Name: signal types by time and amplitude
Uploaded: 2024-09-26T13:16:53.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.8

Classification of Signals

信号可分为连续时间信号或离散时间信号、周期信号或非周期信号、模拟信号或数字信号，以及因果信号或非因果信号。
连续时间信号在每一时刻都有取值，而离散时间信号仅在特定时刻有取值。
离散时间信号通常用 x of n 表示，其中 n 为整数，通常用于表示具有本质离散变量的现象。
一个连续时间周期信号（例如正弦波）每 T 秒重复一次，满足周期性条件。任何不满足周期性条件的信号称为非周期信号。
一个周期为正整数 N 的离散时间周期信号，在经历 N 的时间平移后保持不变。离散时间周期信号可以表示为复指数的和，尤其是在使用傅里叶级数进行分析时。
模拟信号是一种连续时间信号，其幅度值可在给定范围内连续变化。数字信号是一种离散时间信号，其幅度值被限制在有限个可能的电平范围内。
如果一个信号在所有负时间值处均为零，则该信号被称为因果信号。若一个信号在负时间值处存在，则称为非因果信号。

信号的分类

在信号处理中，可以将信号以不同的特征来进行分类：连续时间信号与离散时间信号、周期信号与非周期信号、模拟信号与数字信号、因果信号与非因果信号。每个类别都强调了理解和处理这些信号的关键特征。

连续时间信号在每个时刻内都会保持一个值，从而使其能够无缝地表示信息。相反，离散时间信号只会在特定的时刻内保持相应的值，通常会将其表示为 x(n)，其中的 n 是整数。离散时间信号通常是由具有固有离散变量的现象所产生的，例如数字音频采样。

周期信号是一种随时间的重复模式。连续时间周期信号（如正弦波）通常会每隔 t 秒重复一次，并且满足周期性条件。
<img alt="Equation1" src="/files/ftp_upload/16030/16030_%20PT%20EQUATION_1.svg" style="height: 14px;">

不满足这一条件的信号则称为非周期信号。对于离散时间信号来说，周期性意味着信号会在 n 个周期的时间移位后仍然是保持不变的，具体描述如下：
<img alt="Equation2" src="/files/ftp_upload/16030/16030_%20PT%20EQUATION_2.svg" style="height: 32px;">

这些信号也可以用复指数的形式来进行表示，这对于许多应用场景来说是至关重要的。

模拟信号和数字信号是根据幅度来进行区分的。由于模拟信号在时间上是连续的，因此可以在一定范围内将其假设为的任意值，从而使其能够以平滑的数据来进行表示。这里的数字信号是一种离散时间信号，只能从有限的集合中进行取值，因此该信号只适用于数字系统和计算。

信号的因果关系是由其在时间上的存在状态所决定的。如果连续时间信号在所有的负时间实例中都为零，则该信号为因果信号，表明该信号无法预期未来的值。相反，如果非因果信号能够在负时间内保持值，则意味着它依赖于未来的输入值。了解这些分类对于在电信、控制系统和数字信号处理等领域进行有效的信号分析和处理来说是至关重要的。

信号可分为连续时间信号或离散时间信号、周期信号或非周期信号、模拟信号或数字信号，以及因果信号或非因果信号。  
连续时间信号……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Introduction to Signals and Systems

信号与系统导论

KEY TERMS AND CONCEPTS

关键术语与概念

signal types by time and amplitude

Signals in signal processing are grouped by time behavior, amplitude, and whether they start before or after time zero. These signal classes help students describe and compare signals before they are analyzed or processed.

A continuous-time signal has a value at every instant in time. A discrete-time signal has values only at specific moments, often written as x(n), where n is an integer. Discrete-time signals often come from systems with naturally discrete values, such as digital audio samples.

Signals can also be periodic or aperiodic. A periodic signal repeats its pattern over time. A continuous-time periodic signal, such as a sinusoidal wave, repeats every T seconds and satisfies the periodicity condition. Signals that do not repeat in this way are aperiodic. For discrete-time signals, periodicity means the signal repeats after a time shift of n periods, and these signals can also be written in complex exponential form, which is useful in many applications.

