What Does a Chirp Signal Look Like in FFT and STFT?
When learning signal processing, one of the most confusing parts is understanding how a signal behaves across different domains.
You might hear terms like
But what do they actually look like?
In this article, weโll use a simple exampleโa chirp signalโto see how the same signal appears in different ways. The goal is not to go deep into theory, but to build an intuitive understanding by looking at real visual results.
What Is a Chirp Signal?
A chirp signal is a signal whose frequency changes over time.
There are two common types
Because the frequency is constantly changing, chirp signals are a great way to understand how different analysis methods behave.
Time Domain: How the Signal Changes Over Time
Increasing chirp signal where frequency rises over time (up-chirp)
At the beginning, the waveform is relatively slow and smooth. As time goes on, the oscillations become faster and denser.
This simply means that the frequency in signal is increasing.
Decreasing chirp signal where frequency drops over time (down-chirp)
Here, the behavior is reversed.
The signal starts with very rapid oscillations (high frequency), and gradually becomes slower as time progresses.
FFT: What Frequencies Exist, But Not When
Now letโs look at the FFT result of these signals.
FFT result showing frequency components spread across the full range (refer to Samples/chirp spectrogram.mmj)
The FFT shows that the signal contains a wide range of frequenciesโfrom low to high.
But there is an important limitation here.
The FFT tells us "What frequencies exist in the signal".
But it does not tell us "When those frequencies occur".
So even though the signal clearly changes over time, the FFT compresses everything into a single frequency representation. Therefore we can't distinguish up and down chirp by FFT itself!
STFT: Seeing Frequency Changes Over Time
To understand how frequency evolves, we need a different approach.
STFT spectrogram showing frequency increasing over time (refer to Samples/chirp spectrogram.mmj)
In this plot, time is on the horizontal axis and frequency is on the vertical axis.
You can see a bright diagonal line moving upward.
This means
Exactly what we expected from the signal.
STFT spectrogram showing frequency decreasing over time (refer to Samples/chrip spectrogram.mmj)
This time, the diagonal line moves downward.
That tells us
Again, this matches the original signal perfectly.
Why This Comparison Is Useful
By looking at the same signal in three different ways, we can see
The time domain shows how the waveform changes
The FFT shows which frequencies are present
The STFT shows how those frequencies change over time
Each method gives a different perspective, and none of them alone tells the full story.
FFT vs STFT in Practice
A simple way to think about it
Chirp signals are a classic example where STFT provides much more insight.
Conclusions
Chirp signals are simple, but they reveal an important idea in signal processing. Not all signals can be fully understood from a single viewpoint.ย FFT gives you the overall frequency components, but STFT allows you to see how that content evolves over time. If you are just starting out, looking at these kinds of visual comparisons can make a big difference in understanding.
And in practice, having a way to quickly switch between time domain, FFT, and STFT views can make exploring these concepts much more intuitive.
Suggested Further Reading
#You may also find these topics helpful:
What Does a Chirp Signal Look Like in FFT and STFT?
When learning signal processing, one of the most confusing parts is understanding how a signal behaves across different domains.
You might hear terms like
time domain
frequency domain (FFT: Fast Fourier Transform)
time-frequency analysis (STFT: Short-Time Fourier Transform)
But what do they actually look like?
In this article, weโll use a simple exampleโa chirp signalโto see how the same signal appears in different ways. The goal is not to go deep into theory, but to build an intuitive understanding by looking at real visual results.
What Is a Chirp Signal?
A chirp signal is a signal whose frequency changes over time.
There are two common types
Increasing chirp โ frequency goes up over time
Decreasing chirp โ frequency goes down over time
Because the frequency is constantly changing, chirp signals are a great way to understand how different analysis methods behave.
Time Domain: How the Signal Changes Over Time
Increasing chirp signal where frequency rises over time (up-chirp)
At the beginning, the waveform is relatively slow and smooth. As time goes on, the oscillations become faster and denser.
This simply means that the frequency in signal is increasing.
Decreasing chirp signal where frequency drops over time (down-chirp)
Here, the behavior is reversed.
The signal starts with very rapid oscillations (high frequency), and gradually becomes slower as time progresses.
FFT: What Frequencies Exist, But Not When
Now letโs look at the FFT result of these signals.
FFT result showing frequency components spread across the full range (refer to Samples/chirp spectrogram.mmj)
The FFT shows that the signal contains a wide range of frequenciesโfrom low to high.
But there is an important limitation here.
The FFT tells us "What frequencies exist in the signal".
But it does not tell us "When those frequencies occur".
So even though the signal clearly changes over time, the FFT compresses everything into a single frequency representation. Therefore we can't distinguish up and down chirp by FFT itself!
STFT: Seeing Frequency Changes Over Time
To understand how frequency evolves, we need a different approach.
STFT spectrogram showing frequency increasing over time (refer to Samples/chirp spectrogram.mmj)
In this plot, time is on the horizontal axis and frequency is on the vertical axis.
You can see a bright diagonal line moving upward.
This means
low frequencies at the beginning
high frequencies as time goes on
Exactly what we expected from the signal.
STFT spectrogram showing frequency decreasing over time (refer to Samples/chrip spectrogram.mmj)
This time, the diagonal line moves downward.
That tells us
high frequencies at the beginning
lower frequencies later
Again, this matches the original signal perfectly.
Why This Comparison Is Useful
By looking at the same signal in three different ways, we can see
The time domain shows how the waveform changes
The FFT shows which frequencies are present
The STFT shows how those frequencies change over time
Each method gives a different perspective, and none of them alone tells the full story.
FFT vs STFT in Practice
A simple way to think about it
Use FFT when the signal is relatively stable (stationary)
Use STFT when the signal changes over time (non-stationary)
Chirp signals are a classic example where STFT provides much more insight.
Conclusions
Chirp signals are simple, but they reveal an important idea in signal processing. Not all signals can be fully understood from a single viewpoint.ย FFT gives you the overall frequency components, but STFT allows you to see how that content evolves over time. If you are just starting out, looking at these kinds of visual comparisons can make a big difference in understanding.
And in practice, having a way to quickly switch between time domain, FFT, and STFT views can make exploring these concepts much more intuitive.
Suggested Further Reading
#You may also find these topics helpful: