Abstract: The Poorman's Transform: Approximating the 
          Fourier Transform without multiplication

Appeared: IEEE Transactions in Signal Processing, Vol 41, No. 3, 1993.

A time domain to frequency domain transformation for sampled signals is
described, which is computed with only additions and trivial complex
multiplications.  This Poorman's transform is an
approximation to the usual Fourier transform, obtained by quantizing the
Fourier coefficients to the four values  $\{ \pm 1, \pm j \}$, 
and is especially useful when multiplication is expensive.
For the general case of an $N$-point quantization, an analytic formula is given
for the error in the approximation, which involves only contributions from
aliased harmonics. Continuous time signals are considered, where the 
approximation is exact for band-limited signals.


Michael Lamoureux
University of Calgary