Using the floor function to define a periodic function

Question

Is it possible to define the function defined in the following image using the floor function? If so, how?

Update

I tried your suggestion with Matlab's symbolic toolbox,

syms x clear
clear f
f(x)=abs(x-2*floor(x/2));
fplot(f(x),[0,8])

but I got the following picture, which is not correct.

Sure. Why do you want to use the floor function specifically? — TomGrubb, Nov 07 '18 at 05:42
@RushabhMehta I tried your suggestion, but it did not work. See my update above. Did I interpret your symbolism correctly? Thanks. — David, Nov 07 '18 at 07:17
@TomGrubb Because Matlab's Symbolic Toolbox will give the Laplace transform of a function defined by the floor function. — David, Nov 07 '18 at 07:18

score 1 · Accepted Answer · answered Nov 08 '18 at 18:09

Define the fractional part $\{x\}$ to be $$ x = \left\lfloor x \right\rfloor + \left\{ x \right\}\quad \Rightarrow \quad 0 \le \left\{ x \right\} < 1 $$ note that it does not actually reach to $1$.

Then stretch and shift it so to obtain $$ 1 - 2\left\{ {{x \over 2}} \right\} $$

Finally take the absolute value $$ f(x) = \left| {\,1 - 2\left\{ {{x \over 2}} \right\}\,} \right| = \left| {\,1 - x + 2\left\lfloor {{x \over 2}} \right\rfloor \,} \right| $$

Using the floor function to define a periodic function

1 Answers1