System Identification Methods Explained: Impulse vs Swept Sine vs White Noise (FRF Comparison)
System identification is one of the most fundamental tasks in signal processing and engineering.
Whether you're analyzing a mechanical structure, an acoustic system, or an electronic filter,
you need a reliable way to understand how a system responds to inputs.
In this article, we compare three widely used excitation signals
- Impulses
- Swept sine (chirp)
- White noise
And more importantly
Do two systems produce the same Frequency Response Function (FRF)?
Using MALMIJAL, we will explore how different input signals affect system identification results.
Why Input Signal Matters
At first glance, it might seem that
โAs long as I measure input and output, I should get the same FRF.โ
But in reality
- Noise sensitivity
- Frequency coverage
- Energy distribution
all influence the accuracy of your result.
Input Signals in MALMIJAL
Below are the three input signals used in this example.
Impulse, swept sine, and white noise signals generated for system identification (refer to Samples/system IDs.mmj)
Impulses
- Extremely short signal
- Contains all frequencies theoretically
- Fast measurement
But
- Low energy โ noise-sensitive
ย
Swept Sine (Chirp)
- Frequency(Hz) increases over time
- High energy per frequency
Advantages
- Excellent signal-to-noise ratio
- Very accurate FRF
White Noise
- Random signal
- Equal energy across frequencies
Advantages
- Good statistical averaging
- Suitable for real-time analysis
System Response with Different Inputs
Now let's pass each signal through the same system (filter).
Filter output responses for impulse, swept sine, and white noise inputs (refer to Samples/system IDs.mmj)
Key Observation
- Impulse โ sharp response, short duration
- Swept sine โ structured response
- White noise โ highly random output
Completely different in time domain
Frequency Response Function (FRF) Comparison
Now comes the most important part.
FRF comparison of impulse, swept sine, and white noise inputs (refer to Samples/system IDs.mmj)
Check magnitude-squared coherences for the reliability of FRF (refer to Samples/system IDs.mmj)
Key Insight
Despite very different input signals, the resulting FRFs are almost identical
Why?
Because FRF is defined as
As long as
- Input excites all frequencies
- Measurement is accurate
The system response is invariant.
When Results Differ
In real-world scenarios, differences can appear
| Situation | Best Signal |
|---|
| Noisy environment | Swept sine |
| Fast measurement | Impulses |
| Continuous monitoring | White noise |
Practical Engineering Insight
Impulses
- Fast
- Simple
- But noise-sensitive and hard to realize ideal impulse
Swept sine
White noise
- Flexible
- Good for averaging
Why This Matters
Choosing the wrong excitation signal can lead to
- Poor FRF estimation
- Misleading system characteristics
- Wrong engineering decisions
MALMIJAL Advantage
With MALMIJAL, you can
- Generate multiple excitation signals instantly
- Compare system responses side-by-side
- Compute FRF in a single workflow
- Compute coherence whether FRF measurements are reliable
Making system identification intuitive and fast
Conclusions
Even though impulse, swept sine, and white noise look completely different.
They can produce the same system characteristics โ if used correctly.
However, the choice of input signal directly impacts accuracy, robustness, and usability.
Suggested Further Reading
You may also find these topics helpful:ย
System Identification Methods Explained: Impulse vs Swept Sine vs White Noise (FRF Comparison)
System identification is one of the most fundamental tasks in signal processing and engineering.
Whether you're analyzing a mechanical structure, an acoustic system, or an electronic filter,
you need a reliable way to understand how a system responds to inputs.
In this article, we compare three widely used excitation signals
And more importantly
Using MALMIJAL, we will explore how different input signals affect system identification results.
Why Input Signal Matters
At first glance, it might seem that
But in reality
all influence the accuracy of your result.
Input Signals in MALMIJAL
Below are the three input signals used in this example.
Impulses
But
ย
Swept Sine (Chirp)
Advantages
White Noise
Advantages
System Response with Different Inputs
Now let's pass each signal through the same system (filter).
Filter output responses for impulse, swept sine, and white noise inputs (refer to Samples/system IDs.mmj)
Key Observation
Completely different in time domain
Frequency Response Function (FRF) Comparison
Now comes the most important part.
Key Insight
Despite very different input signals, the resulting FRFs are almost identical
Why?
Because FRF is defined as
As long as
The system response is invariant.
When Results Differ
In real-world scenarios, differences can appear
Practical Engineering Insight
Impulses
Swept sine
White noise
Why This Matters
Choosing the wrong excitation signal can lead to
MALMIJAL Advantage
With MALMIJAL, you can
Making system identification intuitive and fast
Conclusions
Even though impulse, swept sine, and white noise look completely different.
They can produce the same system characteristics โ if used correctly.
However, the choice of input signal directly impacts accuracy, robustness, and usability.
Suggested Further Reading
You may also find these topics helpful:ย