Wavelet transformIn mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
Discrete wavelet transformIn numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
WaveletA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.
Continuous wavelet transformIn mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral where is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.
Angular velocityIn physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
Haar waveletIn mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar.
Morlet waveletIn mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision. Wavelet#History In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as atoms, and which provide the best trade-off between spatial and frequency resolution.
Angular momentumIn physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.
VelocityVelocity is the speed and the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.
WalkingWalking (also known as ambulation) is one of the main gaits of terrestrial locomotion among legged animals. Walking is typically slower than running and other gaits. Walking is defined by an 'inverted pendulum' gait in which the body vaults over the stiff limb or limbs with each step. This applies regardless of the usable number of limbs—even arthropods, with six, eight, or more limbs, walk. In humans, walking has health benefits including improved mental health and reduced risk of cardiovascular disease and death.
Angular accelerationIn physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis. Angular acceleration has physical dimensions of angle per time squared, measured in SI units of radians per second squared (rads-2).
Gait (human)A gait is a manner of limb movements made during locomotion. Human gaits are the various ways in which humans can move, either naturally or as a result of specialized training. Human gait is defined as bipedal forward propulsion of the center of gravity of the human body, in which there are sinuous movements of different segments of the body with little energy spent. Varied gaits are characterized by differences such as limb movement patterns, overall velocity, forces, kinetic and potential energy cycles, and changes in contact with the ground.
Upper limbThe upper limbs or upper extremities are the forelimbs of an upright-postured tetrapod vertebrate, extending from the scapulae and clavicles down to and including the digits, including all the musculatures and ligaments involved with the shoulder, elbow, wrist and knuckle joints. In humans, each upper limb is divided into the arm, forearm and hand, and is primarily used for climbing, lifting and manipulating objects. In formal usage, the term "arm" only refers to the structures from the shoulder to the elbow, explicitly excluding the forearm, and thus "upper limb" and "arm" are not synonymous.
Autonomous robotAn autonomous robot is a robot that acts without recourse to human control. The first autonomous robots environment were known as Elmer and Elsie, which were constructed in the late 1940s by W. Grey Walter. They were the first robots in history that were programmed to "think" the way biological brains do and meant to have free will. Elmer and Elsie were often labeled as tortoises because of how they were shaped and the manner in which they moved. They were capable of phototaxis which is the movement that occurs in response to light stimulus.
Limb (anatomy)A limb is a jointed, muscled appendage of a tetrapod vertebrate animal used for weight-bearing and terrestrial locomotion. The distalmost portion of a limb is known as its extremity. The limbs' bony endoskeleton, known as the appendicular skeleton, is homologous among all tetrapods, who use their limbs for walking, running and jumping, swimming, grasping and climbing. All tetrapods have four limbs that are organized into two bilaterally symmetrical pairs, with one pair at each end of the torso, which phylogenetrically correspond to the four paired fins (pectoral and pelvic fins) of their fish ancestors.
Device fileIn Unix-like operating systems, a device file or special file is an interface to a device driver that appears in a as if it were an ordinary . There are also special files in DOS, OS/2, and Windows. These special files allow an application program to interact with a device by using its device driver via standard input/output system calls. Using standard system calls simplifies many programming tasks, and leads to consistent user-space I/O mechanisms regardless of device features and functions.
Human legThe human leg is the entire lower limb of the human body, including the foot, thigh or sometimes even the hip or buttock region. The major bones of the leg are the femur (thigh bone), tibia (shin bone), and adjacent fibula. The thigh is between the hip and knee, while the calf (rear) and shin (front) are between the knee and foot. Legs are used for standing, many forms of human movement, recreation such as dancing, and constitute a significant portion of a person's mass.
Wearable technologyWearable technology is any technology that is designed to be used while worn. Common types of wearable technology include smartwatches and smartglasses. Wearable electronic devices are often close to or on the surface of the skin, where they detect, analyze, and transmit information such as vital signs, and/or ambient data and which allow in some cases immediate biofeedback to the wearer.
Relativistic angular momentumIn physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics. Angular momentum is an important dynamical quantity derived from position and momentum. It is a measure of an object's rotational motion and resistance to changes in its rotation.
Smart deviceA smart device is an electronic device, generally connected to other devices or networks via different wireless protocols (such as Bluetooth, Zigbee, near-field communication, Wi-Fi, LiFi, or 5G) that can operate to some extent interactively and autonomously. Several notable types of smart devices are smartphones, smart speakers, smart cars, smart thermostats, smart doorbells, smart locks, smart refrigerators, phablets and tablets, smartwatches, smart bands, smart keychains, smart glasses, and many others.
