Another piece of the puzzle

I often tackle the same question multiple times. With each new answer to the same question, the different angle of attack seems to illuminate the lightbulb of understanding for at least one person. An aha! moment. For me, that's reason enough to keep trying. We're all perhaps a bit weary of me beating the DSD horse. I get it. But, I am also convinced that most of my readers don't quite understand the difference between the two main formats: PCM and PDM. And I think it's important to shine a light on it. One of our HiFi Family members, Tony Plachy is a retired physicist with a gift for explaining hard-to-follow concepts. Here's from one of his comments:

"There is something very special about DSD256. I will try to explain what it does and how it does it. First, lets call DSD256 what it is. PDM ( Pulse Density Modulation ) which is a special case of PWM ( Pulse Width Modulation). I have been to seminars and lectures where notable mastering and recording engineers have said that the remarkable thing about PDM is that when the sampling rate is high enough ( and DSD256 is certainly high enough ) and you make a digital copy of analog music and the convert the copy back to analog what you get back sounds like the original. To say it another way is DSD256 makes exact copies. I have a DSD recorder that i use to make copies of my best vinyl. It copies at DSD128 and the plays it back at DSD64. During the recording I can toggle between the copy and the original listening to the headphone feed from the recorder. To these old ears the mastering and recording engineers are correct. How can this be? What does this happen with PDM and why does PCM ( Pulse Code Modulation ) seem to leave a digital footprint on the results? The answer is two things, one of witch I have all ready mentioned. First, the sampling rate must be high enough ( DSD256 or at least DSD128 ). Second, with PDM the amplitude of the analog signal is NOT ( yes, is NOT ) digitized. You can see this for yourself if you go online and find an article that shows the DSD output of digitizing a sine wave. Even if you are not an EE ( Electrical Engineer ) it should be obvious that all you need to do is use an analog low pass filter to get the sine wave back. Do not ever try this if you have the PCM output from digitizing a wave, all you will hear is horrible noise. So does PDM do this for all music? The answer is yes, it does. To understand this you need to go online again and first look up a guy named Fourier and then look up how a square wave is made from a Fourier series. If you understand this it will be obvious that PDM can make exact copies of all music. End of lecture, do your homework, this will be on the final exam! 😉"

Thanks, Tony!