How to combine 2 function handles of different variables?

Strangely enough I was not able finding an answere to this sinewy problem:

Given 2 function handles

mu = @(n, dmu, mubar) mubar + n*dmu/4; 

f = @(t, mu) cos(2*pi*mu*t);

How do I combine them into one? Obviously (in my disfavor) adding doesn't work:

f = f + mu % Error

Please tell me there is a way around just creating a handle manually. Eventually I want something like this:

f  = @(n, dmu, mubar, t) cos(2*pi*(mubar + n*dmu/4)*t);

Answer 1

[Karim]

You need to add the input parameter in order to evaluate the functions. See below for demonstration using some random inputs.

You can indeed add the results of the function handles if the outputs have the same dimensions.

mu = @(n, dmu, mubar) mubar + n*dmu/4; 

f = @(t, mu) cos(2*pi*mu*t);


% assume some values
n_in     = rand(1);
dmu_in   = rand(1);
mubar_in = rand(1);
t_in     = rand(1);

% evaluate f1 = f + mu
f1 = f(t_in, mu(n_in, dmu_in, mubar_in)) + mu(n_in, dmu_in, mubar_in)

f1 = -0.3532

If you want to cobine merge the function handles, you can use the symbolic toolbox:

syms n dmu mubar t

% create symbolic expression for mu
mu = mubar + n*dmu/4

mu = 

% create symbolic expression for f (define this after mu, since matlab will
% fill in the equation)
f = cos(2*pi*mu*t)

f = 

% convert the symbolic expression into a function handle
f = matlabFunction(f)

f = function_handle with value:
    @(dmu,mubar,n,t)cos(t.*pi.*(mubar+(dmu.*n)./4.0).*2.0)

Answer 2

[KSSV]

mu = @(n, dmu, mubar) mubar + n*dmu/4; 
f = @(t, mu) cos(2*pi*mu*t);
fmu = @(x) f(mu)