Fourier

(To be removed) Perform Fourier analysis of signal

The Specialized Power Systems library will be removed in R2026a. Use the Simscape™ Electrical™ blocks and functions instead. For more information on updating your models, see Upgrade Specialized Power System Models to use Simscape Electrical Blocks.

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Libraries:
Simscape / Electrical / Specialized Power Systems / Sensors and Measurements

Description

The Fourier block performs a Fourier analysis of the input signal over a running window of one cycle of the fundamental frequency of the signal. The Fourier block can be programmed to calculate the magnitude and phase of the DC component, the fundamental, or any harmonic component of the input signal.

Recall that a signal f(t) can be expressed by a Fourier series of the form

$$f(t)=\frac{a_0}{2}+{\displaystyle \sum _{n=1}^{\infty }{a}_n}\cos (n\omega t)+b_n\sin (n\omega t)$$

where n represents the rank of the harmonics. (n = 1 corresponds to the fundamental component.) The magnitude and phase of the selected harmonic component are calculated by these equations:

$$\left|H_n\right|=\sqrt{a_n^2+b_n^2}$$

$$\angle H_n=\text{atan}\left(\frac{a_n}{b_n}\right)$$

where

$$a_n=\frac{2}{T}{\displaystyle \underset{t-T}{\overset{t}{\int }}f(t)}\cos (n\omega t)dt$$

$$b_n=\frac{2}{T}{\displaystyle \underset{t-T}{\overset{t}{\int }}f(t)}\sin (n\omega t)dt$$

$$T=\frac{1}{f_1}$$

$$f_1:\text{Fundamental frequency}$$

As this block uses a running average window, one cycle of simulation must complete before the outputs give the correct magnitude and angle. For the first cycle of simulation, the outputs are held to the values specified by the initial input parameter.

Characteristics

Sample Time	Specified in the Sample Time parameter. Continuous if Sample Time = 0.
Scalar Expansion	Yes, of the parameters.
Dimensionalized	Yes.

Ports

Input

Input — Signal to analyze

scalar | vector

Signal to analyze. Typical input signals are voltages or currents measured by Current Measurement or Voltage Measurement blocks.

Output

|u| — Magnitude of specified harmonic component

scalar

Magnitude of the specified harmonic component, in the same units as the input signal.

∠u — Phase of specified harmonic component

scalar

Phase, in degrees, of the specified harmonic component.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Fundamental frequency (Hz) — Frequency of fundamental signal

60 (default) | scalar

Fundamental frequency, in hertz, of the input signal.

Harmonic n (0 = DC, 1 = fundamental) — Harmonic component for Fourier analysis

1 (default) | nonnegative scalar

Harmonic component for the Fourier analysis. Enter 0 to analyze the DC component. Enter 1 to analyze the fundamental frequency, or enter a number corresponding to the desired harmonic.

Initial input [ Mag, Phase (degrees) ] — Initial magnitude and phase of output signal

[0, 0] (default) | scalar

Initial magnitude and phase in degrees of the output signal.

Sample time — Block sample time

0 (default) | nonnegative scalar

Sample time of the block, in seconds. Set to 0 to implement a continuous block.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2013a