Butterworth order and curves

[Speckie]

Root mean square voltage is the equivalent voltage in constant DC that will give the same averaged power as the AC waveform (when averaged in integer periods of the AC waveform, or if the number of periods in non-integral, large number of periods). Since power = voltage² / resistance (for resistive loads), the math just works out that way.

See:

RMS Voltage: What it is? (Formula And How To Calculate It) | Electrical4U

A SIMPLE explanation of RMS Voltages. Learn what RMS Voltage is, how to calculate RMS voltage, the formula, and peak voltage vs RMS voltage vs peak-to-preak voltage. For square waves ...

www.electrical4u.com

In the computation details.

The area of rectangle is length times height, but it is not a square shape so one is not supposed to square it. So the reason it squares the V is to get Power = V^2/R. But why doesn't it include R in the computation?

 

[NTK]

The area of rectangle is length times height, but it is not a square shape so one is not supposed to square it. So the reason it squares the V is to get Power = V^2/R. But why doesn't it include R in the computation?

Because the load resistance got cancelled in the calculation.

 

[Speckie]

It is power spectrum. The 32'768 length graph is the same as the one earlier in the post, where power spectrum is compared to linear spectrum.


That's just the default which I use most often but it is not what was used on those graphs. If I used the default, I would label the y-axis "V_peak".


V_rms is different from peak linear spectrum. Peak is

% Convert from power spectrum [V_rms^2] to peak linear spectrum [V_peak]
Y = sqrt(mag2) * sqrt(2);

RMS is:

% Convert from power spectrum [V_rms^2] to linear spectrum [V_rms]
Y = sqrt(mag2);

The discussion earlier was about power spectral density and it made the most sense to me to compare it to power spectrum. So that's the conversion I used.


There already is RMS linear spectrum earlier in the post, where power spectrum is compared to linear spectrum. Peak linear spectrum looks like RMS linear spectrum, only it is scaled by sqrt(2).


Not only. I meant any noise-like signal.

(Do you mean "which is not noise floor"?)

Probably would be better to ask those people.

I don't really focus on noise-like signals, so to me the only advantage is that FFT-size independence.

Do you consider audio or voice as noise-like signals? I thought the purpose of PSD was to smoothen the chaotic output of the FFT like in the following:

If the purpose is just to smoothen the output graphics of the chaotic FFT. How do you do it without using needing to use PSD?

 

[Speckie]

Do you consider audio or voice as noise-like signals? I thought the purpose of PSD was to smoothen the chaotic output of the FFT like in the following:


View attachment 479468


If the purpose is just to smoothen the output graphics of the chaotic FFT. How do you do it without using needing to use PSD?

I mean, if your goal is you just want to have nice graphics output in FFT, without the many amplitudes that might scare people not familiar with FFT like presenting to public (it can convey chaos). I think you just lessen the sample of the FFT which can still maintain the peak, isn't it. Because what I knew FFT vs PSD before we discussed was I thought the PSD just smoothen the output. But then it seems the presentor (like above) just use PSD with very small segment.

Anyway. There is this technique though called "savitzky-golay filter". which can smoothen the FFT. If you know how to implement it in Octave, pls let me know. Thanks.

I'll ask CERN people what they consider signal as noise-like, but they may not reply me as they need to focus on the collider. My interest has to do with particle detector that may never detect it for the lifetime (like dark matter or monopoles). I guess voice and audio are not noise-like, isn't it. But sometimes they just appear like noise.

 

[Speckie]

I mean, if your goal is you just want to have nice graphics output in FFT, without the many amplitudes that might scare people not familiar with FFT like presenting to public (it can convey chaos). I think you just lessen the sample of the FFT which can still maintain the peak, isn't it. Because what I knew FFT vs PSD before we discussed was I thought the PSD just smoothen the output. But then it seems the presentor (like above) just use PSD with very small segment.

Anyway. There is this technique though called "savitzky-golay filter". which can smoothen the FFT. If you know how to implement it in Octave, pls let me know. Thanks.

I'll ask CERN people what they consider signal as noise-like, but they may not reply me as they need to focus on the collider. My interest has to do with particle detector that may never detect it for the lifetime (like dark matter or monopoles). I guess voice and audio are not noise-like, isn't it. But sometimes they just appear like noise.

