MATLAB: How to make a function defined at discrete points

discretefunction

x[n] = { 1 if n=0,

2 if n=1,

3 if n=2,

2 if n=5,

2 if n=6,

0 otherwise }

One possibility:

xn = @(n) [(n==0) (n==1) (n==2) (n==5) (n==6)]*[1; 2; 3; 2; 2];
y = xn(2)
y =
     3

You can first interpolate your data to get a function handle. Then, you can use "integral" to integrate your data:

1. Create 50 sample data to work with

   >> n = 50;
   >> x = linspace(0, 2*pi, n);
   >> y = sin(x) + 0.1*randn(1,n);

2. Plot the data to visualize it

   >> plot(x,y,'x');

3. Create an interpolation of the data, and save it as a function handle:

   >> F = griddedInterpolant(x,y);
   >> fun = @(t) F(t)

4. Plot the function to visualize:

   >> plot(x, fun(x))

5. Integrate the function with respect to x:

   >> q = integral(fun, x(1), x(end))

If you are simulating a discrete system, then use the discrete solver with a fixed time step.

If your system has a 40kHz signal, you can't use a time step that is 1/40k. You need to use a time step that is not larger than 1/40k/2.

Preferably, the time step should be smaller than 1/40k/10.