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Why is Fast Fourier Transform applied to raw EEG data?
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Obe Abdulrazaq
Why is Fast Fourier Transform applied to raw EEG data?
Any periodic waveform can be produced by adding up a series of sin waves of the appropriate frequency and amplitude. The FFT looks at a complex waveform and calculates those frequencies and amplitudes. The result is a new curve which plots amplitude vs frequency. Thus, it transforms the signal from the time domain into the frequency domain.
I don't have any knowledge of EEG signals, but have worked with FFTs. If you wanted to know what frequencies make the largest contribution to the original waveform, the FFT will provide that information.
Here is a paper I found which uses FFT analysis of EEG waveforms to look at the relative contributions of different frequencies. It includes the following table which indicates that "Delta" waves are in the 0.5 to 4 Hz range, Theta waves are in the 4 - 8 Hz range, etc. The FFT analysis quickly breaks the overall waveform down into its constituent frequencies to identify which of these ranges contribute the most or least.
Any periodic waveform can be produced by adding up a series of sin waves of the appropriate frequency and amplitude. The FFT looks at a complex waveform and calculates those frequencies and amplitudes. The result is a new curve which plots amplitude vs frequency. Thus, it transforms the signal from the time domain into the frequency domain.
I don't have any knowledge of EEG signals, but have worked with FFTs. If you wanted to know what frequencies make the largest contribution to the original waveform, the FFT will provide that information.
Here is a paper I found which uses FFT analysis of EEG waveforms to look at the relative contributions of different frequencies. It includes the following table which indicates that "Delta" waves are in the 0.5 to 4 Hz range, Theta waves are in the 4 - 8 Hz range, etc. The FFT analysis quickly breaks the overall waveform down into its constituent frequencies to identify which of these ranges contribute the most or least.
@smeeb - (2) Sorry, I can't help there as far as the biology goes. FFTs are used in a lot of applications where the particular frequencies are important, including mass spectrometry where the specific frequencies allow gas components to be identified; machine analysis where the individual frequencies can be used to identify defects in couplings or bearings; and audio processing where it can be used to remove noise, or analyze the harmonics of a violin. Often, there is a great deal of information within the frequency spectrumMore
graph of amplitude over frequency? Meaning, the original waveform was a single graph of voltage/time: do we now have five graphs of amplitude/frequency, 1 for each rhythm? And More
Fast-Fourier Transform (FFT) transforms a signal from the time domain into the frequency domain. Basically, any time-dependent signal can be broken down in a collection of sinusoids. In this way, lengthy and noisy EEG recordings can be conveniently plotted in a frequency power-spectrum. By doing so, hidden features can become apparent. By adding all the sinusoids up after FFT, the original signal can be restored, so no information is lost.
A notable application of FFT in EEG is shown in Fig. 1, which shows an EEG in an awake person (top blue trace) and an EEG in a propofol-sedated person (bottom red trace). The traces are different, but exactly how different? Scientists like to quantify stuff.
Now look in Fig. 2, which shows the same data but filtered in the delta band (low-pass filtered EEG with a cut-off frequency of 1.5 Hz, left panel). Here it already becomes more apparent what's going on, but what exactly is the difference between the two traces? That difference becomes readily apparent in the frequency domain by using FFT (Fig. 2, right panel); The frequency spectrum has a peak at 0.2 Hz in both traces, but that peak is about twice as big in the anesthetized state than in the normal state. In other words, the anesthetized brain reveals more low-frequency activity.
Fig. 1. Raw EEG of an awake person (blue) and propofol-anesthetized person (red). source: Wang et al (2014).
Fig. 2. Filtered EEGs (<1.5 Hz) of an awake person (blue) and propofol-anesthetized person (red) (left panel) and corresponding FFT spectra (right). source: Wang et al (2014).
This is reminiscent of the drowsiness encountered in slow-wave sleep; which is yet another example of why FFT is useful; various stages of sleep are markedly different in their EEG. For example, early stages of sleep are characterized by slow-wave EEG, while REM sleep is characterized by high-frequency EEG activity. By using FFT, these differences in frequency content can be captured in simple, quantifiable data.
Another widely applied FFT-based application is filtering in the frequency domain. Look at the sleep EEG in Fig. 3. By splitting the raw signal up in frequency bands, the noise can be removed (high-frequency components), but even better, the k-complex (a characteristic hallmark of normal sleep) can be beautifully isolated from a messy EEG signal (bottom trace, 12-15 Hz).
