continuous averaging using VHDL

okay. You mean like this:

process (clk, reset)
begin
    if (reset = '1') then 
    out_val=0;
    elsif(rising_edge(clk)) then
    
case state is
when out_1 =>
    if done='1' then
    data_out <= addr0 & bits;
    counter <= counter + 1;
    data_in_d <= signed(data_in);
    if counter /= 0 then
      sum <= sum + data_in_d;
    else
      sum <= (others => '0');
      avg <= std_logic_vector(sum(21 downto 10));
      stage(1) <= avg(11 downto 0);
for i in 2 to 31 loop
    stage(i) <= stage(i-1);
end loop;
-- subtract last stage from input
 sub_result <= resize(signed(avg),13) - signed(stage(31));
-- accumulate
sum_new <= sum_new + sub_result;
adc_a_out <= std_logic_vector(sum_new(16 downto 5));
    end if;
    state <= out_2;
    endif;
    end process;