This is the linking error:

C:\Qt\2009.04\mingw\bin\..\lib\gcc\mingw32\3.4.5\. .\..\..\..\mingw32\bin\ld.exe: cannot find -llibfftw3-3
collect2: ld returned 1 exit status
In my project, there is a .pro file and a subdirectory named lib that contains all the DLL's required for the project. If a full path is specified, it works, but I've been unable to use any form of a relative path.

None of these have worked:
LIBS += -Llib -llibfftw3-3
LIBS += -L./lib -llibfftw3-3
LIBS += -L".\lib" -llibfftw3-3

but LIBS += -LC:/TheProject/lib -libfftw3-3 works like a charm.