View attachment 479696

Finding dark matter among the noise with Moku:Pro

In a recent case study, we highlighted the use of the Moku:Pro in the search for what is known as “light” dark matter. These types of experiments involve Learn how researchers are leveraging flexible data logging and Python support to fast-track event detection with minimal setup

liquidinstruments.com

Btw.. above is the reference for using PSD on dark matter detection. I understand that creating PSD version is to make the noise floor invariant to change of size or bins. But then I can't understand how they mix the PSD to the time display (instead of PSD display). In days to come. I'll google and ask elsewhere examples of noise-like signal. If you know other words for it, let me know because when I googled it, the following mostly comes out:

"A 'noise signal' refers to an unwanted perturbation that disrupts a desired signal in both analog and digital electronics. It is considered noise due to its similarity to audible noise experienced when listening to a weak radio transmission.".

There is almost no "noise-like signal" hits. And if you remember best examples of noise-like signal. Let me know because at this point I still can't decide whether to use FFT or PSD as I don't know all the exampes of noise-like signal. .

 

[MaxwellsEq]

View attachment 479789

Finding dark matter among the noise with Moku:Pro

In a recent case study, we highlighted the use of the Moku:Pro in the search for what is known as “light” dark matter. These types of experiments involve Learn how researchers are leveraging flexible data logging and Python support to fast-track event detection with minimal setup

liquidinstruments.com

Btw.. above is the reference for using PSD on dark matter detection. I understand that creating PSD version is to make the noise floor invariant to change of size or bins. But then I can't understand how they mix the PSD to the time display (instead of PSD display). In days to come. I'll google and ask elsewhere examples of noise-like signal. If you know other words for it, let me know because when I googled it, the following mostly comes out:

"A 'noise signal' refers to an unwanted perturbation that disrupts a desired signal in both analog and digital electronics. It is considered noise due to its similarity to audible noise experienced when listening to a weak radio transmission.".

There is almost no "noise-like signal" hits. And if you remember best examples of noise-like signal. Let me know because at this point I still can't decide whether to use FFT or PSD as I don't know all the exampes of noise-like signal. .

If you read my post #7 again, you will grasp this a bit better.

To be clear, I feel this is off-topic for a forum focusing on accurate music reproduction in the home!

In HiFi, "noise" is something we are trying to minimise and so it's "bad". This includes: (1) 50/60Hz mains induction or leakage, (2) thermal hissy noise, (3) splats and bangs from induction etc. But in your project these are different types of noise and you are fundamentally focused on (2) above.

If you could slow down time to make each femtosecond a minute long, you would better understand the "scaling" nature of thermal and similar types of noise. It's NOT a signal, but is random sequence of values.

We can make fake noise by using a pseudorandom generator with a long, but known repeat sequence. If we do this, it looks like noise to a 3rd party, but if we pre-know the sequence, it looks like a signal. If we transmit this at the noise floor, we can pass an apparently invisible message. See https://www.researchgate.net/public...dorandom_waveforms_and_their_information_rate

What you are investigating is a thing that generates a noise-like blip in the presence of noise. It happens very infrequently, so you need to collect data over a very long period. Then you need to process this data looking for stochastically different behaviour.

This is absolutely nothing like listening to a recording of David Bowie at home.

 

[Speckie]

If you read my post #7 again, you will grasp this a bit better.

To be clear, I feel this is off-topic for a forum focusing on accurate music reproduction in the home!

In HiFi, "noise" is something we are trying to minimise and so it's "bad". This includes: (1) 50/60Hz mains induction or leakage, (2) thermal hissy noise, (3) splats and bangs from induction etc. But in your project these are different types of noise and you are fundamentally focused on (2) above.

If you could slow down time to make each femtosecond a minute long, you would better understand the "scaling" nature of thermal and similar types of noise. It's NOT a signal, but is random sequence of values.

We can make fake noise by using a pseudorandom generator with a long, but known repeat sequence. If we do this, it looks like noise to a 3rd party, but if we pre-know the sequence, it looks like a signal. If we transmit this at the noise floor, we can pass an apparently invisible message. See https://www.researchgate.net/public...dorandom_waveforms_and_their_information_rate

What you are investigating is a thing that generates a noise-like blip in the presence of noise. It happens very infrequently, so you need to collect data over a very long period. Then you need to process this data looking for stochastically different behaviour.

This is absolutely nothing like listening to a recording of David Bowie at home.

The Moku.pro has range to Mhz and costs $25,000. So I just got an audio range amplifier for lack of budget. Hence the dark signal I'm after is only audio frequency. So it's like I'm trying to listen to dark music. And I need to be familiar with all things audio.

