Dear All, I would like to convolve two complex sequences. Could anybody help me how to define the convolution of two complex sequences please? Thanks in advanced. Regard, nmaedewi This message was sent using the Comp.DSP web interface on www.DSPRelated.com

# complex convolution

Started by ●May 12, 2005

Reply by ●May 12, 20052005-05-12

"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? > > > Thanks in advanced.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

Reply by ●May 15, 20052005-05-15

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

Reply by ●May 15, 20052005-05-15

"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 http://home.earthlink.net/~yatescr