Choosing FFT convolution lengths

On Sun, 20 Feb 2011 12:32:20 -0600, "plarser48"
<plarser48@n_o_s_p_a_m.gmail.com> wrote:

>Thank you all for the very informative and welcoming replies!
>
>I understand that a wireless channel usually a low number of time-domain
>filter tap coefficients to model the multipath and/or propagation effects.
>But there were some concepts that I wasn't sure how you get around not
>having a long-length filter. 
>
>(1) I was reading a section in Rappaport's Wireless Communications (2nd ed)
>book labeled "Frequency Domain Channel Sounding", whereby one sweeps across
>frequencies, and measuring the response across a channel at varying
>frequency ranges. From there an inverse DFT of the S-parameter (Y/X) is
>determined to create a time-domain representation of the channel. I think I
>am confused. If I were to sweep across hundreds of frequencies, wouldn't I
>end up with a very long-length filter resembling the channel from this
>sounding technique? 

You have to keep track of what comes out of the process.   Wireless
channel "delay spread" times, i.e., the length of the channel impulse
response, runs from hundreds of nanoseconds for indoor channels to
tens of microseconds for high-power outdoor channels.  Your channel
filter doesn't have to be any longer than that.   You may get more
samples out of the process than that, but they'll all be zero or of
negligible energy.

>(2) Or in another application, consider an audio speaker without any
>wireless channel effects. A spec sheet may provide the frequency response
>of that speaker. Would it be possible to invert that frequency response
>such that if a chirp was passed through it, there'd be a flat response?
>i.e. if at 15 kHz there is a -3dB drop in power caused by the speaker, have
>a pre-filter that boosts 15kHz by 3dB to offset the effect? If so, then
>would a long-length filter be needed to catch the full dynamics of the
>frequency response of that speaker, or is there another method?
>
>Thanks again!

Eric Jacobsen
http://www.ericjacobsen.org
http://www.dsprelated.com/blogs-1//Eric_Jacobsen.php

>Speaker inversion/EQ filters are often indeed quite long.  Not least 
>because the four or so octaves that they have to operate across and the 
>notchiness typical.  The point to understand is that this is not a 
>problem.  There is almost never a suggestion that the signal is time-
>limited, and never a requirement that the response be limited to the same

>time.  (Because it isn't.)

I don't know if there is *never* a requirement for a limited response. For
an example of a time-limited signal, how about an acoustic (or ultrasonic)
rangefinding/radar application? The time-limited signal can be a LFM or a
coded waveform. And a inversion filter can be used to remove and distortion
caused by the speaker or transducer. In that case, the response may be
limited to the same time to maintain system requirements (distance bounds,
dwell timing, etc)?