- #1
p75213
- 96
- 0
Homework Statement
The book defines a 1/2 wave odd symmetrical function as each 1/2 cycle is a mirror image of the next.
[tex]\begin{array}{l}
{a_0} = 0 \\
{a_n} = {\textstyle{4 \over T}}\int_0^{{\raise0.5ex\hbox{$\scriptstyle T$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}} {f(t)\cos n{w_0}t\,dt} {\rm{ - > for n odd}} \\
{a_n} = 0{\rm{ - > for }}n{\rm{ even}} \\
{b_n} = {\textstyle{4 \over T}}\int_0^{{\raise0.5ex\hbox{$\scriptstyle T$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}} {f(t)\sin n{w_0}t\,dt} {\rm{ - > for n odd}} \\
{b_n} = 0{\rm{ - > for }}n{\rm{ even}} \\
\end{array}[/tex]
An odd symmetrical function is described as being symmetrical about the vertical axis. f(-t)=-f(t).
[tex]\begin{array}{l}
{a_0} = 0 \\
{a_n} = 0 \\
{b_n} = {\textstyle{4 \over T}}\int_0^{{\raise0.5ex\hbox{$\scriptstyle T$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}} {f(t)\sin n{w_0}t\,dt} \\
\end{array}[/tex]
Given this I would therefore categorize the attached periodic function as 1/2 wave odd symmetrical. However the book uses the odd symmetrical category and the corresponding formulas.
Can somebody explain why it is odd symmetrical and not 1/2 wave odd symmetrical?