Centar LLC is a provider of fast Fourier transform (FFT) intellectual property (IP) for use in FPGA and ASICbased embedded applications. It has developed a novel parallel matrixbased formulation of the discreet Fourier transform (DFT), which decomposes it into structured sets of
bpoint discreet Fourier transforms. All FFT circuits are constructed from synchronous, finegrained, locally connected, regular arrays of small processing elements (PEs), consisting of a few registers, some multiplexors and an arithmetic element. Salient features of this technology are:
 Speed: The only FPGA FFT circuits with clock rates >500MHz using 65nm technology (e.g., Altera Stratix III).
 Throughput: Data rates as high as ~10G complex samples per second
 Dynamic Range: Combined block floating point and floating point architecture means smaller word lengths can be used
for post processing operations such as equalization.
 Programmability: Easy customization of FFT properties, functionality and I/O interface.
 Nonpowersoftwo transform sizes: A single ROM memory can store control parameters to support any number or size FFTs
 Scalability: Faster transforms can be implemented without architectural changes by increasing the array size along one dimension or duplicating the array structure
 Power: Interconnects are entirely local, reducing parasitic routing capacitances to keep power dissipation low and speed high
 Cyclic Prefix: Circuit architecture is designed to support any prefix value (most FFT circuits require additional circuits to perform this function)
Products
 Poweroftwo FFT: Fixed and variable (runtime selectable) size, 16 to 16,384 points.

Altera 
Centar v1 
Centar v2 
Altera 
Centar 
Transform Size 
256pts 
1024pts 
ALMs/M9Ks 
4414/38 
4024/31 
5063/15 
4770/38 
4357/31 
Transform Time (usec) 
0.68 
0.48 
0.45 
2.72 
1.92 
SQNR 
76.6 
86.7 
86.7 
81.3 
82.9 
mJ/FFT 
1.29 
1.12 

6.36 
4.31 
Example: comparative metrics for "streaming" circuits targeted to
65nm Stratix III FPGAs (C2 speed grade).
 Nonpoweroftwo FFT: The reachable transform sizes for this class of designs are those that can be factored into a composite form based on small integers up to sizes of ~10. For example, the SCFDMA LTE requirements would use the integers {2,3,5} to compute all 35 transform sizes, e.g., N=2^{n}3^{m}5^{q}, where n,m, and q are integers. These can be fixedsize or variable and selectable at runtime.

Average Latency 
Average Throughput 
Resource Block Computation Time 
1200 point Computation Time 
Altera 
2.1 
0.33 
3.0 
2.8 
Xilinx 
1.2 
0.46 
2.1 
2.0 
Centar 
1.0 
1.0 
1.0 
1.0 
Example: LTE SCFDMA relative performance for 65nm FPGA technology (average over 35 different DFT sizes).
Tools
Because there are always a large number of (parallel) circuit architectures that can be obtained from an algorithm specification, Centar has developed an automated CAD tool, Symbolic Parallel Algorithm Development Environment (SPADE), to make the best choices. SPADE is the only such tool in existence that can find latency optimal circuits.