# what are coefficients of a filter??

Started by March 22, 2005
```Dear folks

I am studying about dsp and i need to calculate coefficients of a
filter.

I know that a filter is described by its transfer function H(w)=sum
h(n)exp{-jwt). But I don't know what are coefficents of that filter.

More specifically I need to present the coefficients of a filter g by
the coefficients of a filter h, provided
G(w)=exp(-wj)H(w+pi)

Can I find the coefficients of g by directlly apply the inverse FOurier
formula:

g(n)=1/2pi(integral(G(e)exp(iwt)dw))

if no, any hints of this problem?

Thank you very much/

```
```VijaKhara@gmail.com wrote:
> Dear folks
>
> I am studying about dsp and i need to calculate coefficients of a
> filter.
>
> I know that a filter is described by its transfer function H(w)=sum
> h(n)exp{-jwt). But I don't know what are coefficents of that filter.
>
> More specifically I need to present the coefficients of a filter g by
> the coefficients of a filter h, provided
> G(w)=exp(-wj)H(w+pi)
>
> Can I find the coefficients of g by directlly apply the inverse FOurier
> formula:
>
> g(n)=1/2pi(integral(G(e)exp(iwt)dw))
>
> if no, any hints of this problem?
>
> Thank you very much/

What kind of filter?

If you have homework, don't you have a text?

Do you know that there are programs to calculate the filter?

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```in article 1111549468.996590.18220@l41g2000cwc.googlegroups.com,
VijaKhara@gmail.com at VijaKhara@gmail.com wrote on 03/22/2005 22:44:

> I know that a filter is described by its transfer function H(w)=sum
> h(n)exp{-jwt). But I don't know what are coefficents of that filter.

H(e^jw) = SUM{ h[n]*exp(-j*w*n) }

where w is normalized frequency (-pi < w < pi).

> More specifically I need to present the coefficients of a filter g by
> the coefficients of a filter h, provided
> G(w)=exp(-wj)H(w+pi)
>
> Can I find the coefficients of g by directlly apply the inverse FOurier
> formula:
>
> g(n)=1/2pi(integral(G(e)exp(iwt)dw))

yes (almost).  this is the so-called windowing method or windowed impulse
response method.  not a bad way to approach it.

it should be:

g[n] = 1/(2*pi) * integral{ G(e^jw)*exp(j*w*n) dw}

details are important.

this may give you a g[n] that is longer than you want.  so you window it to
shorten it.  after windowing it, recheck the frequency response (first
equation above) to see if you can live with the result.  Kaiser windows are
really good, but the Hamming window (centered in the middle of your impulse
response if linear phase) is a good place to start.

rots o' ruk.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```Hello Jerry Avins and Robert Bristow:

There is no information about the type of filter. I think it is for a
general case. The full problem text is as follows:
We know: G(w)=exp(-iw).H*(w+pi), and the filter h has real
coefficients. We need express the coefficients of the filter g in terms
of the coefficients of the filter h.

Unfortunately, this should be done by a pencil and paper, I cannot ask
for the aid of a software program.

So in the case of a general filter what are coefficients? I know that
If y(n) is the out put, x(n) is the  input. y(n)=h(n) convolutes with
x(n)

are the set {h(n) (n is from minus infinity  to infinity)} is the set
of coefficients of h?

and in the answer of Mr. Robert Bristow, you said about the windowing
method.
Do you mean in fact the G(w)=exp(-iw).H*(w+pi) is a windowing method?

I read in the textbook, and they said that in a windowing method,
people multiple h(n) with the window function so that in the frequency
domain it will be a convolution operator.

In the problem I see it is a multiply operator in the frequency domain,
it is quite different from textbook (it should be a convolution
operator to be similar to a windowing method in the textbook)

Can you explain in  more detail the solution for me?

P/S in my previous text, I made a mistake, the correct formula:
G(w)=exp(-iw).H*(w+pi)

the incorrect : G(w)=exp(-iw).H(w+pi)  (the difference is the conjugate
of H)

Thank you very much.
I am looking forward to your reply.

```
```VijaKhara@gmail.com wrote:
> Hello Jerry Avins and Robert Bristow:
>
> There is no information about the type of filter. I think it is for a
> general case. The full problem text is as follows:
> We know: G(w)=exp(-iw).H*(w+pi), and the filter h has real
> coefficients. We need express the coefficients of the filter g in terms
> of the coefficients of the filter h.

The filter coefficients are usually the discrete values of h(n).

To solve your problem, try looking at a table of properties of the DFT, and
noting what the operations to the DFT H(w) on the right hand side of your
equation will do to the values of h(n).

The three operations you have are:
- multiply by a complex exponential
- conjugate
- frequency shift by pi

These roughly correspond to delay, reverse, and modify of the h(n) coefficients.

Hope that helps.

Sasha
```