# 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.

## Apps

Linear System Analyzer | Analyze time and frequency responses of linear time-invariant (LTI) systems |

## Functions

## Live Editor Tasks

Create Plot | Interactively create linear analysis response plots in the Live Editor (Since R2022b) |

## Blocks

LTI System | Use linear time invariant system model object in Simulink |

LPV System | Simulate linear parameter-varying (LPV) systems |

## Topics

### Analysis Plots Basics

**Plotting System Responses**

This example shows an overview of 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^{®}.**Use Linearization Offsets to Help Compare Nonlinear and Linearized Responses**

Use offsets from linearization to facilitate the comparison of the nonlinear and linearized responses of a Simulink model.*(Since R2024a)*

### 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.

### Applications

**Analyzing the Response of an RLC Circuit**

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