FFT IP Core: User Guide

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ID 683374
Date 11/06/2017
Public
Document Table of Contents
Document Table of Contents x
1. About This IP Core 2. FFT IP Core Getting Started 3. FFT IP Core Functional Description 4. Block Floating Point Scaling 5. Document Revision History A. FFT IP Core User Guide Document Archive
1. About This IP Core x
1.1. Intel® DSP IP Core Features 1.2. FFT IP Core Features 1.3. General Description 1.4. DSP IP Core Device Family Support 1.5. DSP IP Core Verification 1.6. FFT IP Core Release Information 1.7. Performance and Resource Utilization
1.3. General Description x
1.3.1. Fixed Transform Size FFT 1.3.2. Variable Streaming FFT
2. FFT IP Core Getting Started x
2.1. Installing and Licensing Intel® FPGA IP Cores 2.2. IP Catalog and Parameter Editor 2.3. Generating IP Cores ( Intel® Quartus® Prime Pro Edition) 2.4. Generating IP Cores ( Intel® Quartus® Prime Standard Edition) 2.5. Simulating Intel® FPGA IP Cores 2.6. DSP Builder for Intel® FPGAs Design Flow
2.1. Installing and Licensing Intel® FPGA IP Cores x
2.1.1. Intel® FPGA IP Evaluation Mode 2.1.2. FFT IP Core Intel® FPGA IP Evaluation Mode Timeout Behavior
2.3. Generating IP Cores ( Intel® Quartus® Prime Pro Edition) x
2.3.1. IP Core Generation Output ( Intel® Quartus® Prime Pro Edition)
2.4. Generating IP Cores ( Intel® Quartus® Prime Standard Edition) x
2.4.1. IP Core Generation Output ( Intel® Quartus® Prime Standard Edition)
2.5. Simulating Intel® FPGA IP Cores x
2.5.1. Simulating the Fixed-Transform FFT IP Core in the MATLAB Software 2.5.2. Simulating the Variable Streaming FFT IP Core in the MATLAB Software
3. FFT IP Core Functional Description x
3.1. Fixed Transform FFTs 3.2. Variable Streaming FFTs 3.3. FFT Processor Engines 3.4. I/O Data Flow 3.5. FFT IP Core Parameters 3.6. FFT IP Core Interfaces and Signals
3.2. Variable Streaming FFTs x
3.2.1. Fixed-Point Variable Streaming FFTs 3.2.2. Floating-Point Variable Streaming FFTs
3.3. FFT Processor Engines x
3.3.1. Quad-Output FFT Engine 3.3.2. Single-Output FFT Engine
3.4. I/O Data Flow x
3.4.1. Streaming FFT 3.4.2. Variable Streaming 3.4.3. Buffered Burst 3.4.4. Burst
3.4.1. Streaming FFT x
3.4.1.1. Using the Streaming FFT 3.4.1.2. Changing the Direction on a Block-by-Block Basis 3.4.1.3. Enabling the Streaming FFT
3.4.2. Variable Streaming x
3.4.2.1. Changing Block Size 3.4.2.2. Changing Direction 3.4.2.3. I/O Order 3.4.2.4. Enabling the Variable Streaming FFT 3.4.2.5. Dynamically Changing the FFT Size 3.4.2.6. I/O Order
3.4.3. Buffered Burst x
3.4.3.1. Enabling the Buffered Burst FFT
3.6. FFT IP Core Interfaces and Signals x
3.6.1. Avalon-ST Interfaces in DSP IP Cores 3.6.2. FFT IP Core Avalon-ST Signals
3.6.2. FFT IP Core Avalon-ST Signals x
3.6.2.1. Component Specific Signals
4. Block Floating Point Scaling x
4.1. Possible Exponent Values 4.2. Implementing Scaling 4.3. Unity Gain in an IFFT+FFT Pair
4.2. Implementing Scaling x
4.2.1. Example of Scaling
1. About This IP Core
2. FFT IP Core Getting Started
3. FFT IP Core Functional Description
4. Block Floating Point Scaling
5. Document Revision History
A. FFT IP Core User Guide Document Archive

4.1. 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{log4N}, where N is the transform length

R = 0 if log2N is even, otherwise R = 1

Single output range = (–3P+R, P+R–4)

Quad output range = (–3P+R+1, P+R–7)

These equations translate to the values in Table A–1.

Table 13.  Exponent Scaling Values for FFT / IFFT      (1)
N P Single Output Engine Quad Output Engine
Max  (2) Min  (2) Max  (2) Min  (2)
64 3 –9 –1 –8 –4
128 4 –11 1 –10 –2
256 4 –12 0 –11 –3
512 5 –14 2 –13 –1
1,024 5 –15 1 –14 –2
2,048 6 –17 3 –16 0
4,096 6 –18 2 –17 –1
8,192 7 –20 4 –19 1
16,384 7 –21 3 –20 0
Note to Table A–1 :
  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.
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