Name: tandem mass spectrometry for biomolecule analysis
Uploaded: 2023-04-30T06:31:22.000Z
Duration: 7 min 9 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

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

Waves and Their Applications in Technologies for Information Transfer

HS-PS4-5

Tandem Mass Spectrometry

在串联质谱分析中，从生物样品中分离出目标生物分子，然后将其裂解为多个亚单位，以帮助阐明其组成和序列。该过程通过串联的质谱仪实现：第一台质谱仪对样品进行离子化，并筛选出具有特定质荷比的离子；筛选后的离子被进一步裂解，然后传递至第二台质谱仪，对裂解产生的片段进行分析。
本视频介绍了串联质谱的基本原理，包括质荷比选择和解离方法。同时展示了一种利用碰撞诱导解离进行串联质谱分析生物化学化合物的一般步骤。应用部分涵盖了选择反应监测、蛋白质翻译后修饰的鉴定，以及血液中他克莫司水平的检测。

串联质谱法

在串联质谱分析中，从生物样品中分离出目标生物分子，然后将其裂解为多个亚单位，以帮助阐明其组成和序列。该过程通过串联的质谱仪实现：第一台质谱仪对样品进行离子化，并筛选出具有特定质荷比的离子；筛选后的离子被进一步裂解，产生的碎片随后进入第二台质谱仪进行分析。
本视频介绍了串联质谱的基本原理，包括质荷比选择和解离方法。同时展示了一种利用碰撞诱导解离进行串联质谱分析生物化学化合物的一般步骤。应用部分涵盖了选择反应监测、蛋白质翻译后修饰的鉴定，以及血液中他克莫司浓度的检测。
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串联质谱技术将多个质谱阶段结合在一起，首先分离特定生物分子，然后分析其化学组成。生物分子具有庞大而复杂的结构，使其分子构成难以确定。串联质谱技术可选择目标分子，并将其碎裂为多个亚单位，从而有助于阐明该分子的身份及其序列。本视频将介绍串联质谱技术的基本原理、通用实验流程，以及其在生物化学中的一些应用。
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串联质谱技术始于典型的质谱仪器：首先通过离子源将样品转化为离子，然后利用质量分析器根据离子的质荷比对其进行分离。一种常见的质量分析器是四极杆，它仅允许具有特定质荷比的离子通过，而其他离子则会撞击仪器中的杆状电极而被消除。被允许通过的离子称为前体离子，即所关注的生物分子。该离子随后进入碰撞池（通常为另一个四极杆），在此施加能量，使离子以可预测的模式发生碎裂。
这些碎片离子随后进入另一个质量分析器（例如飞行时间分析器），对&#34;产物离子&#34;进行分离。随后，产物离子被送至检测器，如同常规质谱仪一样。对于未知蛋白质而言，所得谱图包含大量重叠的碎片，难以直接生成该生物分子的完整确切序列。然而，特定蛋白质的谱图模式具有独特性。分析软件将该谱图与已知肽段序列数据库进行比对，从而通过重叠的碎片信息鉴定出未知蛋白质。
根据样品性质及所需的碎裂程度，可采用多种不同的碎裂方法。碎裂模式取决于能量的传递方式、能量大小以及其在前体离子中的分布情况。能量可通过中性粒子、辐射或电子进行传递。使用中性原子的方法称为碰撞诱导解离（CID），主要在氨基酸之间的肽键处发生断裂，非常适合用于肽段的鉴定。
在了解了该技术的基本原理之后，接下来我们将观察碰撞诱导解离（CID）串联质谱技术如何被用于研究细菌细胞包膜的一种组分。
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与所有质谱实验一样，第一步是对样品进行离子化。对于生物分子，通常采用基质辅助激光解吸或电喷雾电离方法。随后通过调节离子光学参数来优化前体离子信号。完成后，选择目标离子并确定碎裂方法，例如碰撞诱导解离（CID）。
施加电压的强度会影响前体离子进入碰撞池时的碎裂程度。逐渐增加该电压，直至前体离子的丰度约为最丰产物离子的10%。采集多个谱图并进行平均，直到获得足够的信噪比。所需扫描次数取决于原始前体离子的信号强度，通常在3到300次之间。
本示例中的分析物为来自大肠杆菌K-12的脂质A，在CID后产生19个主要碎片离子。脂质A的通用结构已被充分阐明，因此可通过软件从样品数据中重建其特定组成。
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在了解了实验步骤之后，让我们来看一下串联质谱在生物化学中的一些应用方式。
串联质谱中一种常见的扫描模式是选择反应监测（selected reaction monitoring，SRM）。在SRM中，两个质量分析器均被固定在选定的质荷比上，从而专注于特定的前体离子和产物离子。由于SRM具有高度的灵敏性，因此可以利用已知浓度的肽段标准品的质谱图，并将其与未知样品进行比较，从而实现对目标蛋白质的定量分析。
蛋白质在翻译后通常会发生修饰，常见的是添加甲基、磷酸基团或糖类（称为糖链）等功能基团。这些修饰在细胞信号传导过程中具有重要作用，有助于阐明细胞之间的相互通讯机制。由于串联质谱可将蛋白质裂解为较小的片段，因此可以确定翻译后修饰（PTM）的具体位置，精确到某一碎片甚至某个氨基酸。某些修饰（如乙酰化和三甲基化）仅凭质荷比难以区分，因此在质谱分析前需进行色谱分离。
患者血液中的许多待测物浓度低于常规质谱检测的下限。SRM的另一优势在于其仅保留一个产物离子而舍弃其余离子，从而提高灵敏度，并将检测下限最多提升100倍。在此示例中，免疫抑制剂他克莫司（tacrolimus）可在浓度低至1 ng/mL的水平被检测到。
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<div class="chapter_text" id="script_4">
您刚刚观看了 JoVE 关于串联质谱的视频。该视频介绍了仪器的原理，概述了一般操作流程，并解释了该技术当前应用的一些方式。感谢观看！
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在串联质谱分析中，从生物样本中分离出目标生物分子，然后将其裂解成多个亚基，以帮助……

