FFT analysis in Simulink - Step-by-Step Execution

Concept Flow - FFT analysis in Simulink

Input Signal

↓

Simulink FFT Block

↓

Compute FFT

↓

Magnitude & Phase Calculation

↓

Display Spectrum

↓

Analyze Frequency Components

The input signal flows into the FFT block, which computes the frequency spectrum. Then magnitude and phase are calculated and displayed for analysis.

Execution Sample

Simulink

1. Input Signal (e.g., sine wave)
2. FFT block computes frequency components
3. Calculate magnitude spectrum
4. Display spectrum on scope

This Simulink model takes a signal, computes its FFT, and shows the frequency spectrum.

Execution Table

Step	Action	Input	Output	Notes
1	Generate input signal	Sine wave at 50 Hz	Signal vector (time domain)	Signal ready for FFT
2	FFT block processes signal	Signal vector	Complex FFT result	Frequency components in complex form
3	Calculate magnitude	Complex FFT result	Magnitude spectrum	Magnitude shows strength of frequencies
4	Display spectrum	Magnitude spectrum	Graph on scope	Visual frequency analysis
5	End	-	-	FFT analysis complete

💡 All steps complete, FFT spectrum displayed for input signal

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
Input Signal	None	Sine wave samples	Sine wave samples	Sine wave samples	Sine wave samples
FFT Result	None	None	Complex frequency data	Complex frequency data	Complex frequency data
Magnitude Spectrum	None	None	None	Magnitude values	Magnitude values

Key Moments - 3 Insights

Why does the FFT output contain complex numbers?

FFT outputs complex numbers because it represents both amplitude and phase of frequency components, as shown in step 2 of the execution table.

Why do we calculate magnitude after FFT?

Magnitude shows the strength of each frequency component, which is easier to interpret than complex values. This is step 3 in the execution table.

What does the displayed spectrum represent?

The displayed spectrum shows how strong each frequency is in the input signal, helping analyze its frequency content (step 4).

Visual Quiz - 3 Questions

Look at the execution table, what is the output of step 2?

A Magnitude spectrum

B Complex FFT result

C Input signal vector

D Graph on scope

💡 Hint

Check the 'Output' column for step 2 in the execution table.

At which step do we convert complex FFT data to magnitude?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look for 'Calculate magnitude' in the 'Action' column of the execution table.

If the input signal frequency changes, which variable in variable_tracker changes after step 1?

A Input Signal

B Magnitude Spectrum

C FFT Result

D None

💡 Hint

Check the 'Input Signal' row values after step 1 in variable_tracker.

Concept Snapshot

FFT analysis in Simulink:
- Input signal flows into FFT block
- FFT computes complex frequency data
- Magnitude spectrum calculated from FFT
- Spectrum displayed for frequency analysis
- Helps identify signal frequency components

Full Transcript

In Simulink, FFT analysis starts with an input signal, such as a sine wave. The signal is fed into the FFT block, which computes the frequency components as complex numbers. Next, the magnitude of these components is calculated to show the strength of each frequency. Finally, the magnitude spectrum is displayed on a scope for visual analysis. This process helps understand the frequencies present in the signal.

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