A sine with a fade in fade out window will still have an infinite spectrum (therefore some compromise in the reconstruction will be required). The faded sine is an intermediate case between the hard windowed sine spectrum shown here Linear Physical Systems - Erik Cheever and the pure infinite sine spectrum; that means the longer the fade in/out the closer the Fourier transform will be to a delta(fo).
Intuitively, when the fade in/out duration increases, the two sinc in the above Fourier transform for a hard windowed sine will close each other, their amplitude will increase and the overall sinc tails will go down faster, so indeed you can claim that a fade in/out sine is less demanding in terms of bandwidth compared with a hard windowed sine.
I can dig for the exact Fourier transform, but it appears you are not interested in an analytic expression (has a closed form).
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It’s not that I am not interested. It is that I can not make use of it. (you know it but you are polite
)George
Most likely you both were talking past each other. Hans Polak most likely meant the same (that you've expressed above about the limit before A/D) with his line about the "brickwall before NRZ" (after the first brickwall, i.e. the antialiasing filter, and A/D, there simply exist no NRZ, its just the numbers) and of course one needs another brickwall (i.e. antiimaging filter) for the NRZ (i.e. zero-order-hold or ZOH) that is presented by the D/A at its output.
It's analog. It's blurry and you can see the grain of the film.
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Very likely we did talk past.. When he said before the NRZ, I did assume he meant band limiting before the ADC.
Happy new year to all.
John
Oh I have too, otherwise wouldn;t have said it
. I still can't work out how Seurat didn't go blind.I think Hans is factually correct here even if you don’t like his attitude.
The NRZ in a real commercial implementation of an audio DAC happens after the digital brickwall oversampling (reconstruction) filter. The point is to relax the analog post-filter requirements and they are typically 2nd or 3rd order with high Fc.
Edit- seems this confusion has already been addressed on the previous page.
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In reference to reproducing cymbals:
On the third FM radio station I participated in building (I did the studios someone else did the already existing transmitter and antenna.) The ability to compare what was being received off air and going out was available in the three studios and main equipment bay. There were four types of sources; records, CDs, .Wav files and live.
The standard for transmitting analog FM stereo signals is that there is a 19,000 hertz pilot tone transmitted to identify a stereo signal, the baseband signal with a bandpass of 30 to 15,000 hertz was left and right combined as monaural and a subcarrier at 38,000 hertz caries the left - right signal. By adding the sub carriers program to the base band you got the left channel and by inverting the subcarrier and adding it to the base band signal you got the right channel.
As I was setting things up the systems compressor designed to make sure the FM deviation did not exceed the 75,000 hertz deviation was rarely engaged. (This changed later when the station manager wanted his station to be as loud as the other ones!) When comparing what went to the transmitter to the off air signal there was a bit of difference, but not much, except for cymbals. They just sounded dull, unless it was a live broadcast where at least one fellow hearing the comparison wanted to know what was broken!
My interpretation is that most folks aren't aware of the bandwidth limitation of FM stereo or even CDs, but those with experience or the ability to make comparisons do notice.
On the third FM radio station I participated in building (I did the studios someone else did the already existing transmitter and antenna.) The ability to compare what was being received off air and going out was available in the three studios and main equipment bay. There were four types of sources; records, CDs, .Wav files and live.
The standard for transmitting analog FM stereo signals is that there is a 19,000 hertz pilot tone transmitted to identify a stereo signal, the baseband signal with a bandpass of 30 to 15,000 hertz was left and right combined as monaural and a subcarrier at 38,000 hertz caries the left - right signal. By adding the sub carriers program to the base band you got the left channel and by inverting the subcarrier and adding it to the base band signal you got the right channel.
As I was setting things up the systems compressor designed to make sure the FM deviation did not exceed the 75,000 hertz deviation was rarely engaged. (This changed later when the station manager wanted his station to be as loud as the other ones!) When comparing what went to the transmitter to the off air signal there was a bit of difference, but not much, except for cymbals. They just sounded dull, unless it was a live broadcast where at least one fellow hearing the comparison wanted to know what was broken!
My interpretation is that most folks aren't aware of the bandwidth limitation of FM stereo or even CDs, but those with experience or the ability to make comparisons do notice.
Over modulation was probably one of the reasons FCC compliance went to the stations instead of the first class license holder. Years ago in a previous career a local FM station was interfering with the police due to a crappy spectrum. Most TV and radio chiefs were more than happy to help even offering to turn their transmitters off. One was not and was very defensive and rude. I was very happy to see them fined for this and an illegal antenna change. I wasn't a 20 year old punk with a spectrum analyzer to the FCC, they had smart capable people.
Wayne,
I do have the ability to look at the spectrum. Almost every FM station overmodulates. I also have been in a station when the chief engineer got the call that the FCC was in town!
The worst offender locally did 200%! They were traipsing on a local public station. A courtesy call yielded no improvement. BTY it was so far over the audio signal was distorted. For some funny reason shortly thereafter things improved.
The upside is at a local stadium concert the sound company was told they were interfering with coast guard frequencies. (The stadium is on the river front.) They told the Coastie to F.O. They got fined $30,000.00 by the Friendly Candy Company!
I do have the ability to look at the spectrum. Almost every FM station overmodulates. I also have been in a station when the chief engineer got the call that the FCC was in town!
The worst offender locally did 200%! They were traipsing on a local public station. A courtesy call yielded no improvement. BTY it was so far over the audio signal was distorted. For some funny reason shortly thereafter things improved.
The upside is at a local stadium concert the sound company was told they were interfering with coast guard frequencies. (The stadium is on the river front.) They told the Coastie to F.O. They got fined $30,000.00 by the Friendly Candy Company!
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