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Digital Filter Sample Rate

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dknguyen

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For an FIR filter, are there any benefits to sampling at a rate greater than double the frequency of your desired output bandwidth? For example, a low-pass filter with a cut off of 100Hz...is there any benefit to sampling at greater than 200Hz?
 

crutschow

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Depending upon the type of signal you are sampling, there could be aliased noise. What is the signal source? Is it an A/D converter and, if so, what is it's sample rate?
 

dknguyen

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It's an AD converter, but why don't we just assume that we have a set of digitally sampled data points that have already been filtered enough so there is no aliasing (and let's forget about high frequency noise for now too). But not we want to digitally filter it to feed it into a system that has even lower bandwidth than the original, unaliased set of sampled data.

I'm wondering more along the lines of whether or not there is an increase in accuracy or anything like that (ie. sampleing a signal at double it's bandwidth will allow you to redraw a unique signal based on sampled points...but it won't be as close a representation to the actual signal as if you sampled it by 16x the sample rate).
 
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crutschow

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If you have a sampled signal with frequency components higher than your filter freqeuncy, then they will be aliased into the passband if you try to subsample the data. If you think about it, it's the same as if you were to sample the original data at the lower sample rate without an antialias filter. So your filter sample rate should be the same as your orignal data rate to minimize aliasing.

As for the question of fidelity of signal, sampling at just over twice the highest frequency of interest preserves amplitude data in the passband, but not phase information. That's one argument that the audio fanatics use against CD recordings as compared to vinyl. So it just depends upon whether signal phase information is important to you.
 

dknguyen

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Okay. Let's say i have am receiving unaliased data samples from a filtered ADC with a bandwidth of 100Hz at a rate 1600 samples per second.

This data needs to fed into a control loop, but the control loop only has a bandwidth (or reaction speed) of 50Hz, so I want to filter this data down to 50Hz before feeding it into the control loop, but *NO DOWNSAMPLING* is occuring. The control loop will still be processing the samples at 1600 samples per second.

My question is, is there any advantage to keeping the ADC output data rate at 1600Hz as opposed to simply lowering it to 200Hz (and having the control loop process the samples at a rate of 200Hz)?

(You are saying that the 1600Hz data rate will preserve the phase data better than the 200Hz data rate?)

Another scenario is if the same 100Hz bandwidth, 1600sps ADC only had it's output data read at 200Hz so that only 1 out of every 8 samples were used and the rest thrown away. Apparently this would cause aliasing and is why decimation filters exist...but I don't understand why throwing away the other 7 samples would cause aliasing in this case since the effective sample rate is 200Hz and the bandwidth of the signal was only 100Hz to begin with.
 
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crutschow

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You can safely under-sample as long as the 1600sps data has no significant signal or noise above 1/2 the under-sample rate, in other words, it has a low-pass analog filter on the A/D input that suppresses any signal or noise above that point (1/2 the under-sample frequency) to below your desired noise level. (It's the same as if you were operating the converter at the under-sample frequency to begin with.)

As far as the phase information, it mostly affects the phase of the higher frequency components, similar to a low-pass filter.
 
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