Finding Support for Spectral Decimation Section
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Informal research notes by Phil dated 3.17.13, written to find support for the spectral decimation section of his spectral theory book. He reviews web sources on oversampled DAC interpolation filters, polyphase and multistage filter implementations, and the DSP Guru definition of decimation. He concludes that what he was calling decimation is really zero-stuffing. Figures from the sources are not captured in the text.
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Finding Support for Spectral Decimation Section PhL 3.17.13
www.analog.com/static/imported-files/tutorials/MT-017.pdf
This paper draws this picture,
which suggested to me two things:
(1) there is no decimation here.
(2) my brick wall filter in this context is called an "interpolation filter".
http://www.scribd.com/doc/20203269/Interpolation-filters-for-oversampled-audio-DACs
This paper is cannot be downloaded without paying, but you can see it. Early comment:
He refers to decimation as "zero-stuffing" but he does not say why one might do this. Also, it seems wrong that the two signals shown have the same spectrum, I think this might be wrong.
What I find is that decimation broadens the sinc function which has good and bad news. The good news is that you have less sinx/x distortion on the central peak, but the bad news is that you have added a lot of closer in image spectra! That is what decimation does, and I want to find someone who agrees with me.
Another figure is this one:
What do these notations mean? Here it is again
I think the leftmost box does both decimation and Low pass filter. As for filter implementation,
He shows how you can do this with a polyphase idea to reduce hardware, seems reasonable. It is a good paper, but I need another source.
www.hit.bme.hu/~papay/edu/Conv/pdf/Jonas.pdf
This guy also uses an up arrow
He doesn't say if the box does zero-stuffing or not.
http://books.google.com/books?id=Kvo7cjmaEpkC&pg=PA391&lpg=PA391&dq=decimation+oversampling+DAC&source=bl&ots=77M7ekBiLK&sig=9YGbS-d2F29NKcbIrhzZcLDD3HE&hl=en&sa=X&ei=zytGUceiEuj7ygG_s4DABA&ved=0CGAQ6AEwCA#v=onepage&q=decimation%20oversampling%20DAC&f=false
This one has an interesting idea of doing a filter in stages,
Each stage runs 2x faster than the one before. Fast clock uses more power, but filters have fewer taps so less power. I like it. What is the rule of "sample and hold" here?
http://www.dspguru.com/dsp/faqs/multirate/decimation
Loosely speaking, "decimation" is the process of reducing the sampling rate. In practice, this usually implies lowpass-filtering a signal, then throwing away some of its samples.
The most immediate reason to decimate is simply to reduce the sampling rate at the output of one system so a system operating at a lower sampling rate can input the signal. But a much more common motivation for decimation is to reduce the cost of
So I am using decimation incorrectly! I am really doing zero-stuffing.