filter function gives the filter response for both IIR and FIR systems whereas conv function performs linear convolution of the input signals. For FIR filters the functions might perform similar operation but for IIR filters the outputs from both the functions are different.
The output length of filter function is equal to input vector length whereas conv function output length equal to length(filter_vector) + length(input_vector) - 1.
Instead replacement to filter function with conv function in the code can be considered by taking symbolic coeffients
syms z
F = (0.5 + 0.5*z^(-1))/(1-z^(-1)+0.5*z^(-2)); % Symbolic Function
h_sym = iztrans(F); % Inverse z transform
h = double(subs(h_sym,n)); % filter coefficients
y_conv = conv(h,x); % convolution
y_out = y_conv(1:length(x));
