Filter iir trasposed structure

assume input x is 16 bits signed

y_out is 16 bits signed

coeffs 16 bits signed

then you can either use integer computation or signed.

to simplify example, let us assume we can truncate y_int below without check,

I also assume a coeff of say 2 means 2 in terms of gain.

This code is untested but should give you an idea.

signal y1 : signed(32 downto 0) := (others => '0');
signal y2 : signed(33 downto 0) := (others => '0');
signal y_int : signed(34 downto 0) := (others => '0');
constant b0 : signed(15 downto 0) := x"0001"; 
constant b1 : signed(15 downto 0) := x"0002"; 
constant b2 : signed(15 downto 0) := x"0003"; 
constant a1 : signed(15 downto 0) := x"0002"; 
constant a2 : signed(15 downto 0) := x"0001"; 
begin
process
begin
wait until clk = '1';
   y1 <= x*b2  + y_int(15 downto 0)*a2;        -- 16*16 + 16*16cbits, needs 33 bits
   y2 <= x*b1  + y_int(15 downto 0)*a1 + y1; -- 16*16 + 16*16 + 33bits, needs 34 bits
end process;
y_int <= x*b0 + y2; -- 16 * 16 + 34 bits, requires 35 bits
y <= y_int(15 downto 0);