Fast-Fourier Transform (FFT) transforms a signal from the time domain into the frequency domain. Basically, any time-dependent signal can be broken down in a collection of sinusoids. In this way, lengthy and noisy EEG recordings can be conveniently plotted in a frequency power-spectrum. By doing so, hidden features can become apparent. By adding all the sinusoids up after FFT, the original signal can be restored, so no information is lost.
A notable application of FFT in EEG is shown in Fig. 1, which shows an EEG in an awake person (top blue trace) and an EEG in a propofol-sedated person (bottom red trace). The traces are different, but exactly how different? Scientists like to quantify stuff.
Now look in Fig. 2, which shows the same data but filtered in the delta band (low-pass filtered EEG with a cut-off frequency of 1.5 Hz, left panel). Here it already becomes more apparent what's going on, but what exactly is the difference between the two traces? That difference becomes readily apparent in the frequency domain by using FFT (Fig. 2, right panel); The frequency spectrum has a peak at 0.2 Hz in both traces, but that peak is about twice as big in the anesthetized state than in the normal state. In other words, the anesthetized brain reveals more low-frequency activity.
Fig. 1. Raw EEG of an awake person (blue) and propofol-anesthetized person (red). source: Wang et al (2014).
Fig. 2. Filtered EEGs (<1.5 Hz) of an awake person (blue) and propofol-anesthetized person (red) (left panel) and corresponding FFT spectra (right). source: Wang et al (2014).
This is reminiscent of the drowsiness encountered in slow-wave sleep; which is yet another example of why FFT is useful; various stages of sleep are markedly different in their EEG. For example, early stages of sleep are characterized by slow-wave EEG, while REM sleep is characterized by high-frequency EEG activity. By using FFT, these differences in frequency content can be captured in simple, quantifiable data.
Another widely applied FFT-based application is filtering in the frequency domain. Look at the sleep EEG in Fig. 3. By splitting the raw signal up in frequency bands, the noise can be removed (high-frequency components), but even better, the k-complex (a characteristic hallmark of normal sleep) can be beautifully isolated from a messy EEG signal (bottom trace, 12-15 Hz).
A few followup questions if you don't mind: (1) my understanding of the processing flow was: Capture Raw EEG Data -> Perform FFT -> Analyze Component Frequencies (Alpha, Delta, etc.). But it sounds like you are saying that the typical "flow" is: Capture Raw EEG Data -> Filter by a Particular Frequency -> Perform FFT on that Frequency -> Analyze the Frequency. More
Any periodic waveform can be produced by adding up a series of sin waves of the appropriate frequency and amplitude. The FFT looks at a complex waveform and calculates those frequencies and amplitudes. The result is a new curve which plots amplitude vs frequency. Thus, it transforms the signal from the time domain into the frequency domain.
I don't have any knowledge of EEG signals, but have worked with FFTs. If you wanted to know what frequencies make the largest contribution to the original waveform, the FFT will provide that information.
Here is a paper I found which uses FFT analysis of EEG waveforms to look at the relative contributions of different frequencies. It includes the following table which indicates that "Delta" waves are in the 0.5 to 4 Hz range, Theta waves are in the 4 - 8 Hz range, etc. The FFT analysis quickly breaks the overall waveform down into its constituent frequencies to identify which of these ranges contribute the most or least.
Any periodic waveform can be produced by adding up a series of sin waves of the appropriate frequency and amplitude. The FFT looks at a complex waveform and calculates those frequencies and amplitudes. The result is a new curve which plots amplitude vs frequency. Thus, it transforms the signal from the time domain into the frequency domain.
I don't have any knowledge of EEG signals, but have worked with FFTs. If you wanted to know what frequencies make the largest contribution to the original waveform, the FFT will provide that information.
Here is a paper I found which uses FFT analysis of EEG waveforms to look at the relative contributions of different frequencies. It includes the following table which indicates that "Delta" waves are in the 0.5 to 4 Hz range, Theta waves are in the 4 - 8 Hz range, etc. The FFT analysis quickly breaks the overall waveform down into its constituent frequencies to identify which of these ranges contribute the most or least.
