help needed in sine generation of vhdl code.

[senthil]

hello friends,

for the fft and ifft part of dsp, w.r to twiddle factor, we need the
cosine and sine terms. for that i do my sine code w.r to sine series
formulae.

sin(x) = x - x3/3(fact) + x5/5(fact) _ ...

i took only 3 terms.

and my coding was given below


term : =1
sum := 1

for n in 1 to 3 loop

term := (-term)*input **2/real((2n*(2n+1)));
sum := sum + term;
end loop

output <= input * sum;

i found one problem , ie., if i give input = 3.534, i got an output =
-0.596
that is wrong answer.
but actual value from the calculator, is sin(3.534) = -0.3818..

what is the problem behind that.
give some guidance.

tool : modelsim 5.5 SE vhdl.

 

[David Brown]

"senthil" <bhuvasen@hotmail.com> wrote in message
news:3045a319.0402112104.297e17b5@posting.google.com...

hello friends,

for the fft and ifft part of dsp, w.r to twiddle factor, we need the
cosine and sine terms. for that i do my sine code w.r to sine series
formulae.

sin(x) = x - x3/3(fact) + x5/5(fact) _ ...

i took only 3 terms.

That formula for calculating sin is fine for doing theoretical maths, but it
is not good as a calculation method, since it converges very slowly. In
particular, it gets worse the further you go from 0 - to converge sin(3.534)
to four decimal places (to the correct value of -0.3824, not the one you
gave below) takes 8 terms.

If you move your input closer to 0, such as by using sin x == sin (pi - x),
and try calculating sin(-0.3924), you get four decimal places after 3 terms.

Where you go from here depends on what you actually want to do with the
sines - if you are only looking for simulation and don't care about speed,
then just pick a big enough number of terms. If you need high accuracy and
can use floating point, then look for tchebychev (sp?) polynomials. Typical
synthesisable solutions use lookup tables.

and my coding was given below


term : =1
sum := 1

for n in 1 to 3 loop

term := (-term)*input **2/real((2n*(2n+1)));
sum := sum + term;
end loop

output <= input * sum;

i found one problem , ie., if i give input = 3.534, i got an output =
-0.596
that is wrong answer.
but actual value from the calculator, is sin(3.534) = -0.3818..

what is the problem behind that.
give some guidance.

tool : modelsim 5.5 SE vhdl.

 

[Egbert Molenkamp]

Maybe you can use the IEEE package math_real.
This package contains often used constants (math_e, math_pi, ..) and
functions (sqrt, exp, log, log2, sin, arccos, sinh, ..).
(not synthesisable)

ModelSim has this package.

Here an example

library ieee;
use ieee.std_logic_1164.all;
use ieee.math_real.all;
entity math is
end math;

architecture demo of math is
signal s, c, this_should_be_one : real := 0.0;
begin
stimulirocess
constant delta : real := 10.0E-4;
variable x : real := 0.0;
begin
x:=0.0;
while x < 4.0*MATH_PI loop
s <= sin(x);
c <= cos(x);
wait for 1 ns;
x:=x+delta;
end loop;
report "finished";
wait;
end process;

this_should_be_one <= s**2 + c**2;
end demo;


And if you use the macro file beneath you get a nice waveform.

vsim math
onerror {resume}
quietly WaveActivateNextPane {} 0
add wave -noupdate -format Analog-Step -offset -1.0 -scale 40.0 /math/s
add wave -noupdate -format Analog-Step -offset -0.58 -scale 40.0 /math/c
add wave -noupdate -format Analog-Step -offset -0.14 -scale 40.0
/math/this_should_be_one
run -all

Egbert Molenkamp

"senthil" <bhuvasen@hotmail.com> wrote in message
news:3045a319.0402112104.297e17b5@posting.google.com...

hello friends,

for the fft and ifft part of dsp, w.r to twiddle factor, we need the
cosine and sine terms. for that i do my sine code w.r to sine series
formulae.

sin(x) = x - x3/3(fact) + x5/5(fact) _ ...

i took only 3 terms.

and my coding was given below


term : =1
sum := 1

for n in 1 to 3 loop

term := (-term)*input **2/real((2n*(2n+1)));
sum := sum + term;
end loop

output <= input * sum;

i found one problem , ie., if i give input = 3.534, i got an output =
-0.596
that is wrong answer.
but actual value from the calculator, is sin(3.534) = -0.3818..

what is the problem behind that.
give some guidance.

tool : modelsim 5.5 SE vhdl.