Besides. In the 2000s. I was very interested in music and accurate music reproduction in the home. But after buying many sets of amplifiers and loudspeakers. I still couldn't find one with treble and bass in the right mix. In those days there was no internet to ask questions. A music lover sold me an amplifier, he said old 1970s-80s transistor based amplifier was the best, and that modern IC based amplifier couldn't match it anymore. Is it true? When I was about to buy small bose cube speakers. He said old speakers were better so I bought his. But when listening to it, the sound seems thin. I bought a floor tall Morley speakers, but they also didn't sound solid. Discouraged. I sold all of them.

Now 20s later. What are the reasonably price amplifiers and sets of speakers that sound complete. It doesn't have to be in the $2000. But $500 will do. I'll try a second time for accurate music reproduction at home which I failed before.

Btw.. can you use FFT to tell if the audio amplifier has poor treble or bass or midrange.. or other aspect?

 

[Speckie]

I read this and want to try FFT on a high quality cd class song.

Deep Learning 101: Lesson 23: The Basics of Audio Signal Processing with FFT

This article is part of the “Deep Learning 101” series. Explore the full series for more insights and in-depth learning here.

muneebsa.medium.com

Where can I download a wav file of CD quality 44.1kHz (sample) so I can check it out. The following is the FFT of the previous song Beauty and the Beast I got in youtube. I wonder why there are many low frequency peaks. Is it because of the youtube quality? I would like to see cd quality WAV to see if the peaks would be more uniform.

this is when semilogy (Fs,Y) used a ylim (-130 130) used:

this is when semilogx used, I wonder why there is big difference to semilogy;

 

[Speckie]

I read this and want to try FFT on a high quality cd class song.

Deep Learning 101: Lesson 23: The Basics of Audio Signal Processing with FFT

This article is part of the “Deep Learning 101” series. Explore the full series for more insights and in-depth learning here.

muneebsa.medium.com

Where can I download a wav file of CD quality 44.1kHz (sample) so I can check it out. The following is the FFT of the previous song Beauty and the Beast I got in youtube. I wonder why there are many low frequency peaks. Is it because of the youtube quality? I would like to see cd quality WAV to see if the peaks would be more uniform.

View attachment 480383

this is when semilogy (Fs,Y) used a ylim (-130 130) used:

View attachment 480384

this is when semilogx used, I wonder why there is big difference to semilogy;

View attachment 480385

Here is something bizaare. If I didn't use 20 * log10(Y) in last image above, but only semilogx(freqs, Y); the following comes out with only a flat line at middle. I wonder what 20 * log10(Y) do exactly? Now I'm analyzing signal instead of just noises I need to be familiar with audio analysis to test audio amplifiers and song sources because I got too many lemon before and this may help.

 

[NTK]

Do you notice the highest value in the first plot in your post #88 was about 0.0047? If you do not convert the values into dB, and proceed to plot these numbers with y-axis limits of -130 and +130, all these data points, which their y values are all between 0.0 to 0.0047, will appear as a straight horizontal line.

If you convert the value to "dB" using the formula, 20 * log10(0.0047) = -46.6, it is about the max value of the points in the third plot in post #88. That how the dB scale (or, equivalently, the log scale) works. It compresses the high magnitude numbers together, and expand the small ones. This is done so that, when your signals have frequency component magnitudes of, say, 100, 0.1, 0.01, 0.001 at various different frequencies, you can still tell them apart in the magnitude vs frequency plot.

It appears that your understanding of the fundamentals is deficient. You will have to address this first. What type of background do you have in data analysis, signals and systems, data acquisition, etc.?

 

[Speckie]

Do you notice the highest value in the first plot in your post #88 was about 0.0047? If you do not convert the values into dB, and proceed to plot these numbers with y-axis limits of -130 and +130, all these data points, which their y values are all between 0.0 to 0.0047, will appear as a straight horizontal line.

If you convert the value to "dB" using the formula, 20 * log10(0.0047) = -46.6, it is about the max value of the points in the third plot in post #88. That how the dB scale (or, equivalently, the log scale) works. It compresses the high magnitude numbers together, and expand the small ones. This is done so that, when your signals have frequency component magnitudes of, say, 100, 0.1, 0.01, 0.001 at various different frequencies, you can still tell them apart in the magnitude vs frequency plot.