串联质谱技术将多个质谱阶段结合在一起，首先分离特定生物分子，然后分析其化学组成。生物分子具有庞大而复杂的结构，使其分子组成难以确定。串联质谱技术首先选择目标分子，随后将其断裂为多个亚单位，从而有助于阐明该分子的身份及其序列信息。本视频将介绍串联质谱技术的基本原理、通用实验流程以及其在生物化学中的一些应用。串联质谱技术始于典型的质谱仪器：首先通过离子源将样品转化为离子，然后利用质量分析器根据离子的质荷比对其进行分离。一种常见的质量分析器是四极杆，它仅允许具有特定质荷比的离子通过，而其他离子则会撞击仪器的杆状电极。被允许通过的离子称为前体离子，即所关注的生物分子。该离子随后进入碰撞池，通常为另一个四极杆，在其中施加能量，使离子以可预测的模式发生碎裂。这些片段进入另一个质量分析器（例如飞行时间分析器），将这些“产物离子”进行分离。随后，产物离子被送至检测器，如同常规质谱仪中的过程。对于未知蛋白质而言，所得到的谱图包含大量重叠的片段，难以据此生成生物大分子的完整确切序列。然而，每种特定蛋白质的谱图模式具有独特性。分析软件将该谱图与已知肽段序列的数据库进行比对，从而通过重叠的片段鉴定出未知蛋白质。根据样品类型及所需的片段化程度，可采用多种片段化方法。片段化模式取决于能量的传递方式、能量大小及其在前体离子中的分布情况。能量可通过中性粒子、辐射或电子进行传递。使用中性原子时，该过程称为碰撞诱导解离（collision-induced dissociation, CID），主要在氨基酸之间的肽键处发生断裂，适用于氨基酸的鉴定。在介绍了该技术的基本原理之后，让我们来看一下碰撞诱导解离串联质谱法如何被用于研究细菌细胞包膜的一个组分。与所有质谱实验一样，第一步是使样品离子化。对于生物分子，通常采用基质辅助激光解吸或电喷雾电离方法。随后通过调节离子光学参数来优化前体离子信号。完成后，选择目标离子进行分离，并确定碎裂方法，例如碰撞诱导解离（CID）。施加电压的强度会影响前体离子进入碰撞池后的碎裂程度，该电压会逐步增加，直至前体离子的丰度约为最丰产物离子的10%。需采集并平均多个质谱图，直至达到足够的信噪比。所需扫描次数取决于原始前体离子的信号强度，通常在3到300次之间。本示例中的分析物为来自大肠杆菌 K-12 的脂质 A，在 CID 作用下产生了 19 个主要碎片。脂质 A 的一般结构已知，因此软件可据此从样品中重建其特定组成。现在我们已经了解了该实验流程，接下来让我们探讨串联质谱技术在生物化学中的一些应用方式。串联质谱中一种常见的扫描模式是选择反应监测（SRM）。在SRM中，两个质量分析器均固定于选定的质荷比，以聚焦特定的前体离子和产物离子。由于SRM具有高度灵敏性，因此可以利用已知浓度的肽段标准品的谱图，并将其与未知样品的谱图进行比较，从而实现对目标蛋白质的定量分析。蛋白质在翻译后通常会经过修饰，常见的方式是添加甲基、磷酸基团或糖类（称为聚糖）等功能基团。这些修饰在细胞信号传导过程中具有重要作用，有助于阐明细胞之间如何相互交流。由于串联质谱能够将蛋白质裂解成更小的组分，因此可以确定翻译后修饰（PTM）在特定片段甚至某个氨基酸上的具体位置。某些修饰（如乙酰化和三甲基化）仅通过质荷比难以区分，因此在质谱分析前需进行色谱分离。患者血液中的许多分析物浓度低于常规质谱检测的检测限。选择反应监测（SRM）的另一个优势在于，它会舍弃除一种产物离子外的所有离子，从而提高灵敏度，并将最低检测限增强高达100倍。在此示例中，免疫抑制剂药物他克莫司（tacrolimus）可在1 ng/mL的水平被检测到。您刚刚观看了 JoVE 关于串联质谱的视频。该视频介绍了仪器的原理，概述了一般操作流程，并解释了该技术当前应用的一些方式。感谢观看！

