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Time and Frequency Domain Analysis

System responses such as Bode plots and step responses; system characteristics such as response time and overshoot; simulation

Time-domain and frequency-domain analysis commands let you compute and visualize SISO and MIMO system responses such as Bode plots, Nichols plots, step responses, and impulse responses. You can also extract system characteristics such as rise time and settling time, overshoot, and stability margins. Most linear analysis commands can either return response data or generate response plots. To get started with plotting commands, see Plotting System Responses. To create plots whose properties are customizable at the command line, see Plot Customization.


Linear System AnalyzerAnalyze time and frequency responses of linear time-invariant (LTI) systems


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stepStep response plot of dynamic system; step response data
stepinfoRise time, settling time, and other step-response characteristics
impulseImpulse response plot of dynamic system; impulse response data
initialInitial condition response of state-space model
lsimPlot simulated time response of dynamic system to arbitrary inputs; simulated response data
lsiminfoCompute linear response characteristics
gensigCreate periodic signals for simulating system response with lsim
covarOutput and state covariance of system driven by white noise
stepDataOptionsOptions for the step command
bodeBode plot of frequency response, or magnitude and phase data
bodemag Magnitude-only Bode plot of frequency response
nyquistNyquist plot of frequency response
nicholsNichols chart of frequency response
ngridSuperimpose Nichols chart on Nichols plot
sigmaSingular value plot of dynamic system
freqrespFrequency response over grid
evalfrEvaluate frequency response at given frequency
dcgainLow-frequency (DC) gain of LTI system
bandwidthFrequency response bandwidth
getPeakGainPeak gain of dynamic system frequency response
getGainCrossoverCrossover frequencies for specified gain
fnormPointwise peak gain of FRD model
normNorm of linear model
db2magConvert decibels (dB) to magnitude
mag2dbConvert magnitude to decibels (dB)


LTI SystemUse linear time invariant system model object in Simulink
LPV SystemSimulate Linear Parameter-Varying (LPV) systems


Analysis Plots Basics

Plotting System Responses

This example shows an overview of commands for generating time-domain and frequency-domain response plots.

Time-Domain Analysis

Time-Domain Responses

Generate and visualize time-response data such as step response and impulse response.

Time-Domain Characteristics on Response Plots

Visualize time-domain system characteristics such as settling time and overshoot on response plots.

Numeric Values of Time-Domain System Characteristics

Use the stepinfo function to obtain numeric values of step response characteristics such as rise time, settling time, and overshoot.

Response from Initial Conditions

Compute and plot the response of a state-space (ss) model to specified initial state values.

Simulate Models with Arbitrary Inputs and Initial Conditions

Use the Linear Simulation Tool to simulate system responses to arbitrary input signals and initial conditions.

Import LTI Model Objects into Simulink

Use the LTI System block to import linear system model objects into Simulink®.

Frequency-Domain Analysis

Frequency-Domain Responses

Generate and visualize frequency-response data such as Bode plots and Nichols plots.

Frequency-Domain Characteristics on Response Plots

Visualize frequency-domain system characteristics such as peak response on plots.

Numeric Values of Frequency-Domain Characteristics of SISO Model

Obtain numeric values of frequency-domain characteristics such as peak gain, dc gain, and system bandwidth.

Linear System Analyzer

Joint Time-Domain and Frequency-Domain Analysis

Compare multiple types of responses side by side, including both time-domain and frequency-domain responses, using the Linear System Analyzer app.

Linear Analysis Using the Linear System Analyzer

Analyze the time-domain and frequency-domain responses of one or more linear models using the Linear System Analyzer app.

Analyzing MIMO Models

In analysis plots of multiple-input, multiple output LTI models, there are plot tools for selecting subsystems and grouping I/O pairs.

Systems with Time Delays

Analysis of Systems with Time Delays

The time and frequency responses of delay systems can have features that can look odd to those only familiar with delay-free LTI analysis.

Analyzing Control Systems with Delays

Many processes involve dead times, also referred to as transport delays or time lags. Controlling such processes is challenging because delays cause phase shifts that limit the control bandwidth and affect closed-loop stability.


Analyzing the Response of an RLC Circuit

Analyze the time and frequency responses of a second-order system.