I asked: "can FFT accurately analyze transient non linear signals? "
ChatGPT answered: "
Fast Fourier Transform (FFT) is a technique that is commonly used to analyze and understand the frequency content of signals. In general, FFT can accurately analyze periodic or stationary signals, which have a constant frequency content over time. However, when applied to transient or nonlinear signals, FFT may not provide accurate results.
Transient signals are signals that change rapidly over a short period of time and they can be aperiodic or non-stationary, meaning that the frequency content of the signal is not constant over time. These types of signals have a time-varying frequency content, which makes them challenging to analyze with FFT.
Nonlinear signals are signals that have a non-linear relationship between the input and output, and they may produce harmonics and intermodulation products (IMD) that are not present in the input signal. These signals also have a time-varying frequency content, and their frequency content is not constant over time.
FFT assumes that the signal is periodic and linear, so it may not accurately represent the frequency content of transient or nonlinear signals. There are different techniques that can be used to analyze transient or nonlinear signals such as wavelet transform, Hilbert-Huang transform, and Empirical Mode Decomposition which can provide better results than FFT in certain scenarios.
In summary, FFT is well suited for analyzing periodic or stationary signals, but it may not provide accurate results when applied to transient or nonlinear signals. Other techniques such as wavelet transform, Hilbert-Huang transform, and Empirical Mode Decomposition can be used to analyze transient or nonlinear signals."
Me: "Does musical instruments like drums and bass guitar mainly create periodic or stationary signals, which have a constant frequency content over time or do they create transient and non linear signals?"
ChatGPT: "
Musical instruments like drums and bass guitar can create both periodic and transient signals, depending on how they are played.
Drums, for example, typically produce transient signals when they are struck, as the impact of the drumstick on the drumhead creates a sharp, sudden pressure change that decays rapidly over time. The sound of the drum may also contain some harmonic content, due to the non-linearity of the drumhead.
Bass guitar, on the other hand, can produce both periodic and transient signals. When playing a sustained note, the sound produced by the bass guitar is likely to be periodic and have a relatively constant frequency content over time. However, when playing percussive or staccato notes, the sound produced by the bass guitar may be more transient in nature.
In general, it can be said that most musical instruments produce both periodic and transient signals to some degree, depending on how they are played. The periodic or stationary signals are the fundamental frequency and its harmonics, while the transient signals are usually the result of the attack and decay of the sound. The non-linearity of the instrument and the way it is played can also produce harmonics that were not present in the input signal, and therefore the signal is not linear.
In summary, musical instruments like drums and bass guitar can create both periodic and transient signals, depending on how they are played. The periodic or stationary signals are the fundamental frequency and its harmonics, while the transient signals are usually the result of the attack and decay of the sound, and non-linearity can also produce harmonics that were not present in the input signal."
Me: "is FFT suitable to analyze the sound generated by drums and bass guitar?
ChatGPT: "
Fast Fourier Transform (FFT) is a technique that is commonly used to analyze and understand the frequency content of signals, and it can be used to analyze the sound generated by drums and bass guitar. However, the results obtained from FFT may not be entirely accurate for transient signals or for signals that have a non-linear relationship between the input and output.
For example, when analyzing the sound of a drum, FFT can be used to determine the fundamental frequency and the harmonic content of the sound, but it may not provide an accurate representation of the transient impact of the drumstick on the drumhead. In this case, other techniques such as the wavelet transform or the Hilbert-Huang transform may be more suitable to analyze the transient nature of the sound.
When analyzing the sound of a bass guitar, FFT can be used to determine the fundamental frequency and the harmonic content of the sound, especially when playing sustained notes. However, when playing percussive or staccato notes, the transient nature of the sound may be more dominant and FFT may not provide an accurate representation of the sound.
In general, FFT can be a useful tool for analyzing the frequency content of a sound, but it may not be entirely suitable for analyzing transient or non-linear signals. In these cases, other techniques such as the wavelet transform or the Hilbert-Huang transform may be more appropriate. Additionally, the results obtained from FFT should be interpreted with caution, especially when analyzing transient or non-linear signals, as they may not be entirely accurate."