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Fast-Fourier Transform (FFT) transforms a signal from the time domain into the frequency domain. Basically, any time-dependent signal can be broken down in a collection of sinusoids. In this way, lengthy and noisy EEG recordings can be conveniently plotted in a frequency power-spectrum. By doing so, hidden features can become apparent. By adding all the sinusoids up after FFT, the original signal can be restored, so no information is lost.
A notable application of FFT in EEG is shown in Fig. 1, which shows an EEG in an awake person (top blue trace) and an EEG in a propofol-sedated person (bottom red trace). The traces are different, but exactly how different? Scientists like to quantify stuff.
Now look in Fig. 2, which shows the same data but filtered in the delta band (low-pass filtered EEG with a cut-off frequency of 1.5 Hz, left panel). Here it already becomes more apparent what's going on, but what exactly is the difference between the two traces? That difference becomes readily apparent in the frequency domain by using FFT (Fig. 2, right panel); The frequency spectrum has a peak at 0.2 Hz in both traces, but that peak is about twice as big in the anesthetized state than in the normal state. In other words, the anesthetized brain reveals more low-frequency activity.
Fig. 1. Raw EEG of an awake person (blue) and propofol-anesthetized person (red). source: Wang et al (2014).
Fig. 2. Filtered EEGs (<1.5 Hz) of an awake person (blue) and propofol-anesthetized person (red) (left panel) and corresponding FFT spectra (right). source: Wang et al (2014).
This is reminiscent of the drowsiness encountered in slow-wave sleep; which is yet another example of why FFT is useful; various stages of sleep are markedly different in their EEG. For example, early stages of sleep are characterized by slow-wave EEG, while REM sleep is characterized by high-frequency EEG activity. By using FFT, these differences in frequency content can be captured in simple, quantifiable data.
Another widely applied FFT-based application is filtering in the frequency domain. Look at the sleep EEG in Fig. 3. By splitting the raw signal up in frequency bands, the noise can be removed (high-frequency components), but even better, the k-complex (a characteristic hallmark of normal sleep) can be beautifully isolated from a messy EEG signal (bottom trace, 12-15 Hz).
Fig. 3. EEG FFT-based filtering. source: Neurology
Reference
- Wang et al., Front Syst Neurosci (2014); 00215
Fast-Fourier Transform (FFT) transforms a signal from the time domain into the frequency domain. Basically, any time-dependent signal can be broken down in a collection of sinusoids. In this way, lengthy and noisy EEG recordings can be conveniently plotted in a frequency power-spectrum. By doing so, hidden features can become apparent. By adding all the sinusoids up after FFT, the original signal can be restored, so no information is lost.
A notable application of FFT in EEG is shown in Fig. 1, which shows an EEG in an awake person (top blue trace) and an EEG in a propofol-sedated person (bottom red trace). The traces are different, but exactly how different? Scientists like to quantify stuff.
Now look in Fig. 2, which shows the same data but filtered in the delta band (low-pass filtered EEG with a cut-off frequency of 1.5 Hz, left panel). Here it already becomes more apparent what's going on, but what exactly is the difference between the two traces? That difference becomes readily apparent in the frequency domain by using FFT (Fig. 2, right panel); The frequency spectrum has a peak at 0.2 Hz in both traces, but that peak is about twice as big in the anesthetized state than in the normal state. In other words, the anesthetized brain reveals more low-frequency activity.
Fig. 1. Raw EEG of an awake person (blue) and propofol-anesthetized person (red). source: Wang et al (2014).
Fig. 2. Filtered EEGs (<1.5 Hz) of an awake person (blue) and propofol-anesthetized person (red) (left panel) and corresponding FFT spectra (right). source: Wang et al (2014).
This is reminiscent of the drowsiness encountered in slow-wave sleep; which is yet another example of why FFT is useful; various stages of sleep are markedly different in their EEG. For example, early stages of sleep are characterized by slow-wave EEG, while REM sleep is characterized by high-frequency EEG activity. By using FFT, these differences in frequency content can be captured in simple, quantifiable data.
Another widely applied FFT-based application is filtering in the frequency domain. Look at the sleep EEG in Fig. 3. By splitting the raw signal up in frequency bands, the noise can be removed (high-frequency components), but even better, the k-complex (a characteristic hallmark of normal sleep) can be beautifully isolated from a messy EEG signal (bottom trace, 12-15 Hz).
Fig. 3. EEG FFT-based filtering. source: Neurology
Reference
- Wang et al., Front Syst Neurosci (2014); 00215
More
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