## What is the reason for this 'linear error'

Started by 6 years ago●5 replies●latest reply 6 years ago●131 viewsHi!

Here's MIM (Magnitude Invariance Method) paper (press the "View PDF" to get the paper/matlab code in hands) and here's a plot showing the issue I'm trying to solve:

Magnitude responses for one pole LP filter at few frequency locations.

As plot shows, there's some issue in MIM's function **c2dn() **implementation, which 'moves' the fc point especially at low fc values. *IIRC, same type of issue happens when changing the fs.*

Analog prototype LPF is calculated as:

w0 = 2*pi*fc; Analogb = 1; Analoga = [1 w0]; Analog = tf(Analogb, Analoga); Analog = Analog/dcgain(Analog);

which is then given as an input for to calculate the MIM filter:

fs=44100; mimpim = 'mim'; samplingtime = 1/fs; numofsamples = 2048; [Dz1] = c2dn(Analog, samplingtime, mimpim, 1, numofsamples); %[a2, b2, T] = tfdata(Dz1); %coeffs

where **c2dn()** is the function from MIM paper.

Plotting:

fs2 = fs/2; nf = logspace(0, 5, fs2); [mag, pha] = bode(Analog,2*pi*nf); semilogx(nf, 20*log10(abs(mag)), 'color', 'g', 'linewidth', 1.5); axis([10 fs2 -50 1]); hold on;[mag, pha] = bode(Dz1,2*pi*nf); semilogx(nf, 20*log10(abs(mag)), 'color', 'k', 'linewidth', 1.5, 'linestyle', '--');grid on; title('Various TF (LPF 1)'); legend('Analog', 'MIM','location', 'southwest'); xlabel('Hz');ylabel('dB');

So far I found out that the *fc* error is quite linear between certain points (I picked -3dB points for few *fc* and then calculated the trend *f(x)* (R² was 0.99989...)) so, one could probably find the source for "error" by looking the matlab codes for MIM function **c2dn()**.

Here's plot showing the effect of my correction f(x):

Correction formula `f(x) = 0.9704384746x - 51.6991952722`

works well for *fc* in range 60Hz-Nyqvist (fs=44.1kHz). (*Note: correction for fc=10Hz showen in plot is done using another formula so you can omit it as a result of this f(x)*).

Any suggestions regarding the source for this "error"?

Hi!

I think it would be convenient if you give explicit examples of expectation vs outcome and also put the related formulas and/or code snippets so the reader doesn't have to waste time studying the paper and code in order to help you. Because just looking at the plot I don't understand what is "MIM" and where the "linear error" is that you are trying to explain (and/or fix or avoid).

Cheers

Looks like the 1st image showing the error was not present anymore? I added it and also added some Octave code which I used in making the LP filters and 1st plot.

Matlab code for function **c2dn()** is copyrighted so I can't list it here.

One more note: Decreasing the value of **numofsamples** parameter improves response at lower fc (and vice versa) ?

*% minimum phase sequence r^mn*" which changes

*h*data by taking lmn data (

matrix[128] lmn = [0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

(above matrix actual when numofsamples = 128)) from "homomorphic filtering" block and calculates new values for h:

h = h.*lmn';

When this line is in comments magnitude plots looks good (if the **numofsamples** parameter has suitable (big) value):

Problem is that commenting the line effects directly to the aliasing issue this type of filter has

Any thoughts if this (r^mn thingy) can be improved somehow?