Problems began with you younger guys when they stopped teaching the multiplication tables and being able to do long division on paper. Math is becoming a lost art.
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FWIW I am listening to Rudolf Serkin playing Schubert at present and at the level around which i would normally listen to piano music my gadget is showing 29.8 dB min, 64.6 dBLeq and 82.2 dB max.
I see higher peaks with symphonies.
I see higher peaks with symphonies.
FifyMeth is for the weak.
Just gave a quick look out of curiosity.
Cheap RS SPL meter C/Fast reading in the high 80s 86-88 peaks.
Old man levels but that's about as high as I run things now, very protective of what little hearing I have left. Super anal at the shooting range each week wearing foam plugs plus good muffs on top at all times.
Cheap RS SPL meter C/Fast reading in the high 80s 86-88 peaks.
Old man levels but that's about as high as I run things now, very protective of what little hearing I have left. Super anal at the shooting range each week wearing foam plugs plus good muffs on top at all times.
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Problems began with you younger guys when they stopped teaching the multiplication tables and being able to do long division on paper. Math is becoming a lost art.
Well they still taught the times tables up to 12 when I was in school. They had developed flashcards for that purpose by then.
I learned long division one summer day after first grade. My Mom had taken a job when I started school. So I called her on the phone during her lunch hour. I asked her how to do batting averages. So she taught me long division over the phone there. Checked to make sure I had it right later that evening. It made it convenient when they got to long division in school as I already knew it. Unfortunately, I don't think Mom will be any help on Bessel functions.
Here is the explanation without math. I will probably create a mini-article out of it later.
The key to understanding this is to realize what is being measured. The core is the idea of how would an ideal analog to digital converter work when sampling an analog signal into discrete digital values. Wiki has a nice picture of this although I am sure we all can imagine it also:
The top graph shows the analog waveform in blue and discrete, sampled values by the analog to digital converter. Naturally since we don't have infinite sample resolution, we can't track the original signal completely faithfully. The graph below shows the error between what we sampled digitally and the difference between the two.
We can compute this error if we assume the source is sinusoidal:
Doing this then yields the value of signal to noise ratio = 6* number of bits + 1.67
SFDR is computed using the same assumption of sinusoidal input but now we look at the spectrum of the distortion products generated as a result of fixed quantization and compute its highest peak.
Let's look at a real simulation. I created a floating point 1 Khz tone in Adobe Audition. Floating point gives us much more resolution than fixed point 16 or 24 used in audio and as such can be thought of being near analog in resolution. Here is the frequency spectrum of that:
We see our main tone at the 1 Khz. No distortion products are visible.
Now I truncate the samples to 8 bits. I don't apply any dither which would simulate sampling an analog signal without dither into 8 bits and look at its spectrum again:
Our original tone is on the left at 0 dbfs without change. But what is changed is that I now have tons of distortion products. If we eyeball the highest one we find one around 3 Khz. Again an eyeball shows it to be at -65 dbFS. Per notation on the graph, SFDR is 9 times number of bits minus a fudge factor of "c." The fudge factor is there because this is an approximation. "c" for high-resolution systems is 6 so using that we see that the formula predicts the highest peak to be at -66 dbFS which is essentially a match for our -65 dbFS eyeballing.
The connection to bessel function is that it describes the distribution we see of the distortion products. Using that we can compute the individual peak values. Hence the reason the derivation uses that.
Hope this is more clear now.
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Here is the explanation without math. I will probably create a mini-article out of it later.
The key to understanding this is to realize what is being measured. The core is the idea of how would an ideal analog to digital converter work when sampling an analog signal into discrete digital values. Wiki has a nice picture of this although I am sure we all can imagine it also:
The top graph shows the analog waveform in blue and discrete, sampled values by the analog to digital converter. Naturally since we don't have infinite sample resolution, we can't track the original signal completely faithfully. The graph below shows the error between what we sampled digitally and the difference between the two.
We can compute this error if we assume the source is sinusoidal:
Doing this then yields the value of signal to noise ratio = 6* number of bits + 1.67
SFDR is computed using the same assumption of sinusoidal input but now we look at the spectrum of the distortion products generated as a result of fixed quantization and compute its highest peak.
