FFT analysis in Simulink

Introduction

FFT analysis helps you see the different frequencies inside a signal. It turns a signal from time view into frequency view.

To find the main tones in a sound recording.

To check vibrations in a machine for maintenance.

To analyze electrical signals in circuits.

To study heartbeats or brain waves in health data.

Syntax

Simulink

1. Open Simulink and create a new model.
2. Add a Signal Generator block to create a test signal.
3. Add an FFT block from the DSP System Toolbox.
4. Connect the Signal Generator output to the FFT input.
5. Add a Spectrum Analyzer block to view the FFT result.
6. Run the simulation to see the frequency spectrum.

The FFT block computes the Fast Fourier Transform of the input signal.

The Spectrum Analyzer shows the frequency content graphically during simulation.

Examples

This setup shows the frequency of a simple sine wave.

Simulink

Signal Generator (sine wave) -> FFT block -> Spectrum Analyzer

This shows multiple frequencies in one signal.

Simulink

Signal Generator (sum of sine waves) -> FFT block -> Spectrum Analyzer

Sample Program

This example creates a simple sine wave and uses FFT to find its frequency. The Spectrum Analyzer shows a clear peak at 50 Hz, confirming the signal's frequency.

Simulink

1. Open Simulink and create a new model.
2. Add a Signal Generator block and set it to produce a sine wave at 50 Hz.
3. Add an FFT block from DSP System Toolbox.
4. Connect Signal Generator output to FFT input.
5. Add a Spectrum Analyzer block and connect FFT output to it.
6. Run the simulation for 1 second.

# After running, the Spectrum Analyzer will display a peak at 50 Hz, showing the frequency of the sine wave.

Important Notes

Make sure the simulation time is long enough to get a clear frequency result.

FFT works best with signals sampled at a constant rate.

You can adjust FFT block parameters like window size for better accuracy.

Summary

FFT analysis converts signals from time to frequency view.

Simulink uses blocks like Signal Generator, FFT, and Spectrum Analyzer for this.

It helps find frequencies inside signals easily during simulation.

Practice

1. What is the main purpose of using FFT analysis in Simulink?

easy

A. To filter out noise from a signal

B. To generate random signals for simulation

C. To display signals only in the time domain

D. To convert a signal from time domain to frequency domain

Solution

1. Step 1: Understand FFT function

   FFT (Fast Fourier Transform) changes signals from time view to frequency view.

2. Step 2: Identify Simulink FFT usage

   Simulink uses FFT blocks to analyze frequency components inside signals.

3. Final Answer:

   To convert a signal from time domain to frequency domain -> Option D

4. Quick Check:

   FFT = Time to Frequency [OK]

Hint: FFT always changes time signals to frequency signals [OK]

Common Mistakes:

• Confusing FFT with signal generation
• Thinking FFT filters noise directly
• Assuming FFT shows only time domain

2. Which Simulink block is used to generate a test signal for FFT analysis?

easy

A. Signal Generator

B. Spectrum Scope

C. FFT

D. Gain

Solution

1. Step 1: Identify signal source blocks

   Signal Generator block creates test signals like sine waves for simulation.

2. Step 2: Match block to purpose

   FFT block analyzes signals, Spectrum Scope displays frequency, Gain changes amplitude.

3. Final Answer:

   Signal Generator -> Option A

4. Quick Check:

   Signal Generator = Test signal source [OK]

Hint: Signal Generator creates signals; FFT analyzes them [OK]

Common Mistakes:

• Choosing FFT as signal source
• Confusing Spectrum Scope with signal creation
• Selecting Gain block incorrectly

3. Given this Simulink setup: a sine wave at 50 Hz connected to an FFT block, what frequency peak will the Spectrum Scope show?

medium

A. 0 Hz

B. 100 Hz

C. 50 Hz

D. No peak

Solution

1. Step 1: Understand input signal frequency

   The sine wave frequency is 50 Hz, so the main frequency component is at 50 Hz.

2. Step 2: Analyze FFT output

   FFT shows peaks at frequencies present in the input; here, a peak at 50 Hz appears.

3. Final Answer:

   50 Hz -> Option C

4. Quick Check:

   Sine wave frequency = FFT peak frequency [OK]

Hint: FFT peak matches input sine wave frequency [OK]

Common Mistakes:

• Choosing 0 Hz as peak frequency
• Doubling frequency to 100 Hz incorrectly
• Expecting no peak from sine wave

4. You connected a Signal Generator to an FFT block but see no frequency peaks in Spectrum Scope. What is the likely error?

medium

A. Signal Generator frequency set to 0 Hz

B. FFT block not connected to Signal Generator output

C. Spectrum Scope block missing

D. Signal Generator amplitude set too high

Solution

1. Step 1: Check signal flow connections

   FFT block must be connected to the Signal Generator output to analyze the signal.

2. Step 2: Identify cause of no peaks

   No connection means FFT receives no input, so no frequency peaks appear.

3. Final Answer:

   FFT block not connected to Signal Generator output -> Option B

4. Quick Check:

   Connection missing = no FFT input [OK]

Hint: Always connect blocks properly to see FFT results [OK]

Common Mistakes:

• Assuming zero frequency causes no peaks
• Thinking Spectrum Scope absence causes no peaks
• Blaming amplitude for missing peaks

5. You want to analyze a signal composed of two sine waves at 30 Hz and 70 Hz in Simulink. Which setup will correctly show both frequencies in the FFT output?

hard

A. Use two Signal Generators summed together, connected to FFT block

B. Use one Signal Generator set to 100 Hz connected to FFT block

C. Use one Signal Generator at 30 Hz connected to Spectrum Scope only

D. Use two FFT blocks connected separately to Signal Generators at 30 Hz and 70 Hz

Solution

1. Step 1: Combine signals for FFT input

   Summing two Signal Generators (30 Hz and 70 Hz) creates a combined signal with both frequencies.

2. Step 2: Connect combined signal to FFT block

   FFT block analyzes combined input and shows peaks at both 30 Hz and 70 Hz.

3. Step 3: Evaluate other options

   Single frequency or separate FFT blocks won't show both frequencies together in one spectrum.

4. Final Answer:

   Use two Signal Generators summed together, connected to FFT block -> Option A

5. Quick Check:

   Sum signals before FFT to see all frequencies [OK]

Hint: Sum signals before FFT to capture all frequencies [OK]

Common Mistakes:

• Using one generator at wrong frequency
• Connecting FFT blocks separately without summing
• Not summing signals before FFT