## Problem with 1st order Massberg LPF

Started by 5 years ago●3 replies●latest reply 5 years ago●120 viewsI'm trying to implement this filter in title by following the book "Designing Audio Effect Plug-Ins in C++" By Will Pirkle

Problem I'm facing is the magnitude response error when comparing against analog model of the LP filter. Here is a plot showing the difference:

I get these are values for variables (fc=1000, fs=44100):

>> massberg_test w0 = 0.14248 g1 = 0.045305 gm = 0.70711 wm = 6283.2 Om = 0.071359 Os = 0.10081 g0 = 1.1008 a0 = 0.14612 a1 = 0.055508 b1 = -0.89919 Real: a = [ 0.132736 0.050424 ] b = [ 1.00000 -0.81684 ]

I don't have access to the original paper by M. Massberg so, I can't be sure if the equations in my source book is correct (I've read that the "ac" in g1 formula is just a typo and book errata does not mention other errors for this fileter).

Q:

1. Are the equations found in Pirkle book correct?

2. If 1 is Yes then where to look the issue from?

I think the value for Omega_s is not correct. The value that I get is 0.07121. Since the "b0", "b1", "a0", and "a1" coefficients are computed using Omega_s then they are incorrect too.

Using the equations in the body of the text from the Massberg (2011) paper,

fc=1e3; Fs=44.1e3; Wn=2*pi*fc/Fs; g1=2/sqrt(4+(Fs/fc)^2); % Okay gm=max(sqrt(0.5), sqrt(g1)); % Okay wm=2*pi*fc*sqrt(1-gm^2)/gm; % Okay Om=tan(wm/(2*Fs)); % Okay Os=Om*sqrt((gm^2-g1^2)*(1-gm^2))/(1-gm^2); % Check b0=Os+g1; b1=Os-g1; a0=Os+1; a1=Os-1; b=[b0/a0 b1/a0]; a=[1 a1/a0]; figure; freqz(b, a, 4096, Fs); [bf, af] = lp1(Wn); figure; freqz(bf, af, 4096, Fs);

The Matlab code from the Massberg (2011) paper for the first-order lowpass filter is,

function [b,a] = lp1(Wn) g1 = 2/sqrt(4+(2*pi/Wn)^2); gm = max(sqrt(0.5),sqrt(g1)); Ws = tan(Wn*sqrt(1-gm^2)/(2*gm)) *sqrt((gm^2-g1^2)*(1-gm^2)) /(1-gm^2); b0 = Ws+g1; b1 = Ws-g1; a0 = Ws+1; a1 = Ws-1; b = [b0/a0 b1/a0]; a = [1 a1/a0];

where Wn is,

Wn=2*pi*fc/Fs;

Thanks a lot, you're right. This change fixes the problem.

Very good. I'm glad to have helped.