Hi, I'm (trying to) implement an IIR Hilbert Transformer. I found a reference to a design which provides the z domain poles and zeros as listed at the bottom of this post. The function is 12th order and I figured that I could implement this conveniently with 6 cascaded biquads (which I happen to have available in my FPGA DSP design). I calculated out the IIR filter coeffs by taking the conjugate pole pairs and zero pairs and multiplying them out to provide a function like z^2 + aZ + b to provide the coefficients. These are listed below also: I then simply transplanted these coefficients into my biquad DSP (b coeffs do not need to be negated as is often the case). The response I get is not what I expected. It is flat in magnitude with 45dB gain (should be 0dB) but the phase constantly varies instead of being roughly 90 degrees for most of the band. I also computed the frequency response in Excel and this does not appear to give the response expected either. I assume it's finger trouble but would someone out there mind having a look at this problem in Matlab? I don't have Matlab or Scilab (and not trained up) and I think it would be relatively straightforward for an experienced person to check these calculations. Many thanks if you can spare some time to look at this and please feel free to call me stupid if I have made an obviously bad assumption. Zeros (complex) ========================= a jb -0.834946 -1.459074 -0.834946 1.459074 0.834946 -1.459074 0.834946 1.459074 0 -1.707483 0 1.707483 -1.362397 -0.79655 -1.362397 0.79655 1.362397 -0.79655 1.362397 0.79655 -1.118507 0 1.118507 0 Poles (complex) ============== -0.894071 0 0.894071 0 -0.547048 -0.319837 -0.547048 0.319837 0.547048 -0.319837 0.547048 0.319837 -0.295469 -0.516331 -0.295469 0.516331 0.295469 -0.516331 0.295469 0.516331 0 -0.585696 0 0.585696 Coefficients (numerator coeffs first then denominator): ====================================== a0 a1 a2 1 -1.669892 2.82603176 1 -1.669892 2.82603176 1 1.669892 2.82603176 1 0 2.915498195 1 -2.724794 2.490617488 1 2.724794 2.490617488 1 0 -1.251057909 (1) b1 b2 1 0 -0.799362953 1 -1.094096 0.401557221 1 1.094096 0.401557221 1 -0.590938 0.353899632 1 0.590938 0.353899632 1 0 0.343039804

# IIR Hilbert - Matlab help anyone

Started by ●July 2, 2009

Reply by ●July 3, 20092009-07-03

I made a mistake in my post - the first line of a coefficients was repeated so it should read: Coefficients (numerator coeffs first then denominator): ====================================== a0 a1 a2 1 -1.669892 2.82603176 1 1.669892 2.82603176 1 0 2.915498195 1 -2.724794 2.490617488 1 2.724794 2.490617488 1 0 -1.251057909

Reply by ●July 3, 20092009-07-03

Reply by ●July 3, 20092009-07-03

OK, I managed to install Scilab and plotted the frequency response of my H(z) and it matches what I see in my Excel model. So either my coefficient calculations are wrong or the original poles and zeros provided are wrong. I'm more inclined to think that it is me at fault here! Does anyone know if it is possible to define a syslin in Scilab (not sure of the equivalent Matlab language) in terms of complex poles and zeros rather than real coefficients of z? If I could do this then I could test the poles and zero's as published - this would then allow me to narrow the problem down to my coefficient calculations.

Reply by ●July 3, 20092009-07-03

davew wrote:> In the mean time, I'm currently installing Scilab to see if I can > solve this myself.And I am glad to tell the World that I am currently installing the PL-2303 USB to serial driver. VLV

Reply by ●July 3, 20092009-07-03

I'm just trying to point out that I'm not asking for help without trying to help myself! Good luck with your driver installation.

Reply by ●July 3, 20092009-07-03

Reply by ●July 6, 20092009-07-06

Here is the original paper: http://wwwtw.vub.ac.be/elec/Papers%20on%20web/Papers/RikPintelon/IM90Kollar-Optimal%20FIR%20an%20IIR.pdf I created a H(z) in Scilab using the poles and zeros as specified on page 5 of this document. I made a pole zero plot which is identical to that in the document, however the magnitude and phase plots are nothing like those given. Am I doing something wrong or is the document in error? The author told me that as far as he remembers, the filter "worked" but he hadn't time to re-visit it. Can anyone offer an explanation? Thanks.