ChatGPT's assertion that other techniques, beyond FFT, may be more suitable for analyzing transient or non-linear signals in music, challenges the notion that FFT is the ultimate and only means of signal analysis, and suggests a departure from the simplified understanding that music can be reduced solely to combinations of sine waves. 😉
As in the name of this forum htread.... ChatGPT is a simple and dumb FFT-denier....
ChatGPT answered: "
Fast Fourier Transform (FFT) is a technique that is commonly used to analyze and understand the frequency content of signals. In general, FFT can accurately analyze periodic or stationary signals, which have a constant frequency content over time. However, when applied to transient or nonlinear signals, FFT may not provide accurate results.
Transient signals are signals that change rapidly over a short period of time and they can be aperiodic or non-stationary, meaning that the frequency content of the signal is not constant over time. These types of signals have a time-varying frequency content, which makes them challenging to analyze with FFT.
Nonlinear signals are signals that have a non-linear relationship between the input and output, and they may produce harmonics and intermodulation products (IMD) that are not present in the input signal. These signals also have a time-varying frequency content, and their frequency content is not constant over time.
FFT assumes that the signal is periodic and linear, so it may not accurately represent the frequency content of transient or nonlinear signals. There are different techniques that can be used to analyze transient or nonlinear signals such as wavelet transform, Hilbert-Huang transform, and Empirical Mode Decomposition which can provide better results than FFT in certain scenarios.
In summary, FFT is well suited for analyzing periodic or stationary signals, but it may not provide accurate results when applied to transient or nonlinear signals. Other techniques such as wavelet transform, Hilbert-Huang transform, and Empirical Mode Decomposition can be used to analyze transient or nonlinear signals."
Me: "Does musical instruments like drums and bass guitar mainly create periodic or stationary signals, which have a constant frequency content over time or do they create transient and non linear signals?"
ChatGPT: "
Musical instruments like drums and bass guitar can create both periodic and transient signals, depending on how they are played.
Drums, for example, typically produce transient signals when they are struck, as the impact of the drumstick on the drumhead creates a sharp, sudden pressure change that decays rapidly over time. The sound of the drum may also contain some harmonic content, due to the non-linearity of the drumhead.
Bass guitar, on the other hand, can produce both periodic and transient signals. When playing a sustained note, the sound produced by the bass guitar is likely to be periodic and have a relatively constant frequency content over time. However, when playing percussive or staccato notes, the sound produced by the bass guitar may be more transient in nature.
In general, it can be said that most musical instruments produce both periodic and transient signals to some degree, depending on how they are played. The periodic or stationary signals are the fundamental frequency and its harmonics, while the transient signals are usually the result of the attack and decay of the sound. The non-linearity of the instrument and the way it is played can also produce harmonics that were not present in the input signal, and therefore the signal is not linear.
In summary, musical instruments like drums and bass guitar can create both periodic and transient signals, depending on how they are played. The periodic or stationary signals are the fundamental frequency and its harmonics, while the transient signals are usually the result of the attack and decay of the sound, and non-linearity can also produce harmonics that were not present in the input signal."
Me: "is FFT suitable to analyze the sound generated by drums and bass guitar?
ChatGPT: "
Fast Fourier Transform (FFT) is a technique that is commonly used to analyze and understand the frequency content of signals, and it can be used to analyze the sound generated by drums and bass guitar. However, the results obtained from FFT may not be entirely accurate for transient signals or for signals that have a non-linear relationship between the input and output.
For example, when analyzing the sound of a drum, FFT can be used to determine the fundamental frequency and the harmonic content of the sound, but it may not provide an accurate representation of the transient impact of the drumstick on the drumhead. In this case, other techniques such as the wavelet transform or the Hilbert-Huang transform may be more suitable to analyze the transient nature of the sound.
When analyzing the sound of a bass guitar, FFT can be used to determine the fundamental frequency and the harmonic content of the sound, especially when playing sustained notes. However, when playing percussive or staccato notes, the transient nature of the sound may be more dominant and FFT may not provide an accurate representation of the sound.
In general, FFT can be a useful tool for analyzing the frequency content of a sound, but it may not be entirely suitable for analyzing transient or non-linear signals. In these cases, other techniques such as the wavelet transform or the Hilbert-Huang transform may be more appropriate. Additionally, the results obtained from FFT should be interpreted with caution, especially when analyzing transient or non-linear signals, as they may not be entirely accurate."
