How to use a microphones' impulse response to correct recordings made with it (in MATLAB)?

I have the impulse response IR (time domain) of a recording microphone
(actually a whole set of IRs for the full range of angles of sound
incidence).
I also have recordings of animal vocalisations (from known angles of
sound incidence) made with that microphone.
Now I want to use MATLAB to calculate what the initial signal looked
like (in the time domain) by removing the amplitude and phase effects
caused by the mic.
As I am not an engineer myself, I would highly appreciate some
explanations. Some MATLAB code would perhaps help a lot too.
Thanks a lot to anybody who is able and willing to help me.

mholderi@biologie.uni-erlangen.de wrote:

> I have the impulse response IR (time domain) of a recording microphone
> (actually a whole set of IRs for the full range of angles of sound
> incidence).
> I also have recordings of animal vocalisations (from known angles of
> sound incidence) made with that microphone.
> Now I want to use MATLAB to calculate what the initial signal looked
> like (in the time domain) by removing the amplitude and phase effects
> caused by the mic.
> As I am not an engineer myself, I would highly appreciate some
> explanations. Some MATLAB code would perhaps help a lot too.
> Thanks a lot to anybody who is able and willing to help me.

What you have recorded is the convolution of the original signal and the 
microphone's impulse response. You want to deconvolve the two. A nice 
book, "The Scientist and Engineer's Guide to Digital Signal Processing" 
by Steven W. Smith, is available on line at http://www.dspguide.com/

You will find a discussion of deconvolution on pages 179 and 180 in 
Chapter 9, and with more detail starting on page 300 in Chapter 17. Of 
course, you'll need to read other parts of the book to understand these; 
some of those are mentioned, but you will need to browse. If you aren't 
on a very tight budget, you'll probably buy the book instead of reading 
it on line or printing out all those PDFs.

Others here may suggest more references for you. You'll find the need to 
use and interpret FFTs, and to do arithmetic with complex numbers. There 
is more bibliography and tutorial stuff at http://www.dspguru.com

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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