Interpolate/Decimate with a single filter? This is not a homework question (I'm out of school now 2 years). I'm thinking, let's say you have 2 systems, one at 32khz and the other at 48khz and you want to go between the two. Is there a way to accomplish this with a single filter? I have a feeling that if you make an FIR where every other coefficient is zero and exploit the fact that if fs = 32khz and 48-32=16=fs/2, then zeroing out every other coefficient of an FIR (but how many taps) would do both the zero-padding and the anti-aliasing simultaneously. Am I on the right track or is there some other trickery involved?

EDIT:

Now that I think about it, to go from 32khz to 48khz you interpolate 3x and decimate 2x (32*3=96khz...96/2=48). So in effect you would pad two zeros first but then take out one in the decimation, but just inserting one zero would yield 64khz decimation (with a 32khz lowpass decimation). 

EDIT 2:

Furthermore, wikipedia interpolation:
"Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. For the L > M case, the interpolation filter cutoff,  \tfrac{0.5}{L} cycles per intermediate sample, is the lower frequency."
Yes, you can interpolate and decimate at the same time.  This is called "resampling".  If you google resampling you will find lots of information about it.  And yes, your reasoning about resampling is mostly correct.

When thinking about resampling theoretically you usually put the interpolation first to avoid Nyquist issues.  An interpolator is upsampling followed by a low-pass filter to get rid of the aliases.  A decimator is a low-pass filter followed by dropping samples.  You can combine the two by combining the two low-pass filters into one filter.  If the overall rate change is greater than one, the low-pass filter has the same pass-band/cutoff as the interpolation filter.  If the overall rate change is less than one then it has the same pass-band/cutoff as the decimation filter.  The filter operates at the interpolation sample rate.

You can make the filter more efficient by not actually upsampling the data or dropping filter outputs.  Instead, you use a polyphase filter for the interpolation and simply not calculate the results that will be dropped, but that is a topic for another day and another question.