Another common comparison is analog versus digital. An analog signal is continuous in time and can take any value within a range, so it gives a smooth representation of data. A digital signal is a type of discrete-time signal. It can take only values from a finite set, which makes it useful for digital systems and computation.

Signals are also classified as causal or noncausal based on when they exist. A continuous-time signal is causal if it is zero for all negative time values, which means it does not depend on future values. A noncausal signal has values for negative times, so it may rely on future input values. Knowing these signal categories is important in telecommunications, control systems, and digital signal processing.

Signal Types by Time and Amplitude

signal and system

Signals and Systems in Everyday Data

Signals and systems help describe how data moves through the world. A signal x(t) is a set of data or a time function that represents a variable of interest. It can carry information about atmospheric temperature, humidity, human voice, television images, a dog’s bark, or birdsongs. A signal can also depend on more than one independent variable. An image, for example, depends on horizontal and vertical position, so it can be treated as a two-dimensional signal. In this course, the focus is on...

classification of signals

Signals in signal processing are grouped by time behavior, amplitude, and whether they start before or after time zero. These signal classes help students describe and compare signals before they are analyzed or processed. A continuous-time signal has a value at every instant in time. A discrete-time signal has values only at specific moments, often written as x(n), where n is an integer. Discrete-time signals often come from systems with naturally discrete values, such as digital audio...

energy and power signals

Power and Energy in Electrical Signals

Power and energy in electrical signals are measured from voltage and current across a resistor. These signals help describe how much energy a signal carries and how much power it delivers over time. For a continuous-time signal, total energy is found by integrating the square of the signal's magnitude over a chosen time interval. Time-averaged power is then the total energy divided by the length of that interval. For a discrete-time signal, total energy is found by summing the squares of the...

even and odd signals

Signal Symmetry and Decomposition

Signal symmetry helps classify continuous-time and discrete-time signals as even or odd. An even signal matches its time-reversed version. It mirrors around the vertical axis, so the values at negative time match the values at positive time. An odd signal does not match its time-reversed counterpart. It has antisymmetry about the vertical axis. These symmetry rules are used in both continuous-time and discrete-time signal analysis. Any continuous-time signal can be split into even and odd...

basic continuous time signals

Step, Impulse, and Ramp Signals

Step, impulse, and ramp signals are the main basic continuous-time signals. They are also called singularity functions. These signals are known for discontinuities or for derivatives that are discontinuous. The unit step function, written as u(t), is zero for negative time values and one for positive time values. It has a jump at t = 0. In many cases, it can model an abrupt change, such as the step voltage that appears when a car ignition key is turned. The derivative of the unit step...

rectangular and triangular pulse function

rectangular-and-triangular-pulse-function

Modeling Pulses with Rectangles and Triangles

Rectangular and triangular pulse functions are basic signal shapes used to model waveforms in signal processing. The rectangular pulse has a flat top and is centered at the origin with a height of one unit. It is described by two parameters: T, which gives the center location on the time axis, and τ, which sets the pulse duration. A rectangular pulse can also represent a real signal with a chosen amplitude and length. For example, a pulse with a 5 V amplitude, a 3-second duration, and a center...

exponential and sinusoidal signals

Complex Exponentials in Signal Behavior

Exponential and sinusoidal signals are used to describe how waveforms change over time. The continuous-time exponential function uses constants α and A. When both are real, it shows exponential growth or decay. Graphs of these signals make the rise or drop easy to see. When α is purely imaginary, the signal becomes a complex exponential. In this form, j is the imaginary unit and ω0 is the angular frequency. A complex exponential is periodic when its magnitude is unity. That periodic behavior...