Reply by ●July 6, 20092009-07-06

On 6 July, 10:46, davew <david.wo...@gmail.com> wrote:> Here is the original paper: > > http://wwwtw.vub.ac.be/elec/Papers%20on%20web/Papers/RikPintelon/IM90... > > I created a H(z) in Scilab using the poles and zeros as specified on > page 5 of this document. �I made a pole zero plot which is identical > to that in the document, however the magnitude and phase plots are > nothing like those given. �Am I doing something wrong or is the > document in error? �The author told me that as far as he remembers, > the filter "worked" but he hadn't time to re-visit it. > > Can anyone offer an explanation? > > Thanks.and here is the Scilab code if anyone wants to try it/investigate further: z1 = -0.834946 + -1.459074 * %i; z2 = -0.834946 + 1.459074 * %i; z3 = 0.834946 + -1.459074 * %i; z4 = 0.834946 + 1.459074 * %i; z5 = 0 + -1.707483 * %i; z6 = 0 + 1.707483 * %i; z7 = -1.362397 + -0.79655 * %i; z8 = -1.362397 + 0.79655 * %i; z9 = 1.362397 + -0.79655 * %i; z10 = 1.362397 + 0.79655 * %i; z11 = -1.118507 + 0 * %i; z12 = 1.118507 + 0 * %i; p1 = -0.894071 + 0 * %i; p2 = 0.894071 + 0 * %i; p3 = -0.547048 + -0.319837 * %i; p4 = -0.547048 + 0.319837 * %i; p5 = 0.547048 + -0.319837 * %i; p6 = 0.547048 + 0.319837 * %i; p7 = -0.295469 + -0.516331 * %i; p8 = -0.295469 + 0.516331 * %i; p9 = 0.295469 + -0.516331 * %i; p10 = 0.295469 + 0.516331 * %i; p11 = 0 + -0.585696 * %i; p12 = 0 + 0.585696 * %i; H = (real((%z - z1) * (%z - z2)) * real((%z - z3) * (%z - z4)) * real ((%z - z5) * (%z - z6)) * real((%z - z7) * (%z - z8)) * real((%z - z9) * (%z - z10)) * real((%z - z11) * (%z - z12))) / (real((%z - p1) * (%z - p2)) * real((%z - p3) * (%z - p4)) * real((%z - p5) * (%z - p6)) * real((%z - p7) * (%z - p8)) * real((%z - p9) * (%z - p10)) * real((%z - p11) * (%z - p12))) sys=syslin('d', H); fmin=0.001; fmax=0.5; scf(1);clf; plzr(H); scf(2);clf; bode(sys,fmin,fmax); //Plots frequency response in Bode diagram

Reply by ●July 13, 20092009-07-13

On 6 July, 11:22, davew <david.wo...@gmail.com> wrote:> On 6 July, 10:46, davew <david.wo...@gmail.com> wrote: > > > Here is the original paper: > > >http://wwwtw.vub.ac.be/elec/Papers%20on%20web/Papers/RikPintelon/IM90... > > > I created a H(z) in Scilab using the poles and zeros as specified on > > page 5 of this document. �I made a pole zero plot which is identical > > to that in the document, however the magnitude and phase plots are > > nothing like those given. �Am I doing something wrong or is the > > document in error? �The author told me that as far as he remembers, > > the filter "worked" but he hadn't time to re-visit it. > > > Can anyone offer an explanation? > > > Thanks. > > and here is the Scilab code if anyone wants to try it/investigate > further: > > z1 = -0.834946 �+ -1.459074 * %i; > z2 = -0.834946 �+ 1.459074 * %i; > z3 = 0.834946 � + -1.459074 * %i; > z4 = 0.834946 � + 1.459074 * %i; > z5 = 0 �+ -1.707483 * %i; > z6 = 0 �+ 1.707483 * %i; > z7 = -1.362397 �+ -0.79655 * %i; > z8 = -1.362397 �+ 0.79655 * %i; > z9 = 1.362397 � + -0.79655 * %i; > z10 = 1.362397 �+ 0.79655 * %i; > z11 = -1.118507 + 0 * %i; > z12 = 1.118507 �+ 0 * %i; > > p1 = -0.894071 �+ 0 * %i; > p2 = 0.894071 � + 0 * %i; > p3 = -0.547048 �+ -0.319837 * %i; > p4 = -0.547048 �+ 0.319837 * %i; > p5 = 0.547048 � + -0.319837 * %i; > p6 = 0.547048 � + 0.319837 * %i; > p7 = -0.295469 �+ -0.516331 * %i; > p8 = -0.295469 �+ 0.516331 * %i; > p9 = 0.295469 � + -0.516331 * %i; > p10 = 0.295469 �+ 0.516331 * %i; > p11 = 0 + -0.585696 * %i; > p12 = 0 + 0.585696 * %i; > > H = (real((%z - z1) * (%z - z2)) * real((%z - z3) * (%z - z4)) * real > ((%z - z5) * (%z - z6)) * real((%z - z7) * (%z - z8)) * real((%z - z9) > * (%z - z10)) * real((%z - z11) * (%z - z12))) / (real((%z - p1) * (%z > - p2)) * real((%z - p3) * (%z - p4)) * real((%z - p5) * (%z - p6)) * > real((%z - p7) * (%z - p8)) * real((%z - p9) * (%z - p10)) * real((%z > - p11) * (%z - p12))) > > sys=syslin('d', H); > > fmin=0.001; > fmax=0.5; > > scf(1);clf; > plzr(H); > > scf(2);clf; > bode(sys,fmin,fmax); //Plots frequency response in Bode diagramcan anyone offer an explanation?