# FFT - 2020.2 English

## Vivado Design Suite Reference Guide: Model-Based DSP Design Using System Generator (UG958)

Document ID
UG958
Release Date
2020-11-18
Version
2020.2 English

This block is listed in the following Xilinx® Blockset libraries: DSP, Floating-Point, and Index.

The Xilinx FFT (Fast Fourier Transform) block takes a block of time domain waveform data and computes the frequency of the sinusoid signals that make up the waveform.

FFT is a fast implementation of the discrete Fourier transform. The data of the time domain signal is sampled at discrete intervals. The sampling frequency is twice the maximum frequency that can be resolved by the FFT, based on the Nyquist theorem. If a signal is sampled at 1 kHz, the highest frequency that can be resolved by the FFT is 500 Hz.

fs = fmax/2

where fmax = maximum resolvable frequency and fs = sampling frequency.

The duration of the data sample is inversely proportional to the frequency resolution of the FFT. The longer the sample duration, the higher the number of data points, and the finer the frequency resolution. If a signal sampled at fs for twice the duration, the difference between successive frequency df is halved, resulting in an FFT with finer frequency resolution.

df = 1/T

where df = frequency resolution of the FFT, and T= total sampling time.

The number of samples taken over time T is N, so sampling frequency is N/T samples/sec.

## Description

FFT is a computationally efficient implementation of the Discrete Fourier Transform (DFT). A DFT is a collection of data points detailing the correlation between the time domain signal and sinusoids at discrete frequencies.

The DFT is defined by the following equation:

where N is the transform length, k is used to denote the frequency domain ordinal, and n is used to represent the time-domain ordinal.

The FFT block is ideal for implementing simple Fourier transforms. If your FFT implementation will use more complicated transform features such as an AXI4-Stream-compliant interface, a real time throttle scheme, Radix-4 Burst I/O, or Radix-2 Lite Burst I/O, use the Xilinx Fast Fourier Transform 9.1 block in your design instead of the FFT block.

In the Vivado® design flow, the FFT block is inferred as "LogiCORE IP Fast Fourier Transform v9.1" for code generation. Refer to the document LogiCORE IP Fast Fourier Transform v9.1 for details on this LogicCore IP.

## Block Parameters

The block parameters dialog box can be invoked by double-clicking the icon in your Simulink® model.

Parameters specific to the Xilinx FFT block are as follows.

Transform Length
Select the desired point size ranging from 8 to 65536.
Scale Result by FFT length
If selected, data is scaled between FFT stages using a scaling schedule determined by the Transform Length setting. If not selected, data is unscaled, and all integer bit growth is carried to the output.
Natural Order
If selected, the output of the FFT block will be ordered in natural order. If not selected, the output of the FFT block will be ordered in bit/digit reversed order.
Optimize for
Directs the block to be optimized for either speed (Performance) or area (Resources) in the generated hardware.
Note: If Resources is selected and the input sample period is 8 times slower than the system sample period, the block implements Radix-2 Burst I/O architecture. Otherwise, Pipeline Streaming I/O architecture will be used.
Optional Port
Provide start frame port
Adds `start_frame_in` and `start_frame_out` ports to the block. The signals on these ports can be used to synchronize frames at the input and output of the FFT block. See Adding Start Frame Ports to Synchronize Frames for a description of the operation of these two ports.

## Context Based Pipeline vs. Radix Implementation

Pipelined Streaming I/O and Radix-2 Burst I/O architectures are supported by the FFT block. Radix-4 Burst I/O architecture is implemented when you select Optimize for: Resources block parameter and the sample rate of the inputs is 8 times slower than the system rate. In all other configurations Pipelined Streaming I/O architecture is implemented by default.

## Input Data Type Support

The FFT block accepts inputs of varying bit widths with changeable binary point location, such as Fix_16_0 or Fix_30_10, etc. in unscaled block configuration. For the scaled configuration, the input is supported in the same format as the Fast Fourier Transform 9.1 block. The Fast Fourier Transform 9.1 block accepts input values only in the normalized form in the format of Fix_x_[x-1] (for example, Fix_16_15), so the inputs are 2's complement with a single sign/integer bit.

## Latency Value Displayed on the Block

The latency value depends on parameters selected by the user, and the corresponding latency value is displayed on the FFT block icon in the Simulink model.

## Automatic Fixed Point and Floating Point Support

Signed fixed point and floating point data types are supported.

For floating point input, either scaled or unscaled data can be selected in the FFT block parameters. In the Fast Fourier Transform 9.1 block, the floating point data type is accepted only when the scaled configuration is selected by the user.

## Handling Overflow for Scaled Configuration

The FFT block uses a conservative schedule to avoid overflow scenarios.This schedule sets the scaling value for the corresponding FFT stages in a way that makes sure no overflow occurs.

## Adding Start Frame Ports to Synchronize Frames

Selecting Provide start frame port in the FFT block properties dialog box adds `start_frame_in` and `start_frame_out` ports at the input and output of the FFT block. These ports are used to synchronize frames at the input and output of the FFT block.

Figure 1. Adding Start Frame Ports

You must provide a valid input at the `start_frame_in` port. When the `start_frame_in` signal is asserted, an impulse is generated at the start of every frame to signal the FFT block to start processing the frame. The frame size is the Transform Length entered in the block parameters dialog box.

The `start_frame_out` port provides the information as to when the output frames start. An impulse at the start of every frame on the output side helps in tracking the block behavior.

The FFT block has a frame alignment requirement and these ports help the block operate in accordance with this requirement.

The figure below shows that as soon as the output is processed by the FFT block the `start_frame_out` signal becomes High (1).

Figure 2. Output

The following apply to the Provide start frame port option and the start frame ports added to the FFT block when the option is enabled:

• The Provide start frame port option selection is valid only for Pipelined Streaming I/O architecture. See Context Based Pipeline vs. Radix Implementation for a description of the conditions under which Pipelined Streaming I/O architecture is implemented.
• The option is valid only for input of type fixed point.
• Verilog is supported for netlist generation currently, when the Provide start frame port option is selected.
Note: The first sample input to the FFT block may be ignored and users are advised to drive the input data accordingly.