FIR filter

Hello, good morning. I'm a 1=BA Physics student. I've a problem with a
FIR and I don't know how to solve it. Please, help me. Thanks. It's:

Verify that the FIR:

y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)

generate a sinusoidal wave with w angular frecuency. Supose than at the
moment  t=3D0  y-2=3D0, y-1=3D0, x0=3D1 and in all next moments xn=3D0.

all that I've written betwen ( ) are subindex. The same with the
suposition's numbers..

I think i have to discover something as Asen ... + Bcos... but I don't
know how to do that and it's possible that it's not be correct. I've
read books and i've tried to search in internet bat I've not found
anything.=20

Please, help me.

Thanks very much

aprendiz wrote:

> Hello, good morning. I'm a 1=BA Physics student. I've a problem with a
> FIR and I don't know how to solve it. Please, help me. Thanks. It's:
>
> Verify that the FIR:
>
> y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)
>
> generate a sinusoidal wave with w angular frecuency. Supose than at the
> moment  t=3D0  y-2=3D0, y-1=3D0, x0=3D1 and in all next moments xn=3D0.
>
> all that I've written betwen ( ) are subindex. The same with the
> suposition's numbers..
>
> I think i have to discover something as Asen ... + Bcos... but I don't
> know how to do that and it's possible that it's not be correct. I've
> read books and i've tried to search in internet bat I've not found
> anything.
>
> Please, help me.
>
> Thanks very much

An aside for my education: Is this a FIR? I thought FIRs only depended
on their inputs? Here you are feeding back output samples too.

aprendiz skrev:
> Hello, good morning. I'm a 1=BA Physics student. I've a problem with a
> FIR and I don't know how to solve it. Please, help me. Thanks. It's:
>
> Verify that the FIR:
>
> y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)
>
> generate a sinusoidal wave with w angular frecuency. Supose than at the
> moment  t=3D0  y-2=3D0, y-1=3D0, x0=3D1 and in all next moments xn=3D0.

Assuming that you use the standard notation (y(n) is output,
x(n) is input), this is not an FIR filter, it's an IIR filter.

> all that I've written betwen ( ) are subindex. The same with the
> suposition's numbers..
>
> I think i have to discover something as Asen ... + Bcos... but I don't
> know how to do that and it's possible that it's not be correct. I've
> read books and i've tried to search in internet bat I've not found
> anything.

First, verify that this is an IIR filter, not an FIR.
Second, find the locations of the poles of that IIR filter.

Rune

In article <1163663728.339031.10060@m73g2000cwd.googlegroups.com>, "aprendiz" <saludosquetal@gmail.com> wrote:
>Verify that the FIR:
>
>y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)
>

As Rune said, if you using standard notation, this is an IIR filter.  I 
suggest tnat you investigate FIR filters.  They are very easy to use and 
stable.  If they are symetrical, there is no phase distortion.  They are also 
easy to design if you know the desired frequency response.  Look into the 
Parks-McClellan software package. 

aprendiz wrote:
> Hello, good morning. I'm a 1=BA Physics student. I've a problem with a
> FIR and I don't know how to solve it. Please, help me. Thanks. It's:
>
> Verify that the FIR:
>
> y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)
>
> generate a sinusoidal wave with w angular frecuency. Supose than at the
> moment  t=3D0  y-2=3D0, y-1=3D0, x0=3D1 and in all next moments xn=3D0.
>
> all that I've written betwen ( ) are subindex. The same with the
> suposition's numbers..
>
> I think i have to discover something as Asen ... + Bcos... but I don't
> know how to do that and it's possible that it's not be correct. I've
> read books and i've tried to search in internet bat I've not found
> anything.
>
> Please, help me.
>
> Thanks very much

As has been pointed out, this is an IIR. You can write a short program
to verify what it does. Set the input to an impulse [1 0 0 0 ... ].
Also, you can z-transform both sides of the equation to solve for the
transfer function H(z) =3D Y(z) / X(z), and inverse transform it back
into the time domain to get the impulse response. Or look up H(z) in a
signals and systems book.

John

Thanks

John Herman wrote:
> In article <1163663728.339031.10060@m73g2000cwd.googlegroups.com>, "aprendiz" <saludosquetal@gmail.com> wrote:
>> Verify that the FIR:
>>
>> y(n) =3D 2y(n-1)*cos(w) - y(n-2) + X(n)
>>
> 
> As Rune said, if you using standard notation, this is an IIR filter.  I 
> suggest tnat you investigate FIR filters.  They are very easy to use and 
> stable.  If they are symetrical, there is no phase distortion.  They are also 
> easy to design if you know the desired frequency response.  Look into the 
> Parks-McClellan software package. 

It would seem from the OP's wording that he wants an oscillator: "Verify 
that ... y(n) = 2y(n-1)*cos(w) - y(n-2) + X(n) generate a sinusoidal 
wave with w angular frequency." There are numerical considerations for 
making a practical oscillator, but stability isn't one of them.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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