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Decimating

Started by Luis Fernando July 8, 2004
In <fb78d2e7.0407090927.50acf218@posting.google.com> Luis Fernando wrote:
> 1) why is it necessary to run a filter when I upsample? I won't be > generating any high frequency doing this, will I?
Maybe this will help. You're probably aware that a digital signal has aliased images that mirror and repeat--that is the reason we need to apply a low pass filter ("anti-imaging filter", "reconstruction filter", etc.) when we convert to analog. You've probably seen frequency graphs that look something like this (use a fixed-width font): 0 a b c d | | | | | ______ ___________ __________ ... \ / \ / \ / \ / It goes in the negative direction too, but here I'm showing the positive half, starting at 0 Hz. Your nice audio content is in the band of 0 though a, and your sample rate is b. (If you converted this signal to analog, you would follow the D/A with a low pass filter with a cutoff at a.) If you double the sample rate without doing anything else, you've simply moved the sample rate to d, increasing the available working bandwidth from 0-a to 0-b. So you can see that you have now "revealed" the aliasing in the area from a to b. You need to low pass filter with a cutoff at a to get rid of that aliased image before applying your non- linear processing. So the answer is that while you haven't generated any new high frequencies, you've widened the audio band so that frequencies that were above the audio band before are now in the new audio band.