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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 of dynamic system
stepinfoRise time, settling time, and other step-response characteristics
impulseImpulse response plot of dynamic system; impulse response data
initialSystem response to initial states 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
RespConfigOptions for step or impulse responses (Since R2023a)
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
freqrespEvaluate system response over a grid of frequencies
evalfrEvaluate system response at specific 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)
getLoopTransferOpen-loop transfer function of control system represented by genss model
getIOTransferClosed-loop transfer function from generalized model of control system
getSensitivitySensitivity function from generalized model of control system
getCompSensitivityComplementary sensitivity function from generalized model of control system

Live Editor Tasks

Create PlotInteractively create linear analysis response plots in the Live Editor (Since R2022b)


LTI SystemUse linear time invariant system model object in Simulink
LPV SystemSimulate linear parameter-varying (LPV) systems


Analysis Plots Basics

Time-Domain Analysis

Frequency-Domain Analysis

Linear System Analyzer

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.