1. Algorithm simulation effect

This system has been developed on the Vivado2019.2 platform, and the Vivado2019.2 simulation results are as follows:

2. Algorithms involve an overview of theoretical knowledge

Fourier Transform (Fourier Transform) is an important signal processing technique, which is used to convert a time-domain signal into a frequency-domain representation and analyze the frequency components of the signal. FFT (Fast Fourier Transform) is an efficient Fourier transform algorithm that can accelerate the calculation process of Fourier transform. Given a time-domain discrete signal sequence $x[n]$, its Fourier transform $X[k]$ is defined as:

FFT is an efficient algorithm for calculating Fourier transform, which can reduce the computational complexity of Fourier transform. For a signal sequence of length $N=2^m$, where $m$ is an integer, the fast Fourier transform can be implemented by divide-and-conquer and butterfly operations. Among them, the divide and conquer method divides the signal into two subsequences, performs Fourier transform respectively, and then combines the results of the subsequences through the butterfly operation. 256-point FFT refers to the process of converting a time-domain signal sequence with a length of 256 into a frequency-domain representation. For a 256-point FFT, the signal sequence length $N=256$ can be computed efficiently using the Fast Fourier Transform algorithm.

The Verilog implementation of 256-point FFT Fourier transform based on FPGA is widely used in digital signal processing, communication system and image processing and other fields. Since FPGA has programmability and parallel computing capability, it can efficiently implement FFT algorithm, so it is widely used in embedded systems, communication systems and high-performance computing fields.

The Verilog implementation of 256-point FFT Fourier transform based on FPGA faces the following main difficulties:

Implementing the FFT module requires understanding and implementing the Fast Fourier Transform algorithm, including the butterfly operation and iterative calculation process. Algorithmic correctness and efficiency are critical to the success of the overall FFT implementation.

In the process of FPGA implementation, the limitation of FPGA resources needs to be considered. Because the FFT module requires a lot of computing and storage resources, how to complete the realization of 256-point FFT under the constraints of limited FPGA resources is a challenge.

Timing and parallelism are important considerations in FPGAs. The timing and parallel design of the FFT module directly affect the performance and stability of the entire implementation, and need to be carefully adjusted and optimized.

The Verilog implementation of 256-point FFT Fourier transform based on FPGA is an important signal processing technology, which is widely used in digital signal processing, communication system and image processing and other fields. Efficient implementation of 256-point FFT Fourier transform on FPGA platform.

3. Verilog core program

`timescale 1ns / 1ps

module TEST();
    
reg i_clk;
reg i_rst;
reg start;  
    
    
    
wire [15 : 0] m_axis_data_tdata;
dds_compiler_0 your_instance_name (
  .aclk(i_clk),                                  // input wire aclk
  .aresetn(~i_rst),                            // input wire aresetn
  .s_axis_config_tvalid(1'b1),  // input wire s_axis_config_tvalid
  .s_axis_config_tdata(32'd10000000),    // input wire [31 : 0] s_axis_config_tdata
  .m_axis_data_tvalid( ),      // output wire m_axis_data_tvalid
  .m_axis_data_tdata(m_axis_data_tdata),        // output wire [15 : 0] m_axis_data_tdata
  .m_axis_phase_tvalid(),    // output wire m_axis_phase_tvalid
  .m_axis_phase_tdata()      // output wire [31 : 0] m_axis_phase_tdata
);
    
wire signed[7:0]Dreal = m_axis_data_tdata[15:8];
wire signed[7:0]Dimag = m_axis_data_tdata[7:0];
    
    
wire signed[27:0]o_fft_abs;
 
    
fft256 fft256_u( 
                  .CLK  (i_clk),
				  .RST  (i_rst),
				  .ED   (1'b1),
				  .START(start),
				  .SHIFT(4'b0000),
				  .DR   ({Dreal[7],Dreal[7],Dreal[7],Dreal[7],Dreal[7],Dreal[7:3]}),
				  .DI   (0),
				  .RDY  (),
				  .OVF1 (),
				  .OVF2 (),
				  .ADDR (),
				  .o_fft_abs  (o_fft_abs)
				  );

initial
begin
i_clk = 1'b1;
i_rst = 1'b1;
start = 1'b0;
#1000
i_rst = 1'b0;
start = 1'b1;
#10
start = 1'b0;
end  
    
always #5 i_clk=~i_clk;
    
endmodule
00_028m

4. Complete algorithm code file

m FPGA-based 256-point FFT Fourier transform verilog implementation, including testbench, without using IP core

1. Algorithm simulation effect

2. Algorithms involve an overview of theoretical knowledge

3. Verilog core program

4. Complete algorithm code file

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