ChatGPT's assertion that other techniques, beyond FFT, may be more suitable for analyzing transient or non-linear signals in music, challenges the notion that FFT is the ultimate and only means of signal analysis, and suggests a departure from the simplified understanding that music can be reduced solely to combinations of sine waves. 😉
As in the name of this forum htread.... ChatGPT is a simple and dumb FFT-denier....
In this forum, we have had discussions about the limitations of FFT in analyzing transient or non-linear signals in music over the years, and I don't recall ever being referred to as an "FFT-denier" directly. However, it has been implied multiple times. I may not be an engineer, but I have developed my own understanding and ideas based on decades of experience in building, studying and learning. I find that the simplified understanding that music is only composed of simple sine waves, "as proven by FFT", does not align with my own perspective.
ChatGPT does a stellar job of explaining what I have been trying to write in many different threads over the years. This is why I post this here in the subwoofer section.
ChatGPT does a stellar job of explaining what I have been trying to write in many different threads over the years. This is why I post this here in the subwoofer section.
ChatGTP tends to be verbose and hard to read in quantity, but the first sentence is right out of the theory.
dave
dave
I think the bot may be right... If you really want to know what a system impulse response look like, better use an impulse as stimuli and a scope. The difference in the jolt of a real impulse and a long slow sweep is tremendous. The math is undeniable - no question; it's just that it assumes an ideal linear system in order to be correct - or?
A speaker is not ideal...
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A speaker is not ideal...
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I'd say that ChatGPT isn't strict enough here by saying it's "challenging". It's just not possible to FFT an aperiodic signal. The periodicity of the signal is one of the basic assumptions in the FFT.
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Nonetheless, windowed DFTs are used all the time to measure noise and noise-like signals.
I still don't know what a nonlinear signal is supposed to be. A nonlinear system is well defined, but a nonlinear signal?
I still don't know what a nonlinear signal is supposed to be. A nonlinear system is well defined, but a nonlinear signal?
A non-linear and non-sinusoidal signal refers to a signal that cannot be easily represented as a combination of simple sinusoidal waves or described by simple mathematical equations.
Me: "can you give some examples of non-linear and non-sinusoidal acoustic signals?"
ChatGPT: "
Yes, here are a few examples of non-linear and non-sinusoidal acoustic signals:
ChatGPT: "
Yes, here are a few examples of non-linear and non-sinusoidal acoustic signals:
- White noise
- Pink noise
- Brown noise
- Chirps (a signal in which the frequency increases or decreases with time)
- Square waves
- Sawtooth waves
- Impulse signals (a signal that is non-zero for a very short duration and zero otherwise)
- Speech signals (which are often non-linear and non-sinusoidal)
- Non-linear echoes, such as those produced by some echo-location systems
- Sound produced by some musical instruments (e.g. guitar distortion, or the sound of a bowed string instrument)"
Any periodic signal (square, sawtooth, etc) is composed of a discrete series of sine waves.
Any non-periodic signal has a continuous spectrum (all frequencies).
Here is a discussion of windows and leakage.
https://www.egr.msu.edu/classes/me451/me451_labs/Fall_2013/Understanding_FFT_Windows.pdf
Any non-periodic signal has a continuous spectrum (all frequencies).
Here is a discussion of windows and leakage.
https://www.egr.msu.edu/classes/me451/me451_labs/Fall_2013/Understanding_FFT_Windows.pdf
My understanding is that instruments are primarily characterised/identified by the ear-brain from its onset or initial transient - could EQ be done by using a real impulse stimuli, convert the recording of the impulse to a frequency response by "wavelet transform, Hilbert-Huang transform, and Empirical Mode Decomposition" (as proposed by the bot) in the hope (my) that an EQ, that retains a more precise reproduction of onset/transient behaviour of the input signal, is obtained. Instead of letting the speaker breeze through a sweep, hit it with a jolt like a very hard stroke of the Bösendorfer A0 key.
As someone said; "monkey first" - i.e. do the hardest part before the...
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As someone said; "monkey first" - i.e. do the hardest part before the...
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It's inconsistent with ChatGPT's earlier answers, when you just wrote non-linear rather than non-linear and non-sinusoidal. It then tried to apply the definition for non-linear systems to signals.
