参数资料
型号: IP-FFT
厂商: Altera
文件页数: 65/70页
文件大小: 0K
描述: IP FFT/IFFT
标准包装: 1
系列: *
类型: MegaCore
功能: 快速傅里叶变换处理器
许可证: 初始许可证
Appendix A: Block Floating Point Scaling
A–5
Achieving Unity Gain in an IFFT+FFT Pair
Figure A–2 on page A–5 shows the operation of IFFT followed by FFT and derives the
equation to achieve unity gain.
Figure A–2. Derivation to Achieve IFFT/FFT Pair Unity Gain
IFFT
FFT
x0
X0 = IFFT(x0)
x0 = FFT(X0)
× data1 × 2
–exp1
=
1
× IFFTa (x0)
= FFT(
1
)
N
N
× data1 × 2
× FFTa (data1)
=
1
N
–exp1
=
1
N
×2
–exp1
–exp1
=
1
×2
× data2 × 2
–exp2
N
–exp1 –exp2
=
1
×2
× data2
N
where:
x 0 = Input data to IFFT
X 0 = 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
Any scaling operation on X 0 followed by truncation loses the value of exp1 and does
not result in unity gain at x0 . Any scaling operation must be done on X 0 only when it
is the final result. If the intermediate result X 0 is first padded with exp1 number of
zeros and then truncated or if the data bits of X 0 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 – exp1 and use this
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.
f 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 .
November 2013
Altera Corporation
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