  Differential Dynamic Microscopy (DDM) is the combination of optical
microscopy to statistical analysis to obtain information about the dynamical
behaviour of a variety of samples spanning from soft matter physics to biology.
In DDM, the dynamical evolution of the samples is investigated separately at
different length scales and extracted from a set of images recorded at
different times. A specific result of interest is the structure function that
can be computed via spatial Fourier transforms and differences of signals. In
this work, we present an algorithm to efficiently process a set of images
according to the DDM analysis scheme. We bench-marked the new approach against
the state-of-the-art algorithm reported in previous work. The new
implementation computes the DDM analysis faster, thanks to an additional
Fourier transform in time instead of performing differences of signals. This
allows obtaining very fast analysis also in CPU based machine. In order to test
the new code, we performed the DDM analysis over sets of more than 1000 images
with and without the help of GPU hardware acceleration. As an example, for
images of $512 \times 512$ pixels, the new algorithm is 10 times faster than
the previous GPU code. Without GPU hardware acceleration and for the same set
of images, we found that the new algorithm is 300 faster than the old one both
running only on the CPU.
