参数资料
| 型号： | IP-FFT |
| 厂商： | Altera |
| 文件页数： | 62/70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 |
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A–2
Appendix A: Block Floating Point Scaling
Calculating Possible Exponent Values
Calculating Possible Exponent Values
Depending on the length of the FFT/IFFT, the number of passes through the radix
engine is known and therefore the range of the exponent is known. The possible
values of the exponent are determined by the following equations:
P = ceil{log 4 N }, where N is the transform length
R = 0 if log 2 N is even, otherwise R = 1
Single output range = (–3 P + R , P + R –4)
Quad output range = (–3 P + R +1, P + R –7)
Table A–1. Exponent Scaling Values for FFT / IFFT
Single Output Engine
Quad Output Engine
N
P
Max
Min
Max
Min
64
128
256
512
1,024
2,048
4,096
8,192
16,384
3
4
4
5
5
6
6
7
7
–9
–11
–12
–14
–15
–17
–18
–20
–21
–1
1
0
2
1
3
2
4
3
–8
–10
–11
–13
–14
–16
–17
–19
–20
–4
–2
–3
–1
–2
0
–1
1
0
(1) This table lists the range of exponents, which is the number of scale events that occurred internally. For IFFT, the
output must be divided by N externally. If more arithmetic operations are performed after this step, the division by
N must be performed at the end to prevent loss of precision.
(2) The maximum and minimum values show the number of times the data is shifted. A negative value indicates shifts
to the left, while a positive value indicates shifts to the right.
Implementing Scaling
To implement the scaling algorithm, follow these steps:
1. Determine the length of the resulting full scale dynamic range storage register. To
get the length, add the width of the data to the number of times the data is shifted
(the max value in Table A–1 ). For example, for a 16-bit data, 256-point Quad
Output FFT/IFFT with Max = –11 and Min = –3. The Max value indicates 11 shifts
to the left, so the resulting full scaled data width is 16 + 11, or 27 bits.
2. Map the output data to the appropriate location within the expanded dynamic
range register based upon the exponent value. To continue the above example, the
16-bit output data [15..0] from the FFT/IFFT is mapped to [26..11] for an exponent
of –11, to [25..10] for an exponent of –10, to [24..9] for an exponent of –9, and so on.
3. Sign extend the data within the full scale register.
November 2013 Altera Corporation
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