through last nonzero element) before it then settles to zero.

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