Education

教育

JoVE Science Education

Chemistry

化学

Biochemistry

生物化学

串联质谱

tandem mass spectrometry for biomolecule analysis

Tandem mass spectrometry is used to isolate a biomolecule and break it into smaller pieces so its makeup can be studied. Because biomolecules often have large, complex structures, it can be hard to identify their molecular composition and sequence from a single measurement. By linking mass spectrometers in series, the technique first selects one ion and then analyzes the fragments it produces.

The process starts with an ion source that converts the sample into ions. A mass analyzer then separates those ions by their mass-to-charge ratio, also called m/z. In a quadrupole, only ions with a chosen m/z pass through, while the others strike the rods. The selected precursor ion is the molecule of interest.

That ion moves into a collision cell, often another quadrupole, where energy breaks it apart in a predictable pattern. The fragments, called product ions, then enter a second mass analyzer such as a time-of-flight instrument. After separation, the detector records the signals. For an unknown protein, the spectrum can contain many overlapping fragments, but the pattern is still unique. Software can compare it with a database of known peptide sequences to identify the protein.

Different fragmentation methods can be used depending on the sample and the level of detail needed. The outcome depends on how energy is transferred, how much is transferred, and how it spreads through the precursor ion. Energy may come from neutral particles, radiation, or electrons. With collision-induced dissociation, or CID, neutral atoms are used and the peptide bond between amino acids is usually cleaved, which helps with identification.

CID tandem mass spectrometry can also be used to study a bacterial cell envelope component. In that example, the sample is first ionized by matrix assisted laser desorption or electrospray ionization. The precursor ion signal is then optimized by tuning the ion optics, and the target is isolated before CID is selected. The applied voltage controls how much fragmentation occurs, and it is increased until the precursor is about 10% as abundant as the highest product ion. Multiple scans are collected and averaged until the signal-to-noise ratio is strong enough. For lipid A from Escherichia coli K-12, 19 major fragments were observed, and its known structure let software reconstruct the composition.

