I have phase and magnitude and frequency responses of a filtered signal. I want to find the filter coefficients. Thank you in advance.
Covert that phase and magnitude to rectangular form (complex numbers). which will be the required filter coefficients.The conversion will be magnitude*(cos(phase)+i*sin(phase))
Do you know what went into your filter? Was is it an impulse? Or a sum of sinusoids? White noise? Or other?
Do you know if your filter is FIR or IIR? Do you know the filter order?
The frequency response is only meaningful if the filter has reached steady-sate, i.e. after the start-up transient has passed. So if your input was only brief, then the frequency response will not be very useful. You would be better off looking at the impulse response.
If your input is an impulse, then just look at the filter output in the time domain to get the impulse-response of your filter! If the output decays slowly, then your filter is probably IIR. Either way, truncate the response in time, and flip L/R it in time to get the coeffs of an approximate FIR filter.
Hi
If your filter is continuous domain you can apply Z-transform to it and transform to the discrete domain. Z-Transform such as Bilinear is an algebraic transformation between the variables s and z and it can simplify your calculation. If you want to use this method you should consider all of the digitization Issues.
Good Luck
For more information you can refer to this book:
Discrete-Time Signal Processing (3rd Edition) (Prentice Hall Signal Processing)-by Alan V. Oppenheim and Ronald W. Schafer-2009
Also, other DSP books can be a good reference for digitization.
Sorry, I may have misunderstood your question in my earlier response. I initially thought you were trying to do system identification. But perhaps you are looking at filter design, i.e. how do I design a (digital?) filter to achieve a given desired frequency response?
The simplest approach, for an FIR filter, would be to use the window method - take the inverse DFT of your desired frequency response then apply a tapered window (e.g Hamming) in the time domain. You would need to discretise your ideal frequency response at uniformly spaced frequency points before taking the inverse DFT. Increase the number of points to increase the order of your filter.
You will need to consider -ve and +ve frequencies to make sure you end up with real filter coeffs in the time domain.
Finally, generate the frequency response of your filter, to make sure you end up with something that is close to what you wanted.
Sir,
Based on the magnitude response, you have to use FIR filter to find the filter coefficients. You have to use either of the following three methods for your design.
1. FIR design using fourier transform method
2. FIR design using windowing method
3. FIR design using frequency sampling method.
From the above methods you are easily design from your H(e j w ) to h(n)
Please refer the book Digital Signal Processing by John G.Proakias
Suggest
1Express the obtained H(e^iw) =[ H1 H2 ..Hn \ as polar complex numbers
using a+jb = sqrt(a^2+b^2)* e^(atan(b/a) )
2. The above may be treated as the DFT of the filter h(n) viz{h0 h1.. hn}
3. Invert H(e^iw) =[ H1 H2 ..Hn ] using IDFT A simple matrix inversion
of the W matrix [ W ] with wij = exp(i*j* 2pi/N) may also be used
Cheers
On further reading of the question , it appears that you want the filter coefficients h(n) given input and output Fourier transformss . Then in that case we have to consider H(w) as sigout(w)/ sigi(w) in above suggestion
Cheers
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