Name: system properties: linearity, causality, memory
Uploaded: 2024-09-26T13:16:54.000Z
Duration: 1 min 26 s
Channel: JoVE

Doğrusallık, homojenliği ve katkı payını birleştiren, doğrudan giriş-çıktı ilişkisine sahip bir sistem özelliğidir.
Homojenlik, bir girdi bir sabitle çarpılırsa, çıktının aynı sabitle çarpılmasını gerektirir. Toplam, birden çok girdiye verilen yanıtın, bireysel yanıtlarının toplamı olduğu anlamına gelir.
Hem homojenlik hem de katkı özelliklerine sahip bir sistem, doğrusal bir sistem olarak sınıflandırılır.
Doğrusal sistemler, süperpozisyon ilkesine uyan dirençler, kapasitörler ve indüktörler içeren devreleri içerir.
Tersine, doğrusallık denklemine uymayan sistemler, genellikle doğrultucular ve diyotlar gibi cihazlar dahil olmak üzere doğrusal olmayan olarak sınıflandırılır.
Nedensel bir sistem, gelecekteki girdi değerlerinden bağımsız bir akım tepkisi ile karakterize edilir. Bir örnek, gelecekteki sürüş eylemlerini tahmin edemeyen bir arabanın hareketi olabilir.
İdeal filtreler gibi nedensel olmayan sistemler fiziksel olarak gerçekleştirilemez ve nedensellik ilkesini takip etmez.
Dinamik sistemler, çıktının hem geçmiş hem de gelecekteki girdilerden etkilendiği belleği gösterir.
Statik sistemler, akım çıkışının yalnızca mevcut girişe dayandığı belleksiz veya anlık sistemlerdir.

sistemlerin sınıflandırılması-i

Doğrusallık, homojenlik ve toplamsallığı birleştiren doğrudan bir girdi çıktı ilişkisiyle karakterize edilen bir sistem özelliğidir. 
Homojenlik, bir x(t) girdisi c sabiti ile çarpılırsa y(t) çıktısının da aynı sabitle çarpılacağını belirtir. Matematiksel olarak bu şu şekilde ifade edilir:
<img alt="Equation1" src="/files/ftp_upload/16045/16045_PT%20EQUATION_1.svg" style="height: 14px;">
Toplamsallık, birden fazla girdinin toplamına verilen yanıtın, bunların tekli yanıtlarının toplamı olduğu anlamına gelir. Sırasıyla y_1(t) ve y_2(t) çıktılarını üreten x_1(t) ve x_2(t) girdileri için:
<img alt="Equation2" src="/files/ftp_upload/16045/16045_PT%20EQUATION_2.svg" style="height: 14px;">
Homojenlik ve toplamsallığın birleştimi doğrusal bir sistemin denklemini verir: 
<img alt="Equation3" src="/files/ftp_upload/16045/16045_PT%20EQUATION_3.svg" style="height: 14px;">
Doğrusal sistemler, süperpozisyon ilkesine uyan dirençler, kapasitörler ve indüktörler içeren devreler barındır. Tersine, doğrusallık denklemine uymayan sistemler, örneğin doğrultucular ve diyotlar gibi, doğrusal olmayan olarak sınıflandırılır. 
Nedensel sistem, mevcut tepkinin gelecekteki giriş değerlerinden bağımsız olduğu bir sistemdir. Örneğin, bir arabanın hareketi gelecekteki sürüş eylemlerini öngöremez ve bu da onu nedensel bir sistem yapar. Buna karşılık, ideal filtreler gibi nedensel olmayan sistemler, nedensellik ilkesini takip etmedikleri için fiziksel olarak gerçekleştirilemezdir.
Dinamik sistemler, çıktının geçmiş ve şimdiki girdilere bağlı olduğu hafızayı sergiler. Bunun bir örneği, şimdiki çıktının geçmiş girdilerden etkilendiği kapasitörlü veya indüktörlü bir elektrik devresidir. Hafızasız veya anlık sistemler olarak da bilinen statik sistemler, yalnızca o andaki girdiye dayalı çıktılara sahiptir, örneğin basit bir direnç devresinde çıkış geriliminin mevcut giriş gerilimine doğrusal bir fonksiyonla bağlı olması. 
Bu özelliklerin anlaşılması - doğrusallık, nedensellik ve hafıza - çeşitli mühendislik alanlarındaki sistemleri analiz etmek ve tasarlamak için önemlidir.

Sistemlerin Sınıflandırılması-I

Doğrusallık, homojenliği ve katkı payını birleştiren, doğrudan giriş-çıktı ilişkisine sahip bir sistem özelliğidir.
Homojenlik, bir girdinin ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

Introduction to Signals and Systems

Sinyaller ve Sistemlere Giriş

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 to a sum of inputs equals the sum of the separate responses. Together, these rules define a linear system, and circuits with resistors, capacitors, and inductors can follow the superposition principle.

Systems that do not satisfy the linearity equation are non-linear. Diodes and rectifiers are examples of non-linear systems. Causality is another key property. A causal system depends only on the present input and past inputs, not on future values.

A car’s motion is a simple example of a causal system, because it cannot depend on future driving actions. Non-causal systems, such as ideal filters, are not physically realizable because they do not follow causality. Memory is the last major property. Dynamic systems have memory, so their output depends on past and present inputs, as in circuits with capacitors or inductors. Static systems, also called memoryless or instantaneous systems, depend only on the present input. A simple resistor circuit is an example, since its output voltage is a direct function of the current input voltage.

System Properties: Linearity, Causality, Memory

system-properties-linearity-causality-memory

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

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...

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 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

Explore linearity, causality, and memory in system behavior. Learn how linear, non-linear, causal, dynamic, and static systems differ in engineering.

System Properties: Linearity, Causality, Memory | JoVE K12

JoVE Core Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

System Properties: Linearity, Causality, Memory

Description

Transcript

Tags