Tandem mass spectrometry is also used for selected reaction monitoring, or SRM. In SRM, both mass analyzers are fixed to a chosen m/z so the instrument focuses on specific precursor and product ions. This high sensitivity makes it useful for comparing peptide standards of known concentration with unknown samples to measure proteins of interest. The method is also helpful for detecting post-translational modifications, or PTMs, such as methyl groups, phosphate groups, and sugars called glycans, which play roles in cell signaling. Because the sample is broken into smaller pieces, the modification can sometimes be placed on a specific fragment or amino acid.

Some PTMs, such as acetylation and trimethylation, are hard to tell apart by mass alone, so chromatographic separation is done before mass spectrometry. SRM can also improve detection of very low-level compounds in blood. By removing all but one product ion, it can raise sensitivity and lower the detection limit by up to 100 fold. In the example shown, the immunosuppressant tacrolimus was detected at 1 ng/mL.

Tandem Mass Spectrometry for Biomolecule Analysis

tandem-mass-spectrometry-for-biomolecule-analysis

dialysis: diffusion based separation

Dialysis for Buffer Exchange in Biochemistry

Dialysis is a common biochemistry technique for buffer exchange and desalting. It separates molecules by diffusion through a semipermeable membrane, which lets small molecules pass while holding larger biomolecules inside the sample. The membrane is the key part of the setup. Its pores create a molecular weight cutoff, so a membrane such as a 10 kDa membrane usually keeps molecules larger than 10 kilodaltons inside. This cutoff is not exact, because membranes have a range of pore sizes.

enzyme assays and kinetics

Measuring Enzyme Reaction Rates

Enzyme reaction rates can be measured with assays that track how substrate or product levels change over time. Enzymes are proteins, or sometimes RNAs, that speed up chemical reactions by lowering the activation energy needed to start them. They act on a specific substrate and help form a product that supports life processes. Enzymatic reactions are often described in three steps. First, the substrate binds to the enzyme active site and forms an enzyme-substrate complex. That complex can fall...

maldi-tof mass spectrometry

How MALDI-TOF Reads Biomolecules

MALDI-TOF mass spectrometry reads biomolecules by using a laser, a matrix, and a time-of-flight analyzer. MALDI, or matrix-assisted laser desorption ionization, helps fragile molecules keep their structure while they are moved into the mass analyzer. The analyzer then separates compounds based on size and charge. In MALDI, the sample is mixed into a matrix, usually an organic compound with aromatic and conjugated double bonds. A laser pulse strikes the spot, and the matrix absorbs most of the...

tandem mass spectrometry

Tandem mass spectrometry is used to isolate a biomolecule and break it into smaller pieces so its makeup can be studied. Because biomolecules often have large, complex structures, it can be hard to identify their molecular composition and sequence from a single measurement. By linking mass spectrometers in series, the technique first selects one ion and then analyzes the fragments it produces. The process starts with an ion source that converts the sample into ions. A mass analyzer then...

protein crystallization

Protein Crystals for Structure Analysis

Protein crystals help scientists study protein structure and function. A crystal is a solid lattice made from purified protein molecules. These crystals are useful in structural biology because they reveal details that methods like mass spectrometry and SDS-PAGE cannot show on their own. Protein crystallization is paired with recombinant protein expression and x-ray diffraction to support this work. The process starts with a large amount of very pure protein. Researchers often make that...

chromatography-based biomolecule purification methods

chromatography-based-biomolecule-purification-methods

Protein Purification with SEC and IMAC

Protein purification with size-exclusion chromatography and affinity chromatography helps isolate biomolecules from complex mixtures. These methods are common in biochemistry because purified samples are needed before a biomolecule’s properties and activity can be studied. The video focuses on the principles behind size-exclusion chromatography, affinity chromatography, and immobilized metal affinity chromatography, or IMAC. Size-exclusion chromatography, or SEC, separates molecules by size. A...

two-dimensional gel electrophoresis

Protein Mapping with 2D Gel Electrophoresis

Protein mapping with 2D gel electrophoresis separates complex protein mixtures across two steps. The method combines isoelectric focusing, or IEF, with sodium dodecyl sulfate polyacrylamide gel electrophoresis, or SDS-PAGE. Together, these methods can resolve thousands of biomolecules from a single sample by their isoelectric point and molecular weight. The first dimension is IEF. Each protein has an isoelectric point, or pI, which is the pH where its net charge is zero. Proteins are loaded...