Some of the examples are also inconsistent with post #7: a square wave or triangle wave can easily be mathematically described. sgn(sin(x)) for a square wave, for example.
What do you use the EQ for? If it is to equalize the magnitude and phase responses of a system that is to a good approximation linear and time-invariant, then equalization should improve its transient behaviour.
The Hilbert-Huang transform a.k.a. empirical mode decomposition is a quite non-linear and somewhat empirical method to discover components with changing frequencies and/or amplitudes in a complex signal. It might be usable for analysing music, recognizing the pitches of various instruments and voices, although I don't know if that has been tried by anyone.
I use it to improve my system, i.e. to make it a more truthful reproducer. A completely agree on your first sentence - no doubt. The only thing I was questioning is and want to be really sure about is that we use the most correct scientific approach. I mean, we have been doing stupid things for long time before we really understood and changed our ways... 🙂 perhaps even so in audio...
But you have no doubt about that sweep->sFFT->FR_EQ has no "ignored" problems?
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But you have no doubt about that sweep->sFFT->FR_EQ has no "ignored" problems?
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In principle, as long as a system is linear and time invariant, you can characterize it completely by (for each combination of input and output) measuring the steady-state magnitude and phase response for sinewaves of all frequencies, or the impulse response, or the step response, or the response to any other signal that has all frequencies in it. Once you have characterized it, you know how to equalize it, and equalizing it will improve the transient response.
In reality, all systems are non-linear to some extent, which complicates things. For example, measuring the response to a Dirac impulse (which is by definition infinitely high and infinitisemally short) is not practically possible, and when you measure with wideband noise but the system is weakly non-linear, you have to make sure that intermodulation products don't affect the measurement too much.
I don't see how alternative spectrum analysis methods can help with this, but then again, I know very little about alternative spectrum analysis methods.
In reality, all systems are non-linear to some extent, which complicates things. For example, measuring the response to a Dirac impulse (which is by definition infinitely high and infinitisemally short) is not practically possible, and when you measure with wideband noise but the system is weakly non-linear, you have to make sure that intermodulation products don't affect the measurement too much.
I don't see how alternative spectrum analysis methods can help with this, but then again, I know very little about alternative spectrum analysis methods.
For me, ChapGPT is right on the dot here. FFT analysis assumes that the signal is periodic. If it is transient/non-periodic, you can sort of force it to be periodic by applying a window that tapers off the transient parts, and you can get a usefull FFT return.
If the signal is really transient or the system is not time-invarient, you won't get anything meaningful from an FFT and other methods of analysis are required.
So I don't see your 'ChatGPT is an FFT denier'.
Jan
ChatGPT has obviously been fed with audiophile textbooks 🙂
Q:
Do audio measurements show anything and everything that constitutes dac performance?
ChatGPT:
Audio measurements can provide important information about the performance of a digital-to-analog converter (DAC), but they do not necessarily show everything that constitutes DAC performance.
Some measurements that are commonly used to evaluate DAC performance include signal-to-noise ratio (SNR), total harmonic distortion (THD), and intermodulation distortion (IMD). These measurements can provide information about the accuracy of the DAC's digital-to-analog conversion process, as well as its ability to accurately reproduce the original audio signal.
However, there are other factors that can affect the overall performance of a DAC, such as the quality of the analog output stage, the design of the power supply, and the quality of the clock oscillator. These factors can also affect the overall sound quality of the DAC, but they may not be directly measurable through traditional audio measurements.
Additionally, some people may argue that the personal preferences, the audio system and the room acoustics also play a major role in the overall perceived performance of a DAC and it's not only about technical measurements.
So, while audio measurements can provide important information about DAC performance, they are not the only factor to consider when evaluating the overall sound quality of a DAC.
Q:
Does The human ear detect signals well below the noise level of the DAC?
ChatGPT:
The human ear is capable of detecting very faint sounds, well below the noise level of a typical digital-to-analog converter (DAC). The threshold of human hearing, or the quietest sound a person can hear, is around 0 decibels (dB) SPL (sound pressure level). The noise level of a typical DAC is typically around -90 dB SPL or lower, which means that the human ear can detect sounds that are much quieter than the noise generated by the DAC. However, the sensitivity of the human ear varies greatly from person to person and also changes with age and exposure to loud sounds.
