Matlab: how to write a vector of a few points as a continuous function? -

i have 2 vectors:

x = [0; 1; 2] y = [2.0000; 0; -14.7781]

if plot x , y see 3 points on xy-plane. want connect 3 points , them continuous function:

y = f(x), y(0) = 2; y(1) = 0; y(2) = -14.7781; y(0.5) = value between 2 , 0.

for example y can treated zoh (zero order held) continuous signal.

i saw matlab has function called d2c, converts model discrete continuous time. have no idea how link vector have already. how matlab?

ok, latest edit improves situation lot.

however, still not demarcate problem sufficiently.

zoh simple

    >> x = [0; 1; 2];     >> y = [2.0000; 0; -14.7781];     >> f = @(new_x) y(find(x <= new_x, 1, 'last'));     >> f(0.5)      ans =         2

however, not think mean, y(0.5) = value between 2 , 0 part of question indicates.

perhaps want linearly interpolated value:

>> f = @(new_x) interp1(x,y, new_x); >> f(0.5)  ans =      1

or cubic splines interpolation:

>> f = @(new_x) interp1(x,y, new_x, 'spline'); >> f(0.5)  ans =         2.5973

what i'm asking is: model best describes signal when sample time decrease infinitesmal values?

Kiastu