metabolic labeling

Tracking Cell Chemistry with Metabolic Labels

Metabolic labeling tracks cell chemistry by using chemical analogs that cells take up and build into biomolecules. These labels help scientists follow biochemical changes and modifications inside cells. The labeled products can then be studied with tools such as SDS-PAGE and NMR to learn more about metabolic pathways. Several labeling strategies are shown here. Isotopic labeling uses analogs that match the natural molecule but contain uncommon isotopes, such as carbon-13 and nitrogen-15 in an...

electrophoretic mobility shift assay (emsa)

electrophoretic-mobility-shift-assay-emsa

Detecting Protein-DNA Binding by EMSA

Electrophoretic mobility shift assay, or EMSA, is a biochemical method used to detect binding between proteins and nucleic acids. It is also called a gel shift assay. The test compares how a labeled nucleic acid moves through a gel before and after it binds a protein. EMSA is used to see whether a specific protein binds to a specific nucleic acid. First, the nucleic acid is labeled to make a probe. The transcript describes radioactive phosphorus-32 as a common label. The probe is then mixed...

photometric protein determination

Measuring Protein Concentration with Absorbance

Measuring protein concentration with absorbance is a key step in many biochemical assays. Photometric methods use the fact that samples with more light-absorbing material transmit less light. Because concentration and absorption are directly related, this makes it possible to measure an unknown sample. The core idea comes from the Beer-Lambert Law. This law states that the concentration of a light-absorbing species is proportional to its absorbance. The video also introduces the Bradford assay...

density gradient ultracentrifugation

Sucrose Gradient Separation in an Ultracentrifuge

Sucrose gradient separation in an ultracentrifuge is a lab method for isolating cell parts and biomolecules. It uses differences in density to make particles sink or rise in a liquid. A high-speed ultracentrifuge speeds up this process so components can be separated without destroying them. The basic idea starts with a suspension, which is particles mixed in a liquid solvent. Particles that are denser than the solvent sediment, while less dense particles float. A rotor inside the...

co-immunoprecipitation and pull-down assays

co-immunoprecipitation-and-pull-down-assays

Protein Interaction Capture Methods in Cells

Co-immunoprecipitation and pull-down assays are laboratory methods used to capture stable protein-protein interactions. Protein-protein interactions help control many biological functions, but many of them have not yet been identified. These assays are related to immunoprecipitation, which isolates a target protein from a mixed sample using an antibody. In co-immunoprecipitation, or CoIP, an antibody binds the target protein, and that protein is already attached to another protein that the...

reconstitution of membrane proteins

Membrane Proteins in Liposome Models

Membrane proteins can be moved into liposome models so their function can be studied outside a cell. Reconstitution means restoring an isolated biomolecule to a working form. For membrane proteins, that usually means placing a purified protein into an artificial lipid membrane. Cell membranes are made mainly of phospholipids and membrane proteins. The phospholipids form a bilayer with hydrophilic phosphate heads facing water and hydrophobic fatty acid tails facing inward. Some membrane...

f&#246;rster resonance energy transfer (fret)

FRET as a Molecular Ruler in Cells

Föster resonance energy transfer, or FRET, is a way to study close-range biochemical interactions using light-emitting molecules. A donor fluorophore can pass energy to an acceptor fluorophore when their emission and absorption spectra overlap. This transfer happens only when the pair is very close together, usually within 10 nm. Because FRET depends on distance, it is often called a molecular or spectroscopic ruler. The strength of the signal is measured as FRET efficiency, which describes...

surface plasmon resonance (spr)

SPR Biosensors for Tracking Binding Kinetics

Surface plasmon resonance, or SPR, is a way to track biomolecular binding on a label-free biosensor. It is used to measure molecular affinity, kinetics, specificity, and concentration. The method works with a thin metal layer on a prism, where changes in reflected light reveal interactions in real time. SPR sensors use a thin layer of a noble metal on the face of a prism. Light is reflected from the prism-metal interface into a photodetector. At one specific angle, called the surface plasmon...

biochemistry

本系列介绍了常用的纯化方法, 如亲和层析, 以及分析方法, 如 MALDI。此外, 视频展示了评估生物相互作用和功能的方法, 如 co-immunoprecipitation 和代谢标记。

Learn how tandem mass spectrometry isolates biomolecules, fragments them, and helps detect proteins, PTMs, and low-level drugs in blood.

