How to define function

Hello!

Could you, please, suggest an answer:

How to define function f (x), which for x from -1 to 1, f (x) = 1; and outside these limits f (x) = 0.

Thank in advance!

[Rik]

This is your homework. What have you tried so far? And do you want a normal (or anonymous) function, or a symbolic function?

[Viktoriia Buliuk]

I try to define Window function. I have tried with if.

[KSSV]

Show us your code.

Answer 1

[hosein Javan]

function y = f(x)
y = zeros(size(x));
y(abs(x) < 1) = 1;
end

[hosein Javan]

the advantage of such definition is that you can pass inputs to the function as array rather than scalars. it should really help in dealing with fourier transform which requires element-wise product.

[hosein Javan]

however this method could lead to unnecessary computer calculations becasue when you multiply the window function to your signal, the elements that are multiplied eaither by 1 or 0 which is unnecessary. multiplication is for a non-rectangular window function like gaussian,etc,.. . but in the case of rectangular. you only have to select the values of your function that meet the condition by array indexing. if you are planning to do heavy simulation with rectangular window, indexing is more efficient but if it's just a simple calculation function multiplication should be fine.

[Rik]

In this case you can simply convert the logical to double:

f=@(x) double(abs(x)<1);

In most other cases you will need multiplication:

%g={x^2 for -1<x<1
%  {8   for x>2
%  {0   otherwise
g=@(x) ...
    x.^2.*(-1<x & x<1)+...
    8.*(x>2)+...
    0;

[hosein Javan]

ofcourse unless you want to use function file, you need this multiplication only to define your function in anonymous form. correct.

[Viktoriia Buliuk]

Thank you very much!