Fast Fourier Transform Implementation for High Speed
Astrophysics Applications on FPGAs
Tomasz S. Czajkowski, Christopher J. Comis, Mohamed Kawokgy
Edward S. Rogers Department of Electrical and Computer Engineering
University of Toronto, 10 King’s College Road, Toronto, Ontario, M5S 3G4, Canada
{czajkow|comis}@eecg.toronto.edu, kawokgy@vrg.utoronto.ca
Abstract
Research in astrophysics requires high-speed logic circuits to perform real time signal
processing. A common algorithm used in signal processing is the Fast Fourier Transform
(FFT). In this research we have created two distinct FFT implementations targeting small
to medium size Altera Stratix FPGAs. The first implementation focuses on lowering the
number of used built-in multipliers by using only a single complex multiplier in each
stage of the algorithm. The second approach shows an implementation of the algorithm to
lower the latency of the circuit by using several multipliers in parallel in each stage of the
FFT to speed up computation. While both approaches work, the designer may want to
decide which implementation to use based on costs associated with obtaining a device
that can facilitate each of FFT algorithms implementations.
We successfully implemented the architecture with a single complex multiplier per stage,
as this architecture was feasible given our design constraints. We discuss the
methodology used to create this design. Also the results in terms of speed and resource
utilization of the design are discussed.
1. Introduction
One of the most important contributions of Astrophysical research is the discovery of
when major events in the Universe took place. One of such discoveries relates to the
moment in the life of the Universe when it became ionized. To determine various facts
about the Universe, the electromagnetic radiations received on Earth from objects moving
through space, such as Hydrogen I, or HI, particles as they travels away from Earth, need
to be examined.
It is know that stationary HI emits electromagnetic radiation with the frequency of
approximately 1.4GHz [1]. However, as the HI moves through space the frequency of
received radiation is altered due to the Doppler Effect, also known as Doppler Shift [1].
As HI moves away from the earth, it is expected that the frequency of its radiation to be
reduced, or red-shifted, to somewhere between 70MHz and 200MHz, as a result of the
Doppler Effect. To determine the frequency of radiation, we need to sample the
waveform received from atmosphere, at least at twice its maximum frequency, to satisfy
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