  In this paper we establish the accuracy and robustness of a fast estimator
for the bispectrum - the "FFT bispectrum estimator". The implementation of the
estimator presented here offers speed and simplicity benefits over a direct
sampling approach. We also generalise the derivation so it may be easily be
applied to any order polyspectra, such as the trispectrum, with the cost of
only a handful of FFTs. All lower order statistics can also be calculated
simultaneously for little extra cost. To test the estimator we make use of a
non-linear density field, and for a more strongly non-Gaussian test case we use
a toy-model of reionization in which ionized bubbles at a given redshift are
all of equal size and are randomly distributed. Our tests find that the FFT
estimator remains accurate over a wide range of k, and so should be extremely
useful for analysis of 21-cm observations. The speed of the FFT bispectrum
estimator makes it suitable for sampling applications, such as Bayesian
inference. The algorithm we describe should prove valuable in the analysis of
simulations and observations, and whilst we apply it within the field of
cosmology, this estimator is useful in any field that deals with non-Gaussian
data.
