> 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.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by dbell●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 Chris Barrett●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 Rune Allnor●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 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 Chris Barrett●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 Randy Yates●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 Chris Barrett●April 26, 20072007-04-26
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?