It appears that your understanding of the fundamentals is deficient. You will have to address this first. What type of background do you have in data analysis, signals and systems, data acquisition, etc.?

Oh. I thought the Octave command ylim ([-130 130)]; is automatically in dB. Thanks for pointing that it wasn't. I finished electronic engineering. But they didn't teach signal analysis then, so catching up.

Now please someone share the highest quality CD quality WAV samples so I can check if it would also have low frequency peaks or only in youtube.

 

[MaxwellsEq]

Where can I download a wav file of CD quality 44.1kHz (sample) so I can check it out

You must own an audio CD or know someone who has one you can borrow!

A CD contains WAV files at 44.1kHz 16 bits. There are many tools to extract these from the CD container, including Exact Audio Copy, dBpoweramp etc.

 

[Speckie]

You must own an audio CD or know someone who has one you can borrow!

A CD contains WAV files at 44.1kHz 16 bits. There are many tools to extract these from the CD container, including Exact Audio Copy, dBpoweramp etc.

Last time I owned a CD was in the early 2000s. At that time my Pentium 100 desktop pc had the top of the line Turtle Beach Multisound and Roland Sound Canvas for MIDI. I still have the ISA boards. But after 20 years. I still couldn't find ones like them. Do you know what current sound card has Turtle Beach Multisound quality?
Now my laptop only has firmware sound card that doesn't sound good at all.

When MP3 became available. CD was not so much sought after. So it's like there is downhill in audio quality.

Anyway. I found a CD by David Pumaranz, and I tried optimum Exact Audio Copy setting by following the instructions here:

Perfect CD-ripping to FLAC with Exact Audio Copy - Flemming's Blog

If you want to make perfect digital and lossless copies of our music-CDs, then this is for you. By following this guide you should be able to make bit-perfect verified copies so you never have to do it again.This process includes ripping/correcting/verifying the CDs to raw WAV and converting it...

flemmingss.com

Testing "On This Day" song. This is the FFT

It has more low frequency contents below 2500Hz. Do you have an idea why is that? Does our voice have more energy in lower frequency?

this is the Semilogy and Semilogx.

 

[MaxwellsEq]

Do you know what current sound card has Turtle Beach Multisound quality?

Most sensible modern motherboards are better. Any modern quality audio interface is better.

 

[MaxwellsEq]

Does our voice have more energy in lower frequency?

All music has more energy at lower frequencies, even electronic music.

To get far more information, upload the file to
https://andreasarvidsson.github.io/MasvisOnline/

 

[Speckie]

All music has more energy at lower frequencies, even electronic music.

To get far more information, upload the file to
https://andreasarvidsson.github.io/MasvisOnline/

Thanks. How do you get the Normalized Average Spectrum? I set the Octave code to fft_size of 255 and semilogx(freqs, 20*log10(Y)); but the graphs don't match:

Octave set to fft_size of 255 and semilogx(freqs, 20*log10(Y))

 

[NTK]

The average spectrum plot from MasvisOnline did NOT use an FFT size of 255. It was the average spectrum of 255 frames, i.e. the audio is partitioned into 255 frames (partitions) of 1 sec long each (probably zero padding the last frame so all frames are equal length), and the spectrum plotted was the averaged magnitude of these 255 frames.

 

[Speckie]

The average spectrum plot from MasvisOnline did NOT use an FFT size of 255. It was the average spectrum of 255 frames, i.e. the audio is partitioned into 255 frames (partitions) of 1 sec long each (probably zero padding the last frame so all frames are equal length), and the spectrum plotted was the averaged magnitude of these 255 frames.

What is the advantage of getting FFT via averaging the frames like you described above versus getting FFT size and averaging?

 

[NTK]

What is the advantage of getting FFT via averaging the frames like you described above versus getting FFT size and averaging?

Describe what you think the differences are between the two methods. The answer to this question will lead to the answer to your question.

 

[Speckie]

Describe what you think the differences are between the two methods. The answer to this question will lead to the answer to your question.

I tried to imagine it.

Imagine doing 10 frames and the audio has 10,000 bin or size. Divide it into 1000 each. So you cut it into 10 frames like this...

___________|___________|____________| etc to 10 frames

this is compared to taking the entire 10,000 bin and reduce the resolution to say 1000 size/bin.. and taking 10 samples.. (You take the number of averages as total size 10000/1000 = 10 times average, right)?

I still can't imagine the differences of the result.