Q:
Do audio measurements show anything and everything that constitutes dac performance?
ChatGPT:
Audio measurements can provide important information about the performance of a digital-to-analog converter (DAC), but they do not necessarily show everything that constitutes DAC performance.
Some measurements that are commonly used to evaluate DAC performance include signal-to-noise ratio (SNR), total harmonic distortion (THD), and intermodulation distortion (IMD). These measurements can provide information about the accuracy of the DAC's digital-to-analog conversion process, as well as its ability to accurately reproduce the original audio signal.
However, there are other factors that can affect the overall performance of a DAC, such as the quality of the analog output stage, the design of the power supply, and the quality of the clock oscillator. These factors can also affect the overall sound quality of the DAC, but they may not be directly measurable through traditional audio measurements.
Additionally, some people may argue that the personal preferences, the audio system and the room acoustics also play a major role in the overall perceived performance of a DAC and it's not only about technical measurements.
So, while audio measurements can provide important information about DAC performance, they are not the only factor to consider when evaluating the overall sound quality of a DAC.
Q:
Does The human ear detect signals well below the noise level of the DAC?
ChatGPT:
The human ear is capable of detecting very faint sounds, well below the noise level of a typical digital-to-analog converter (DAC). The threshold of human hearing, or the quietest sound a person can hear, is around 0 decibels (dB) SPL (sound pressure level). The noise level of a typical DAC is typically around -90 dB SPL or lower, which means that the human ear can detect sounds that are much quieter than the noise generated by the DAC. However, the sensitivity of the human ear varies greatly from person to person and also changes with age and exposure to loud sounds.
Agree on all - but it is the quoted part above I'm interested in... 🙂
So I can see why a dirac impulse is not possible. But maybe one could modify it i.e. LP and HP filter it in know way to make it usable as a stimuli. If we know the used filters characteristics, the theoretical result of the filtering would be known and we would know what result should come out of a system that tried to reproduce it. Now we have an impulse stimuli that has the suddenness and jolt looking more like that of a percussive musical instrument.
Is this stimuli a harder task to reproduce for a speaker than a sweep? I would imagine that as some physical properties and non-linearities would be more prone to stick out their ugly faces... no?
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Does anybody else remember the old Sound Blaster software bundle from the 90s?
"Hello there! I'm a talking parrot. Please talk to meee!" XD
(Edit: whoops! Not that one. I meant "Dr Sbaitso" hehehe.)
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FFT: round-trip fft + ift conversions are possible with virtually no degradation except for perhaps rounding errors. This implies that all the information is there in plain sight on an FFT graph - it's just a matter of visual resolution and interpreting it. For example, it's possible to reverse the playback direction by playing around with the phase and amplitude.
And the so-vague-it's-almost-meaningless "transient" information is embedded in the sidebands of sinewave peaks.
"Hello there! I'm a talking parrot. Please talk to meee!" XD
(Edit: whoops! Not that one. I meant "Dr Sbaitso" hehehe.)
~~~
FFT: round-trip fft + ift conversions are possible with virtually no degradation except for perhaps rounding errors. This implies that all the information is there in plain sight on an FFT graph - it's just a matter of visual resolution and interpreting it. For example, it's possible to reverse the playback direction by playing around with the phase and amplitude.
And the so-vague-it's-almost-meaningless "transient" information is embedded in the sidebands of sinewave peaks.
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An analogy for performing a Fast Fourier Transform (FFT) analysis on a non-sinusoidal signal can be likened to conducting a dynamic performance test on a vehicle, specifically measuring its fuel efficiency, engine power output and lateral deviation from a predefined straight path, while accelerating from a standstill to a velocity of 70 miles per hour on a level and horizontally aligned smooth road surface. This simulation can´t provide much insight into the vehicle's suitability for a demanding off-road rally event such as the Dakar Rally. All it does is indicate if the car meets the absolute bare minimum of performance to qualify as a very early starting point as a suitable car to modify, tune and optimize for such an event.
Who has claimed that FFT is all encompassing? It is just one tool in the tool set. It is just as silly to claim that listening tests are all it takes.