IPR-FFT Altera, IPR-FFT Datasheet - Page 35

• Manufacturer Part Number: IPR-FFT
• Description: IP CORE Renewal Of IP-FFT
• Manufacturer: Altera
• Type: MegaCorer

Specifications of IPR-FFT

• Software Application: IP CORE, DSP Filters And Transforms
• Supported Families: Arria GX, Cyclone, HardCopy, Stratix
• Features: Bit-Accurate MATLAB Models, Radix-4 And Mixed Radix-4/2 Implementations
• Core Architecture: FPGA
• Core Sub-architecture: Arria, Cyclone, Stratix
• Rohs Compliant: NA
• Function: Fast Fourier Transform Processor
• License: Renewal License
• Lead Free Status / RoHS Status: na
• Lead Free Status / RoHS Status: na

Buffered, Burst, & Streaming Architectures
© December 2010 Altera Corporation
1
The discrete Fourier transform (DFT), of length N, calculates the sampled Fourier
transform of a discrete-time sequence at N evenly distributed points
the unit circle.
The following equation shows the length-N forward DFT of a sequence x(n):
The following equation shows the length-N inverse DFT:
The complexity of the DFT direct computation can be significantly reduced by using
fast algorithms that use a nested decomposition of the summation in equations one
and two—in addition to exploiting various symmetries inherent in the complex
multiplications. One such algorithm is the Cooley-Tukey radix-r decimation-in-
frequency (DIF) FFT, which recursively divides the input sequence into N/r sequences
of length r and requires log
Each stage of the decomposition typically shares the same hardware, with the data
being read from memory, passed through the FFT processor and written back to
memory. Each pass through the FFT processor is required to be performed log
times. Popular choices of the radix are r = 2, 4, and 16. Increasing the radix of the
decomposition leads to a reduction in the number of passes required through the FFT
processor at the expense of device resources.
The MegaCore function does not apply the scaling factor 1/N required for a length-N
inverse DFT. You must apply this factor externally.
A radix-4 decomposition, which divides the input sequence recursively to form
four-point sequences, has the advantage that it requires only trivial multiplications in
the four-point DFT and is the chosen radix in the Altera FFT MegaCore function. This
results in the highest throughput decomposition, while requiring non-trivial complex
multiplications in the post-butterfly twiddle-factor rotations only. In cases where N is
an odd power of two, the FFT MegaCore automatically implements a radix-2 pass on
the last pass to complete the transform.
where k = 0, 1, ... N – 1
where n = 0, 1, ... N – 1
x n ( )
r
N stages of computation.
X k [ ]
=
=
(
1 N ⁄
N 1
n

=
–
)
k
N 1

0
=
x n ( )e
–
0
X k [ ]e
3. Functional Description
– (
j2πnk
(
j2πnk
) N ⁄
) N ⁄
FFT MegaCore Function User Guide
ω
k = 2
π
k/N on
r
N