How to Implement FIR Filter in VHDL

FIR Filter Introduction

Finite Impulse Response (FIR) filters are characterized by a time response depending only on a given number of the last samples of the input signal. For a causal discrete-time FIR filter of order N, each value of the output sequence is a weighted sum of the most recent input values:

 

fir_filter_equation

 

 

 

where:

  • x[n] is the input signal,
  • y[n] is the output signal,
  • N is the filter order; a Nth-order filter has (N+1) terms on the right-hand side
  • bi is the value of the impulse response at the i’th instant for 0<= i <=N of a Nth-order FIR filter. If the filter is a direct form FIR filter then is also a coefficient of the filter (see Figure1).

This computation is also known as discrete convolution.

On Wikipedia FIR web-page, you can find further information on FIR design theory.

fir-direct-form
Figure 1 – FIR Filter direct form implementation

 

FIR Filter Hardware Architecture

Here we want to see how to implement FIR filter architecture in FPGA or ASIC using VHDL.

Figure 2 reports an example of 4 taps FIR direct form that can be simply coded in VHDL. In figure 2, the input x(n) and the coefficient bi are 8-bits signed.

After the filter coefficients multiplication, the multiplier output dynamic will be an 8+8=16 bit.

In fact, when you multiply two numbers of N-bit and M-bit the output dynamic of the multiplication result is (N+M)-bits.

When you perform addition, the number of bit of the result will be incremented by 1. The FIR filter design architecture of figure 2  can be easily extended to a length greater than 4.

4-taps FIR Filter hardware architecture example

FIR Filter Design VHDL Code

Here below is reported the VHDL code for the FIR filter design of figure 2. The VHDL code implements a low pass FIR filter with 4 taps, 8-bit input, 8-bit coefficient.

library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;

entity fir_filter_4 is
port (
  i_clk        : in  std_logic;
  i_rstb       : in  std_logic;
  -- coefficient
  i_coeff_0    : in  std_logic_vector( 7 downto 0);
  i_coeff_1    : in  std_logic_vector( 7 downto 0);
  i_coeff_2    : in  std_logic_vector( 7 downto 0);
  i_coeff_3    : in  std_logic_vector( 7 downto 0);
  -- data input
  i_data       : in  std_logic_vector( 7 downto 0);
  -- filtered data 
  o_data       : out std_logic_vector( 9 downto 0));
end fir_filter_4;

architecture rtl of fir_filter_4 is

type t_data_pipe      is array (0 to 3) of signed(7  downto 0);
type t_coeff          is array (0 to 3) of signed(7  downto 0);

type t_mult           is array (0 to 3) of signed(15    downto 0);
type t_add_st0        is array (0 to 1) of signed(15+1  downto 0);

signal r_coeff              : t_coeff ;
signal p_data               : t_data_pipe;
signal r_mult               : t_mult;
signal r_add_st0            : t_add_st0;
signal r_add_st1            : signed(15+2  downto 0);

begin

p_input : process (i_rstb,i_clk)
begin
  if(i_rstb='0') then
    p_data       <= (others=>(others=>'0'));
    r_coeff      <= (others=>(others=>'0'));
  elsif(rising_edge(i_clk)) then
    p_data      <= signed(i_data)&p_data(0 to p_data'length-2);
    r_coeff(0)  <= signed(i_coeff_0);
    r_coeff(1)  <= signed(i_coeff_1);
    r_coeff(2)  <= signed(i_coeff_2);
    r_coeff(3)  <= signed(i_coeff_3);
  end if;
end process p_input;

p_mult : process (i_rstb,i_clk)
begin
  if(i_rstb='0') then
    r_mult       <= (others=>(others=>'0'));
  elsif(rising_edge(i_clk)) then
    for k in 0 to 3 loop
      r_mult(k)       <= p_data(k) * r_coeff(k);
    end loop;
  end if;
end process p_mult;

p_add_st0 : process (i_rstb,i_clk)
begin
  if(i_rstb='0') then
    r_add_st0     <= (others=>(others=>'0'));
  elsif(rising_edge(i_clk)) then
    for k in 0 to 1 loop
      r_add_st0(k)     <= resize(r_mult(2*k),17)  + resize(r_mult(2*k+1),17);
    end loop;
  end if;
end process p_add_st0;

p_add_st1 : process (i_rstb,i_clk)
begin
  if(i_rstb='0') then
    r_add_st1     <= (others=>'0');
  elsif(rising_edge(i_clk)) then
    r_add_st1     <= resize(r_add_st0(0),18)  + resize(r_add_st0(1),18);
  end if;
end process p_add_st1;

p_output : process (i_rstb,i_clk)
begin
  if(i_rstb='0') then
    o_data     <= (others=>'0');
  elsif(rising_edge(i_clk)) then
    o_data     <= std_logic_vector(r_add_st1(17 downto 8));
  end if;
end process p_output;


end rtl;

 

The FIR filter is implemented fully pipelined, in fact, there is a registration stage at the output of each multiplication or addition.

The output dynamic of the FIR filter is 10-bit, i.e. is not fully dynamic output.

The VHDL code of the FIR filter can be implemented either in ASIC or in FPGA. The implementation should be guarantee full speed for the FIR filter.

Figure 3 shows RTL viewer of Altera Quartus II for the FIR filter VHLD example code above

Figure 3 - FIR Filter Quartus II RTL viewer
Figure 3 – FIR Filter Quartus II RTL viewer

 

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15 thoughts on “How to Implement FIR Filter in VHDL

  1. Thanks Francesco! Compact and very useful codes!
    Question: If the number of taps were generics, how can i generate the seperate process statements for the adder tree? can you give an example?
    Thanks!

      1. Thanks for the reply!

        I think it should be possible to realize a parametrized (Generic) adder tree using GENERATE statement.

        All the best!

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