Did SHARP ever make DACs in 80s?

[Julf]

I'm familiar with nyquist and sampling theory, it's just that alot of lectures don't really go in depth explaining "sample pulses" beyond 44 that much, where they are derived from, or why these pulses fold infinitely.
I was after a better explanation on pulses...

Well, the folding is not so much a pulse thing - even if you don't use a pulse to window the sampling (basically assume an endlessly long time axis, you would still get folding at the sampling frequency.

I got the impression they only repeated in os applications, but revisiting the lavry paper shows they exist even in nos. (though it is not clear seeing as it is the paper on "oversampling" as it implies in the title).

So really, just to confirm they definately are present even in nos applications.

Indeed - they are an intrinsic part of the sampling process, no matter what the implementation.

 

[giro1991]

Ok thanks

assume an endlessly long time axis, you would still get folding at the sampling frequency.

So theres a fold at the sampling frequency (in the image 22 is folded), but see the repeats after 44, are they definatley present in nos?

Appreciate your response

 

[dmills]

Yep, you can think of sampling as mixing (as in multiplying, not summing) with a repetitive pulse chain at the sample frequency (The pulse having a width of Lim ->0).

As these pulses have an infinite series of harmonics the mixer output will have an infinitely repeating series of sidebands centred around N * fs, where N is is a member of the set of all integers.

Incidental the limit is that the bandwidth must be strictly less then Fs/2, equal to Fs/2 will not work correctly.

One way to look at this stuff is to consider a full scale sine wave at Fs/4, which will (If the phase is correct) have sample values as follows: 1, 0, -1, 0.
Now on each sample pulse there is a theoretical unit step change in amplitude at the output of the NOS DAC, and this step (in theory) occurs instantly, now an instantaneous step change requires infinite amount of power and as each harmonic can only have at most unit power (it is a unit step) then there must be an infinite series of harmonics of the sample rate.

Handwavy, but this forum does not support LaTex and I am NOT going to try to write math in html.

Regards, Dan.

 

[giro1991]

Dan, that is an interesting explanation. This is the part I feel is often omitted from lectures such as those linked in this thread.
Do you have any good references that goes into (more) depth about this aspect?

Thanks

 

[Ken Newton]

Ok thanks



So theres a fold at the sampling frequency (in the image 22 is folded), but see the repeats after 44, are they definatley present in nos?

Appreciate your response

Not only are these image bands present via NOS (as confirmed by Dan), they are located much closer to the desired audio band, and to each other than via OS. In a properly oversampled system, the image bands will be centered at integer multiples of the native sampling rate * the oversampling ratio.

For example, a CD based playback system featuring an x8 oversampling ratio will center the first image band at; (1 * 44.1KHz * 8) = 352.8KHz. The next image band is not found until; (2 * 44.1KHz * 8) = 705.6KHz, and so on.