# How do I convert this obscure allpass from matlab into gen code

Blair

Aug 30 2023 | 1:54 am

I found this allpass filter in the form of matlab code. Its a special filter used to create inharmonicty in strings waveguides. I was wondering if anyone would be willing to help me port it to genexpr?
I am unsure where something like a history operator fits in, where the actual input and output signal go,
also little things like the periods which are in some lines, I heard it might be something to do with an array?
another confusing thing is the colons on this line, which i heard is like a counter?phik = pi*[1:2:2*nap-1];

function sos = adf(f0,B,df,beta) % adf.m % % Allpass dispersion filter design % J.S. Abel, V. Valimaki, and J.O. Smith, "Robust, Efficient Design of % Allpass Filters for Dispersive String Sound Synthesis," IEEE Signal % Processing Letters, 2010. % % Parameters: % f0 = fundamental frequency, Hz % B = inharmonicity coefficent, ratio (e.g., B = 0.0001) % df = design bandwidth, Hz % beta = smoothing factor (e.g., beta = 0.85) % % Examples: % sos = adf(32.702,0.0002,2100,0.85); % sos = adf(65.406,0.0001,2500,0.85); % sos = adf(130.81,0.00015,4300,0.85); % % The output array sos contains the allpass filter coefficients % as second-order sections. % % Created: Vesa Valimaki, Dec. 11, 2009 % (based on Jonathan Abel's Matlab code) %% initialization % system variables fs = 44100; %% sampling rate, Hz nbins = 2048; %% number of frequency points %% design dispersion filter % period, samples; df delay, samples; integrated delay, radians tau0 = fs/f0; %% division needed pd0 = tau0/sqrt(1 + B*(df/f0).^2); %% division and sqrt needed mu0 = pd0/(1 + B*(df/f0)^2); phi0 = 2*pi*(df/fs)*pd0 - mu0*2*pi*df/fs; % allpass order, biquads; desired phases, radians nap = floor(phi0/(2*pi)); phik = pi*[1:2:2*nap-1]; % Newton single iteration etan = [0:nap-1]/(1.2*nap) * df; %% division needed pdn = tau0./sqrt(1 + B*(etan/f0).^2); %% division and sqrt needed taun = pdn./(1 + B*(etan/f0).^2); phin = 2*pi*(etan/fs).*pdn; theta = fs/(2*pi) * (phik - phin + (2*pi/fs)*etan.*taun) ./ (taun - mu0); % division needed % compute allpass pole locations delta = diff([-theta(1) theta])/2; cc = cos(theta * 2*pi/fs); eta = (1 - beta.*cos(delta * 2*pi/fs))./(1 - beta); %% division needed alpha = sqrt(eta.^2 - 1) - eta; % sqrt needed % form second-order allpass sections temp = [ones(nap,1) 2*alpha'.*cc' alpha'.^2]; sos = [fliplr(temp) temp];