basic discrete time signals

Discrete-Time Signal Basics and Shapes

Discrete-time signals include several basic sequences used in signal processing. The unit step sequence is 1 for zero and positive values of the integer n. A graph of eight sample points shows it as a step that begins at n = 0 and stays constant after that. The unit impulse, also called the sample sequence, is 0 for every n except at n = 0, where it equals 1. This sequence is written as δ(n). It is the first difference of the unit step sequence, and the unit step sequence u(n) is the...

basic operations on signals

Signal Transformations in Time and Amplitude

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized. Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly. Time scaling...

classification of systems-i

System Properties: Linearity, Causality, Memory

System properties such as linearity, causality, and memory help describe how a system responds to input. These ideas are useful for studying and designing systems in engineering. A system can be checked by looking at how its output changes with different inputs. Linearity means the input-output relationship follows homogeneity and additivity. Homogeneity says that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Additivity means the response...

classification of systems-ii

Continuous and Discrete System Models

Continuous-time and discrete-time systems are two common ways to model signals and their outputs. In continuous-time systems, both input and output signals change smoothly as time moves continuously. These systems are often written with differential or algebraic equations. An RC circuit is one example of a continuous-time system. Its input and output voltage can be related by a differential equation based on Ohm’s law and the capacitor relation. Discrete-time systems work differently. Their...

key terms and concepts

Learn how signals are classified as continuous or discrete, periodic or aperiodic, analog or digital, and causal or noncausal in signal processing.

Signal Types by Time and Amplitude | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Physical Science

HS-PS4-2

Next Generation Science Standards

HS-PS4-5

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS4-5

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. ...

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be ...

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a ...

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the ...

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Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The ...

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problem-solving-tuning-of-a-guitar-string

Problem-Solving: Tuning of a Guitar String

In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or ...

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Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Know wave parameters (i.e. velocity, period, amplitude, frequency, angular frequency) as well as how these quantities are defined in the cases of longitudinal and transverse waves.    Know wave parameters (i.e. velocity, period, amplitude, frequency, angular frequency) as well as how these quantities are defined in the cases of longitudinal and transverse waves.  EXPLANATION: Standard 4.PS4.1 is a student’s introduction to waves. At this time, students address the properties of amplitude, wavelength and direction of a wave and principles of superposition of waves, but not by name. In 8.PS4.1, students revisit the topic adding frequency to their models and beginning to consider wave speed, but without mentioning factors affecting the speed of the waves. PHYS.PS2.3 includes discussion of rotational motion which can pair with discussions of simple harmonic motion to clarify angular velocity and angular speed. Discussions regarding the origin of waves can fully develop these ideas.

PHYS.PS4.1

Speed of Sound in Solids and Liquids

Most solids and liquids are incompressible&#8212;their densities remain constant throughout. In the presence of an external force, the molecules tend to ...

Speed of Sound in Gases

The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. ...

Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid&#39;s elastic modulus and inertia. The two relevant ...

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propagation-speed-of-electromagnetic-waves

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


Consider a plane ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Simple Harmonic Motion

Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke&#39;s law. If the net force can ...

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characteristics-of-simple-harmonic-motion

Characteristics of Simple Harmonic Motion

The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the ...

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oscillations-about-an-equilibrium-position

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable ...

Energy in Simple Harmonic Motion

To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to ...

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Frequency of Spring-Mass System

One interesting characteristic of the simple harmonic motion (SHM) of an object attached to a spring is that the angular frequency, and the period and ...

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Describe parameters of a medium that affect the propagation of a sound wave through it. Describe parameters of a medium that affect the propagation of a sound wave through it. EXPLANATION: The focus of this discussion should be properties of the medium, specifically the density of the material. The density becomes a factor in optics and considering transmission of electromagnetic waves. Students can be led to make their descriptions by experimenting with coiled springs stretched to varying lengths. The topic of linear mass density can be used to explore analogous properties in the air.

PHYS.PS4.2

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second ...

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a ...

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions ...

