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Digital Drive: Re: Domain Dementia... by csown

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Re: Domain Dementia...

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Todd, the response is abs(Sin(x)/x). It doesn't go negative, you can't have a negative response. We're talking about amplitude here which is the modulus.

What you've been thinking about up till now is the sum of fourier coefficients in the time domain summing up to create the impulse response. That is indeed the function A(sin(n.x)/x), a scaled/stretched sinc function - here it does go negative since we are describing the time-domain signal here. The scaling/stretching depends on the fourier coefficients - you can obviously not sample with infinitely fine samples, so you cannot have a perfect top hat function. This is what gives rise to the ringing in the impulse response, and this I know you know.

With non-OS, you can avoid the digital filter ringing because of the zero order hold. The minimum impulse width is 1/ f s , a top hat function (!) made possible by virtue of the ZOH. Just think: real-world impulse response using 40-year-old technology :). Its accuracy is limited only by the slew rate of the DAC and the DAC's post-electronics which, if designed properly, have excellent real-world impulse response way way beyond the audio band. But you don't get it for free - there is still a sinc rolloff in the Bode plot (amplitude/frequency). That is why non-OS DACs that do not employ corrective analog post-filters are not flat across the band. Some non-OS designs will correct for this, some (like me) go on the assumption that this is not a big deal and that phase error due to correction filters muck up the beautiful effects of non-OS so it's not worth it to do it.

Before I forget - I wanted to ask - have you gotten your trial dAck! yet?

-Chris


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Topic - upsampling article - solidgore 08:08:38 08/22/03 ( 47)