Name: discrete-time signal basics and shapes
Uploaded: 2024-09-26T13:16:53.000Z
Duration: 1 min 16 s
Channel: JoVE

Die Schrittfolge der Einheit wird als 1 für Null und positive Werte der ganzen Zahl 'n' ausgedrückt. Dies kann anhand eines Satzes von acht Abtastpunkten grafisch dargestellt werden.
Die Einheit Impuls oder Probensequenz wird mathematisch für alle diskreten Werte von n ausgedrückt. Es ist Null für alle 'n' Werte außer bei Null.
Der Einheitsimpuls ist die erste Differenz des Einheitsschritts, während der Einheitsschritt die kumulative Summe der Einheitsstichprobe ist. Diese Korrelation wird durch ein Diagramm visuell veranschaulicht.
Die Impulssequenz der Einheit kann den Signalwert bei n gleich Null effektiv abtasten, da er nur an diesem Punkt ungleich Null ist.
Die Sequenz der Einheitenrampe weist eine lineare Eskalation des Wertes mit zunehmender Probenzahl auf. Für eine Sequenz von 12 Samples auf einer Einheitsrampe zeigt das Diagramm einen linearen Anstieg der Amplitude mit der Sample-Anzahl.
Eine sinusförmige Sequenz wird durch ihre Amplituden- und Phasenparameter definiert.
Die Exponentialfolge wird durch komplexe Zahlen definiert, wobei exponentiell zerfallende und zunehmende Sequenzen in einem Diagramm dargestellt werden.

grundlegende diskrete zeitsignale

Basic Discrete Time Signals

Der Einheitssprung wird als 1 für Null und positive Werte der Ganzzahl n definiert. Diese Folge kann grafisch mithilfe eines Satzes von acht Abtastpunkten dargestellt werden, wobei eine Schrittfunktion gezeigt wird, die bei n=0 beginnt und danach konstant bleibt.

Die Einheitsimpuls- oder Abtastfolge wird mathematisch für alle n-Werte als Null ausgedrückt, außer bei n=0, wo sie eins ist. Der Einheitsimpuls, bezeichnet mit δ(n), ist die erste Differenz des Einheitssprungs, während der Einheitssprung u(n) die kumulative Summe der Einheitsimpulsfolge ist. Diese Beziehung kann visuell durch ein Diagramm dargestellt werden, das hervorhebt, wie der Einheitsimpuls den Signalwert bei n=0 effektiv abtasten kann.

Die Einheitsrampe weist einen linearen Wertanstieg mit zunehmender Abtastzahl auf. Beispielsweise zeigt eine Sequenz von 12 Samples auf einer Einheitsrampe eine lineare Zunahme der Amplitude mit jeder Sample-Nummer, grafisch dargestellt als gerade Linie.

Eine sinusförmige Sequenz wird durch ihre Amplituden- und Phasenparameter definiert. Diese Sequenz kann wie folgt dargestellt werden:

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_1.svg" style="height: 14px;">

wobei A die Amplitude, ω die Winkelfrequenz und Φ die Phase ist.

Die Exponentialsequenz wird mithilfe komplexer Zahlen definiert, wobei exponentiell abfallende und ansteigende Sequenzen in einem Diagramm dargestellt werden. Eine exponentiell abfallende Sequenz kann wie folgt geschrieben werden:

<img alt="Equation2" src="/files/ftp_upload/16043/16043_PT%20EQUATION_2.svg" style="height: 14px;">

während eine exponentiell ansteigende Sequenz wie folgt ausgedrückt wird:

<img alt="Equation3" src="/files/ftp_upload/16043/16043_PT%20EQUATION_3.svg" style="height: 14px;">

wobei A die Anfangsamplitude und α eine positive Konstante ist. Aufgrund ihrer einzigartigen Eigenschaften und Verhaltensweisen sind diese Sequenzen für die Analyse verschiedener Signalverarbeitungsanwendungen von grundlegender Bedeutung.

Grundlegende diskrete Zeitsignale

Die Schrittfolge der Einheit wird als 1 für Null und positive Werte der ganzen Zahl 'n' ausgedrückt. Dies kann anhand eines Sets von acht ...

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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 cumulative sum of the unit impulse sequence. A graph can show how the impulse samples the signal value at n = 0.

The unit ramp sequence increases linearly as the sample number increases. For example, a 12-sample ramp rises by the same amount at each sample, so its graph appears as a straight line. This makes the ramp easy to recognize on a plot.

A sinusoidal sequence is set by its amplitude and phase. In the expression for this sequence, A is the amplitude, ω is the angular frequency, and Φ is the phase. An exponential sequence uses complex numbers. It can describe both exponentially decaying and exponentially increasing sequences. The decaying form and the increasing form are both shown on graphs, with A as the initial amplitude and α as a positive constant. These basic sequences are important because they help describe many signal-processing applications.

Discrete-Time Signal Basics and Shapes

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basic discrete time signals

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...

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Discrete-Time Signal Basics and Shapes

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