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Understand that the reflection, refraction, and transmission of waves at an interference between two media can be modeled on the basis of the characteristics of specific wave parameters and parameters of the medium.  Understand that the reflection, refraction, and transmission of waves at an interference between two media can be modeled on the basis of the characteristics of specific wave parameters and parameters of the medium. EXPLANATION: The focus of this standard is on developing an understanding for the behavior of waves at a boundary. To demonstrate these principles, it is suggested that students create waves on a coiled spring or string and send these waves towards either a free or fixed end or through a different weight of string. For instance, wave can be created in a section of a lighter string then transmitted towards a point where that string terminates into a heavier segment of string. In doing so, it is possible to observe the effects on wave amplitude and a discussion of energy differences. Students should extend their observations of these mechanical waves to wave behaviors at other scales.

PHYS.PS4.3

Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure ...

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two ...

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Sound Waves: Resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical ...

Beats

The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples ...

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Communicate scientific and technical information about how the principle of superposition explains the resonance and harmonic phenomena in air columns on strings and common sound devices. Communicate scientific and technical information about how the principle of superposition explains the resonance and harmonic phenomena in air columns on strings and common sound devices. EXPLANATION:  In 4.PS4.1, students examine the effects of superposition of waves, but do not explore the behavior of waves at boundaries. Building on 4.PS4.3, the behavior of a wave at a free or fixed boundaries can create patterns where successive waves produced by a source interact with those reflected off a boundary. Discussions should include general development of the idea of harmonics. Once established, this topic can be extended to the specific function of stringed instruments such as guitars of simple open or closed tubes. The phenomena of resonance can be produced using a tuning fork held above a section of rigid tubing which is lowered or lifted into a pail of water. Resonance can be heard clearly at multiple points, providing an opportunity to model the source of resonance and relate the resonance points to the wavelength of the wave produced. The phenomenon of beats can be used to provide an introduction to this topic as it too is an audible phenomenon. Quick demonstrations of beats can be performed without tuning forks using multiple open windows in a browser simultaneously playing different frequencies.

PHYS.PS4.4

Electromagnetic Waves

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

Generating Electromagnetic Radiations

The German physicist Heinrich Hertz (1857&#8211;1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. ...

The Electromagnetic Spectrum

Electromagnetic waves are categorized according to their wavelengths and frequencies, giving the electromagnetic spectrum. These waves are classified as ...

Electromagnetic Wave Equation

Maxwell&#39;s equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose ...

Anatomy of the Eyeball

The eyeball is a hollow fluid-filled structure composed of three layers&#8212;the fibrous, vascular, and inner layers.
The superficial fibrous layer has ...

Accessory Structures of the Eye

The accessory structures of the eyes protect and support the eye but are not directly involved in vision.&#160;&#160;&#160;&#160;&#160;&#160;
Eyebrows, ...

Focusing of Light in the Eye

In a normal human eye, as light rays enter, they bend at the cornea, and the lens, to form an inverted image on the retina. The extent to which rays ...

Evaluate the characteristics of the electromagnetic spectrum by communicating the similarities and differences among the different bands. Research and determine methods and devices used to measure these characteristics. Evaluate the characteristics of the electromagnetic spectrum by communicating the similarities and differences among the different bands. Research and determine methods and devices used to measure these characteristics. EXPLANATION: The visible portion of the electromagnetic spectrum will be familiar to students, as will the ideas of x-rays, microwaves, and radiowaves. However, students often struggle to see these phenomena as multiple manifestations of the same principles. It may be beneficial to relate these discussions to the physiology of the human eye, specifically the function of the rhodopsin photopigment. As a demonstration: the light bulbs on the front of remote controls emit light outside of the visible spectrum; however, inexpensive cell phone cameras lack IR filters (as well as some front facing cameras on more current cell phones). Rendering the IR light visible can help student to understand that many devices function by capturing the energy of electromagnetic waves. An additional option would be the creation of a crystal radio using a germanium diode.

