# complex convolution

Started by May 12, 2005
Dear All,

I would like to convolve two complex sequences. Could anybody help me
how to define the convolution of two complex sequences please?

Regard,
nmaedewi

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"nmaedewi" <nmaedewi@yahoo.com> writes:

> Dear All,
>
>
> I would like to convolve two complex sequences. Could anybody help me
> how to define the convolution of two complex sequences please?
>
>

Hi,

If we have two complex numbers f and g,

f = f_x + i*f_y
g = g_x + i*g_y,

where _x and _y are the real and imaginary
components of the numbers, respectively, then

f * g = (f_x + i*f_y) * (g_x + i*g_y)
= (f_x*g_x - f_y*g_y) + i*(f_y*g_x + f_x*g_y).

Now expand this idea into f and g being two functions
and you'll be a step further. Place that result into
the convolution integral and you'll be done.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Hi Randy,

As you explain we have two form:

f * g = (f_x + i*f_y) * (g_x + i*g_y)
= (f_x*g_x - f_y*g_y) + i*(f_y*g_x + f_x*g_y).

in real and imaginary part.

I am still dont understand how to calculate convolution if we have two
part : real and imaginary. Am I just calculate use the general
convolution formula?

y(n) = h(k).x(n-k)

What is the convolution ouput for will be? in real part only or in
complex form ?

Thanks.

regard,
estdev


"estdev" <nmaedewi@yahoo.com> writes:

> Hi Randy,
>
>
> As you explain we have two form:
>
>  f * g = (f_x + i*f_y) * (g_x + i*g_y)
>         = (f_x*g_x - f_y*g_y) + i*(f_y*g_x + f_x*g_y).
>
> in real and imaginary part.
>
> I am still dont understand how to calculate convolution if we have two
> part : real and imaginary. Am I just calculate use the general
> convolution formula?

> y(n) = h(k).x(n-k)

Yes, and use the fact that \int(a + i*b)dt = \int(a)dt + i*\int(b)dt.

> What is the convolution ouput for will be? in real part only or in
> complex form ?

Complex.
--
%  Randy Yates                  % "And all that I can do
%% Fuquay-Varina, NC            %  is say I'm sorry,
%%% 919-577-9882                %  that's the way it goes..."
%%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO