I have two filters in parallel. The transfer functions are given by H1 and H2. I've illustrated the setup below. .-- H1 ---. | | in --------| (+)------> out | | '-- H2 ---' How do I find the transfer function of two parallel filters? Do I merely sum the two together? sum = H1+H2 I would think this would work, but I would be worried that the phase responses would throw the result off. How do I find the combined transfer function?

# Transfer Function of Two Filters in Parallel

Started by ●April 26, 2007

Reply by ●April 26, 20072007-04-26

Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> writes:> I have two filters in parallel. The transfer functions are given by H1 > and H2. I've illustrated the setup below. > > .-- H1 ---. > | | > in --------| (+)------> out > | | > '-- H2 ---' > > How do I find the transfer function of two parallel filters?One step at a time, using the definition of transfer function: H(w) = Y(w) / X(w). Start by computing the output (in frequency) of H1, Y1(w), in terms of the input (call it X(w)). Then similarly for Y2(w). -- % Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven. %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and %%% 919-577-9882 % Verdi's always creepin' from her room." %%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO http://home.earthlink.net/~yatescr

Reply by ●April 26, 20072007-04-26

Randy Yates wrote:> Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> writes: > > >>I have two filters in parallel. The transfer functions are given by H1 >>and H2. I've illustrated the setup below. >> >> .-- H1 ---. >> | | >>in --------| (+)------> out >> | | >> '-- H2 ---' >> >>How do I find the transfer function of two parallel filters? > > > One step at a time, using the definition of transfer function: > > H(w) = Y(w) / X(w). > > Start by computing the output (in frequency) of H1, Y1(w), in terms of > the input (call it X(w)). Then similarly for Y2(w).Can I sum H1(w) and H2(w) to get H_the_system(w)?

Reply by ●April 26, 20072007-04-26

On Apr 27, 7:54 am, Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> wrote:> I have two filters in parallel. The transfer functions are given by H1 > and H2. I've illustrated the setup below. > > .-- H1 ---. > | | > in --------| (+)------> out > | | > '-- H2 ---' > > How do I find the transfer function of two parallel filters? Do I > merely sum the two together? > > sum = H1+H2 > > I would think this would work, but I would be worried that the phase > responses would throw the result off. How do I find the combined > transfer function?Yes its the sum of the two.

Reply by ●April 27, 20072007-04-27

On 26 Apr, 21:54, Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> wrote:> I have two filters in parallel. The transfer functions are given by H1 > and H2. I've illustrated the setup below. > > .-- H1 ---. > | | > in --------| (+)------> out > | | > '-- H2 ---' > > How do I find the transfer function of two parallel filters? Do I > merely sum the two together? > > sum = H1+H2 > > I would think this would work, but I would be worried that the phase > responses would throw the result off. How do I find the combined > transfer function?The total frequency response is the (complex-valued) sum of the two. That's a property of linear systems. Rune

Reply by ●April 27, 20072007-04-27

Rune Allnor wrote:> On 26 Apr, 21:54, Chris Barrett > <"chrisbarret"@0123456789abcdefghijk113322.none> wrote: > >>I have two filters in parallel. The transfer functions are given by H1 >>and H2. I've illustrated the setup below. >> >> .-- H1 ---. >> | | >>in --------| (+)------> out >> | | >> '-- H2 ---' >> >>How do I find the transfer function of two parallel filters? Do I >>merely sum the two together? >> >> sum = H1+H2 >> >>I would think this would work, but I would be worried that the phase >>responses would throw the result off. How do I find the combined >>transfer function? > > > The total frequency response is the (complex-valued) sum of the two. > That's a property of linear systems. > > Rune >How would I determine whether the system is linear or non-linear?

Reply by ●April 27, 20072007-04-27

On Apr 27, 1:11 pm, Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> wrote:> Rune Allnor wrote: > > On 26 Apr, 21:54, Chris Barrett > > <"chrisbarret"@0123456789abcdefghijk113322.none> wrote: > > >>I have two filters in parallel. The transfer functions are given by H1 > >>and H2. I've illustrated the setup below. > > >> .-- H1 ---. > >> | | > >>in --------| (+)------> out > >> | | > >> '-- H2 ---' > > >>How do I find the transfer function of two parallel filters? Do I > >>merely sum the two together? > > >> sum = H1+H2 > > >>I would think this would work, but I would be worried that the phase > >>responses would throw the result off. How do I find the combined > >>transfer function? > > > The total frequency response is the (complex-valued) sum of the two. > > That's a property of linear systems. > > > Rune > > How would I determine whether the system is linear or non-linear?- Hide quoted text - > > - Show quoted text -You do need to figure this out. If the system is nonlinear then you don't have a transfer function, ... right? Dirk

Reply by ●April 27, 20072007-04-27

Chris Barrett wrote:> Rune Allnor wrote: >> On 26 Apr, 21:54, Chris Barrett >> <"chrisbarret"@0123456789abcdefghijk113322.none> wrote: >> >>> I have two filters in parallel. The transfer functions are given by H1 >>> and H2. I've illustrated the setup below. >>> >>> .-- H1 ---. >>> | | >>> in --------| (+)------> out >>> | | >>> '-- H2 ---' >>> >>> How do I find the transfer function of two parallel filters? Do I >>> merely sum the two together? >>> >>> sum = H1+H2 >>> >>> I would think this would work, but I would be worried that the phase >>> responses would throw the result off. How do I find the combined >>> transfer function? >> >> >> The total frequency response is the (complex-valued) sum of the two. >> That's a property of linear systems. >> >> Rune >> > > How would I determine whether the system is linear or non-linear?The existence of H1 and H2 implies linearity. Nonlinear systems don't have transfer functions per se. Not every input-output relation is a transfer function. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