IPR-FFT Altera, IPR-FFT Datasheet - Page 57

• 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

Appendix A: Block Floating Point Scaling
Achieving Unity Gain in an IFFT+FFT Pair
© December 2010 Altera Corporation
f
Figure A–2. Derivation to Achieve IFFT/FFT Pair Unity Gain
where:
Any scaling operation on X0 followed by truncation loses the value of exp1 and does
not result in unity gain at x0. Any scaling operation must be done on X0 only when it
is the final result. If the intermediate result X0 is first padded with exp1 number of
zeros and then truncated or if the data bits of X0 are truncated, the scaling information
is lost.
One way to keep unity gain is by passing the exp1 value to the output of the FFT
block. The other way is to preserve the full precision of data1×2
value as input to the FFT block. The disadvantage of the second method is a large size
requirement for the FFT to accept the input with growing bit width from IFFT
operations. The resolution required to accommodate this bit width will, in most cases,
exceed the maximum data width supported by the core.
For more information, refer to the Achieving Unity Gain in Block Floating Point
IFFT+FFT Pair design example under DSP Design Examples at www.altera.com.
x0 = Input data to IFFT
X0 = Output data from IFFT
N = number of points
data1 = IFFT output data and FFT input data
data2 = FFT output data
exp1 = IFFT output exponent
exp2 = FFT output exponent
IFFTa = IFFT
FFTa = FFT
x0
IFFT
X0 = IFFT ( x0 )
=
=
N
N
1
1
× IFFTa ( x0 )
× data1 × 2
– exp1
FFT
x0 = FFT ( X0 )
= FFT (
=
=
=
N
N
N
1
1
1
× 2
× 2
× 2
FFT MegaCore Function User Guide
N
1
– exp 1
– exp1
– exp 1
–
× data1 × 2
exp1 and use this
× data2 × 2
– exp2
× FFTa ( data1 )
× data2
– exp1
– exp2
)
A–5