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 are coefficients of a filter??

Started by ●March 22, 2005

Reply by ●March 23, 20052005-03-23

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. �����������������������������������������������������������������������

Reply by ●March 23, 20052005-03-23

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."

Reply by ●March 23, 20052005-03-23

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.

Reply by ●March 23, 20052005-03-23

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