VHDL code for a 4 tap FIR filter

   Finite Impulse Response(FIR) filters are one of the two main type of filters available for signal processing. As the name suggests the output of a FIR filter is finite and it settles down to zero after some time. For a basic FAQ on FIR filters see this post by dspguru.

   A FIR filter output, 'y' can be defined by the following equation:   

Here, 'y' is the filter output, 'x' in the input signal and 'b' is the filter coefficients. 'N' is the filter order. The higher the value of N is, the more complex the filter will be.

For writing the code in VHDL I have referred to the paper, VHDL generation of optimized FIR filters. You can say I have coded the exact block diagram available in the paper, "Figure 2". 

This is a 4 tap filter. That means the order of the filter is 4 and so it has 4 coefficients. I have defined the input as signed type of 8 bits wide. The output is also of signed type with 16 bits width. The design contains two files. One is the main file with all multiplications and adders defined in it, and another for defining the D flip flop operation. 

The main file is given below:

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity fir_4tap is
port(   Clk : in std_logic; --clock signal
        Xin : in signed(7 downto 0); --input signal
        Yout : out signed(15 downto 0)  --filter output
        );
end fir_4tap;

architecture Behavioral of fir_4tap is

component DFF is
   port(
      Q : out signed(15 downto 0);      --output connected to the adder
      Clk :in std_logic;      -- Clock input
      D :in  signed(15 downto 0)      -- Data input from the MCM block.
   );
end component; 
   
signal H0,H1,H2,H3 : signed(7 downto 0) := (others => '0');
signal MCM0,MCM1,MCM2,MCM3,add_out1,add_out2,add_out3 : signed(15 downto 0) := (others => '0');
signal Q1,Q2,Q3 : signed(15 downto 0) := (others => '0');

begin

--filter coefficient initializations.
--H = [-2 -1 3 4].
H0 <= to_signed(-2,8);
H1 <= to_signed(-1,8);
H2 <= to_signed(3,8);
H3 <= to_signed(4,8);

--Multiple constant multiplications.
MCM3 <= H3*Xin;
MCM2 <= H2*Xin;
MCM1 <= H1*Xin;
MCM0 <= H0*Xin;

--adders
add_out1 <= Q1 + MCM2;
add_out2 <= Q2 + MCM1;
add_out3 <= Q3 + MCM0;

--flipflops(for introducing a delay).
dff1 : DFF port map(Q1,Clk,MCM3);
dff2 : DFF port map(Q2,Clk,add_out1);
dff3 : DFF port map(Q3,Clk,add_out2);

--an output produced at every positive edge of clock cycle.
process(Clk)
begin
    if(rising_edge(Clk)) then
        Yout <= add_out3;
    end if;
end process;
   
end Behavioral;

VHDL code for the component DFF is given below:

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity DFF is
   port(
      Q : out signed(15 downto 0);      --output connected to the adder
      Clk :in std_logic;      -- Clock input
      D :in  signed(15 downto 0)      -- Data input from the MCM block.
   );
end DFF;

architecture Behavioral of DFF is

signal qt : signed(15 downto 0) := (others => '0');

begin

Q <= qt;

process(Clk)
begin
  if ( rising_edge(Clk) ) then
    qt <= D;
  end if;      
end process;

end Behavioral;

I have written a small test bench code for testing the design. It contains 8 test inputs which are serially applied to the filter module. See below:

LIBRARY ieee;
USE ieee.std_logic_1164.ALL;
USE ieee.numeric_std.ALL;

ENTITY tb IS
END tb;

ARCHITECTURE behavior OF tb IS

   signal Clk : std_logic := '0';
   signal Xin : signed(7 downto 0) := (others => '0');
   signal Yout : signed(15 downto 0) := (others => '0');
   constant Clk_period : time := 10 ns;

BEGIN

    -- Instantiate the Unit Under Test (UUT)
   uut: entity work.fir_4tap PORT MAP (
          Clk => Clk,
          Xin => Xin,
          Yout => Yout
        );

   -- Clock process definitions
   Clk_process :process
   begin
        Clk <= '0';
        wait for Clk_period/2;
        Clk <= '1';
        wait for Clk_period/2;
   end process;
   
   -- Stimulus process
   stim_proc: process
   begin       
      wait for Clk_period*2;
        Xin <= to_signed(-3,8); wait for clk_period*1;
        Xin <= to_signed(1,8); wait for clk_period*1;
        Xin <= to_signed(0,8); wait for clk_period*1;
        Xin <= to_signed(-2,8); wait for clk_period*1;
        Xin <= to_signed(-1,8); wait for clk_period*1;
        Xin <= to_signed(4,8); wait for clk_period*1;
        Xin <= to_signed(-5,8); wait for clk_period*1;
        Xin <= to_signed(6,8); wait for clk_period*1;
        Xin <= to_signed(0,8);
       
      wait;
   end process;

END;

The simulation waveform is given below:

The code is synthesisable and with a few changes can be ported for a higher order filter.