Let's look at a real simulation. I created a floating point 1 Khz tone in Adobe Audition. Floating point gives us much more resolution than fixed point 16 or 24 used in audio and as such can be thought of being near analog in resolution. Here is the frequency spectrum of that:
View attachment 5479
We see our main tone at the 1 Khz. No distortion products are visible.
Now I truncate the samples to 8 bits. I don't apply any dither which would simulate sampling an analog signal without dither into 8 bits and look at its spectrum again:
View attachment 5480
Our original tone is on the left at 0 dbfs without change. But what is changed is that I now have tons of distortion products. If we eyeball the highest one we find one around 3 Khz. Again an eyeball shows it to be at -65 dbFS. Per notation on the graph, SFDR is 9 times number of bits minus a fudge factor of "c." The fudge factor is there because this is an approximation. "c" for high-resolution systems is 6 so using that we see that the formula predicts the highest peak to be at -66 dbFS which is essentially a match for our -65 dbFS eyeballing.
The connection to bessel function is that it describes the distribution we see of the distortion products. Using that we can compute the individual peak values. Hence the reason the derivation uses that.
Hope this is more clear now.
This is helpful. It is also more or less what I did truncating like that. I see that it works yes. I can accept that no problem. It still leaves a blank spot visualizing this. Which reading the papers and working thru this may fill in.
I suppose it also doesn't matter. As with real digital signals in the analog world we always have thermal noise getting in the way first.
Thermal noise, shot noise, 1/f (N/f) noise, flicker noise, popcorn noise, etc.
The original paper I have (but have not looked at much recently) actually predicts the relative frequency of the highest spur but in the real world that part is much harder to correlate due to phase changes and other noise sources (see above) impacting the measurements. It's also probably worth noting that most all modern-day DACs use noise decorrelation (dither) of some form and that raises the noise floor, decreasing SNR, but may increase SFDR a bit (err, "by a small amount", not adding one bit of resolution). And, the spur floor of a delta-sigma design is a different beast though the 9N rule generally holds true since it is based upon quantizing the signal and nothing else.
Edit: Amir, you should pick up a copy of the IEEE Standard 1241. It has a lot of useful info for testing data converters and a method of getting away without windowing in the FFTs. That is why the plots I have simulated have such narrow signal tones and a flat noise floor. It is also how I have tested my designs over the years.
The original paper I have (but have not looked at much recently) actually predicts the relative frequency of the highest spur but in the real world that part is much harder to correlate due to phase changes and other noise sources (see above) impacting the measurements. It's also probably worth noting that most all modern-day DACs use noise decorrelation (dither) of some form and that raises the noise floor, decreasing SNR, but may increase SFDR a bit (err, "by a small amount", not adding one bit of resolution). And, the spur floor of a delta-sigma design is a different beast though the 9N rule generally holds true since it is based upon quantizing the signal and nothing else.
Edit: Amir, you should pick up a copy of the IEEE Standard 1241. It has a lot of useful info for testing data converters and a method of getting away without windowing in the FFTs. That is why the plots I have simulated have such narrow signal tones and a flat noise floor. It is also how I have tested my designs over the years.
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What is the nature of the error remaining after a DAC converts back to stepless analog?
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https://books.google.com/books?id=Q...4ChDoAQgmMAI#v=onepage&q=sfdr 9n bits&f=false
Assuming you can see this excerpt scroll up to the Fundamentals of SFDR section II. This explanation makes sense to me as to why the number becomes 9 db per bit from an energy conservation viewpoint.
Assuming you can see this excerpt scroll up to the Fundamentals of SFDR section II. This explanation makes sense to me as to why the number becomes 9 db per bit from an energy conservation viewpoint.
Glad you found something you can relate to! I have had that book since the first edition, and even got to speak with Rudy about it at a conference (worked with a friend of his), but didn't think to check it. I have a bunch of books on data converters (and hundreds on various EE subjects of interest from device physics to radar system analysis).
Similar except the highest-frequency content is gone, filtered by the anti-image filter, which makes the overall RSS'd error lower, natch.
Please don't feed the trolls.
Frank, I thought you were going to lay low for a while?
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I have a message for @fas42
I have a message for @fas42
Rock On my brother, Rock On.IF IT'S TOO LOUD, YER TOO OLD...
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