PHYS.PS4.5

Light as Energy

The energy required to carry out photosynthesis is light&#8212; typically electromagnetic radiation from the sun. The range of all possible wavelengths is ...

dual-nature-of-electromagnetic-em-radiation

Dual Nature of Electromagnetic (EM) Radiation

Electromagnetic (EM) radiation consists of electric and magnetic field components oscillating in planes perpendicular to each other and mutually ...

interaction-of-em-radiation-with-matter-spectroscopy

Interaction of EM Radiation with Matter: Spectroscopy

Electromagnetic (EM) radiation can be considered an oscillating electric and magnetic field propagating through a medium that can interact with matter in ...

Plan and conduct controlled scientific investigations to construct explanations of light’s behavior (reflection, refraction, transmission, interference) including the use of ray diagrams. Plan and conduct controlled scientific investigations to construct explanations of light’s behavior (reflection, refraction, transmission, interference) including the use of ray diagrams. EXPLANATION:  In PHYS.PS4.3 students examine the behaviors of mechanical waves moving through a medium. Though the terminology in this standard is comparable, this standard focuses on optics of light. Students should work with lenses and mirrors to build an understanding of the behaviors of light as it interacts with surfaces (reflection, refraction, transmission). In 4.PS4.1 and PHYS.PS4.1, students investigated interference patterns with mechanical waves. Using a pair of speakers and an online tone/frequency generator, it is possible to demonstrate that sound waves, like mechanical waves, can interfere with each other. In such a demonstration, students are able to hear variations in the volume of the sound as they walk in a straight line across the field of sound created by the speakers.

PHYS.PS4.6

The Wave Nature of Light

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms ...

The electromagnetic spectrum consists of all the types of electromagnetic radiation arranged according to their frequency and wavelength. Each of the ...

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a ...

Photoelectric Effect

When light of a particular wavelength strikes a metal surface, electrons are emitted. This is called the photoelectric effect. The minimum frequency of ...

Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model. EXPLANATION:  Most students willingly accept the particle behavior of light. As early as first grade, students have experimented with the behavior of light and observed that shadows can be created if some of the particles of light are blocked. Introductory explanations of the photoelectric effect can provide more advanced evidence for the particle behavior. Properties of wave behavior can be demonstrated by observing interference patterns in Young’s double slit experiment. Simple models using strips of paper to represent waves can provide a more tangible experience to understand the interference phenomena.

PHYS.PS4.7

Signal and System

Signals are sets of data or information.
One-dimensional signals include single-variable functions, such as the variations in air pressure over time in ...

Signals are categorized as Continuous-time or discrete-time, Periodic or aperiodic, Analog or digital, and Causal or noncausal.
A continuous-time signal ...

Ultrasonography

Ultrasonography is an imaging technique that uses high-frequency sound waves to visualize the body&#39;s internal structures. It is a non-invasive and ...

X-ray Imaging

German physicist Wilhelm R&#246;ntgen (1845&#8211;1923) was experimenting with electrical current when he discovered that a mysterious and invisible ...

X-ray Fluorescence (XRF)

Source: Laboratory of Dr. Lydia Finney &#8212; Argonne National Laboratory
X-ray fluorescence is an induced, emitted radiation that can be used to ...

radiological-investigation-i-x-ray-and-ct

Radiological Investigation I: X-ray and CT

Chest X-rays capture images of the chest, heart, lungs, and blood vessels to screen and diagnose respiratory issues.
They detect abnormalities like fluid, ...

Obtain information to construct explanations on how waves are used to produce, transmit, and capture signals and store and interpret information.  Obtain information to construct explanations on how waves are used to produce, transmit, and capture signals and store and interpret information. EXPLANATION:  In 8.PS4.3 students are introduced to the use of waves in communication systems. Further development of these discussions might include a distinction between the differences between analog and digital signals and necessity for digital signals in communication. Additionally, waves can be used for detection in x-rays or ultrasound. Information that is digitized can be stored with very little loss to the quality of the data itself.

Signal Types by Time and Amplitude

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