  We present an efficient frequency-based neural representation termed PREF: a
shallow MLP augmented with a phasor volume that covers significant border
spectra than previous Fourier feature mapping or Positional Encoding. At the
core is our compact 3D phasor volume where frequencies distribute uniformly
along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored
and efficient Fourier transform that combines both Fast Fourier transform and
local interpolation to accelerate na\"ive Fourier mapping. We also introduce a
Parsvel regularizer that stables frequency-based learning. In these ways, Our
PREF reduces the costly MLP in the frequency-based representation, thereby
significantly closing the efficiency gap between it and other hybrid
representations, and improving its interpretability. Comprehensive experiments
demonstrate that our PREF is able to capture high-frequency details while
remaining compact and robust, including 2D image generalization, 3D signed
distance function regression and 5D neural radiance field reconstruction.
