Charles,
I stepped into this little quagmire of yours in another thread and decided to back out 'cuz I didn't have time to do the research then. I withdrew my post in that other thread since I hadn’t really done the proper background work. But, since you've brought this up again, here goes.
No. PCM is not a termolo machine.
Stefan and Nika have pretty much nailed it. You are not using a reconstruction filter, and the signal you are examining with your scope is the output of a zero-order-hold DAC with no reconstruction whatsoever. So I’m not at all surprised that you came to those conclusions. A couple of things should have clued you in.
Chuck wrote on Tue, 15 June 2004 11:21 |
I have used one of the best reconstruction filters available, the DF1704. You think you can up with something better.
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The DF1704 is NOT a reconstruction filter. It is a digital—read,
discrete time—
interpolation filter. Its primary application appears to be for oversampling before input to the PCM1704 which does not do on-board sample rate conversion. That’s a feature that was added to later delta sigma chips.
The point here is that reconstruction filters are continuous time beasts. If you look again at the interpolation formula on your web page, you’ll note that
n is a discrete variable, but
t is continuous. No digital filter will ever give you continuous
t—not ever.
Sure, you could stay in the discrete time domain all you want, upsample to light in a vain attempt to simulate a continuous time signal, but that’s silly. Just stick a reasonable analog filter at the output of your DAC and many of the effects you’re observing will go away. I thought that the MFB filter described in the eval board of the 1704 was pretty reasonable.
Second clue. If you look at where your DF1704 goes in the TI diagrams, you’ll note that it feeds the DAC—it can’t possibly be a reconstruction filter. Reconstruction filters go
after the DAC.
After writing that, I also have to say that it is a good thing to explore the limitations in our applications and implementations of the sampling theorem. So in general, I am sympathetic with what you’re trying to do. It is true that all of our filters contain imperfections. It is true that no real implementation of the reconstruction equation can yield exact results (we’d need infinite precision machines). In spite of that, these errors can be rendered insignificantly small with proper design. And the key to good design is how to make those errors virtually vanish.
I believe that you’re wrong this time, but you shouldn’t be discouraged. There aren’t many posters that actually pick up a scope and try to understand what they’re seeing. That’s a rare and valuable trait and should be encouraged.
-Dennis