Tandem Mass Spectrometry for Biomolecule Analysis | JoVE K12

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-5.

Life Science

matter-and-energy-in-organisms-and-ecosystems

Matter and Energy in Organisms and Ecosystems

HS-LS1-6.

Overview

Principles of Tandem Mass Spectrometry

Instrumental Operation

Applications

Summary

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 ...

/files/media/science-education/science-education-thumbs/14721.jpg

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 ...

/files/media/science-education/science-education-thumbs/14722.jpg

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 ...

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 ...

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium&#39;s ...

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As ...

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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. ...

Doppler Effect - I

The Doppler effect and Doppler shift were named after the Austrian physicist and mathematician Christian Johann Doppler in 1842, who conducted experiments ...

Doppler Effect - II

The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on ...

Shock Waves

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the ...

Echo

The human ear cannot distinguish between two sources of sound if they happen to reach within a specific time interval, typically 0.1 seconds apart. More ...

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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. ...

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 ...

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, ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

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 ...

Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. [Clarification Statement: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the earth.] [Assessment Boundary: Assessment is limited to algebraic relationships and describing those relationships qualitatively.]

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The Electromagnetic Spectrum

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

Classification of Signals

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

Discrete Fourier Transform

Consider a vibration sensor that continuously captures data in the form of a continuous time-dependent signal.
However, in reality, the sensor can only ...

Discrete-Time Fourier Series

The Discrete-Time Fourier Series is a counterpart to the Fourier-series expansion of continuous-time periodic signals.
Calculating the expansion ...

Sampling Theorem

Consider the continuous-time signal x(t), and a train of impulses where Ts,&#xA0; is the sampling interval, and fs, is the sampling frequency.
Multiplying ...

Properties of Fourier Transform I

In radio broadcasting, Fourier Transform properties are applied in simultaneous multi-channel transmission, adjusting audio clip speeds, live broadcast ...

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 ...

Methods of Documentation VII: EMR

Electronic Medical Records (EMRs) primarily center around electronically documenting patients&#39; health information within a single healthcare ...

Fast Fourier Transform

The Fast Fourier Transform, FFT, is a computational algorithm for calculating the Discrete Fourier Transform by breaking the calculations into smaller, ...

reconstruction-of-signal-using-interpolation

Reconstruction of Signal using Interpolation

Consider a continuous signal and its sampled counterpart with a sampling period T.
Applying a zero-order hold to the sampled signal results in a piecewise ...

Downsampling

Consider a sampled sequence with zero values between sampling instants. Replace it by taking every N-th value of the sampled sequence.
The original and ...

Design Example

An engineer designs a circuit for a speaker system with a 2 kHz crossover frequency requirement, considering the speaker&#39;s resistance of 8 ohms.
The ...

Upsampling

Consider a decimated signal with a reduced frequency range due to its lower sampling rate.
Insert zeros between each sample to upsample, that introduces ...

Properties of DTFT I

Consider two discrete-time signals, each with their respective Discrete-Time Fourier Transforms DTFTs.
The signals are first multiplied by constants a and ...

Relation of DFT to z-Transform

The Discrete Fourier Transform (DFT) analyzes the frequency content of discrete-time signals.
It maps the N-sampled discrete time-domain sequence to its ...

Feedback control systems

Feedback control systems are categorized as linear or nonlinear, time-varying or time-invariant, and classified by signal types as continuous or ...

Properties of the z-Transform I

Certain properties provide a solid foundation for analyzing discrete-time systems using the Z-transform.
Considering two discrete-time signals, the ...

Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique based on a phenomenon of nuclear physics discovered in the 1930s, in which ...

Evaluate questions about the advantages of using digital transmission and storage of information. [Clarification Statement: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft.]

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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 ...

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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concept-of-resonance-and-its-characteristics

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano ...

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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 ...

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 ...

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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Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other. [Clarification Statement: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect.] [Assessment Boundary: Assessment does not include using quantum theory.]

HS-PS4-3

Tandem Mass Spectrometry for Biomolecule Analysis

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