# [Tex/LaTex] Missing delimiter (. inserted)

math-mode

The code below produces the error

Missing delimiter (. inserted).

{\it $$E_{k} = 10\log_{10}\left{ \frac{\sum_{i=1}^{M_{k}}{{\left[W_{k}^{P} x(i)\right]}^{2}}}{M_{k}}\right} (dB), \hspace{5em} k = 1,2,....,N\hspace{7em}$$}\\


Let me reformat your code to better understand what's wrong.

{\it
$$E_{k} = 10\log_{10} \left{ \frac{\sum_{i=1}^{M_{k}}{{\left[W_{k}^{P} x(i)\right]}^{2}}}{M_{k}} \right} (dB), \hspace{5em} k = 1,2,....,N\hspace{7em}$$}\\

• There is no need to have a group around the equation.

• The command \it does nothing useful and, besides, it has been deprecated for twenty years

• You don't want \$ inside

• \left{ is illegal; you want to have a growing brace and the command for printing an open brace is \{

• You seem to have lost the count of braces, due to the fraction. You probably wanted

\frac{\sum_{i=1}^{M_{k}} [W_{k}^{P} x(i)]^{2}}{M_{k}}


(note that \left[ and \right] are not necessary, they're even bad!)

• \right} is similar to the above.

• ellipsis should be denoted by \dots

• The final \hspace{7em} serves no purpose

So, here's a better realization

$$E_{k}=10\log_{10} \left\{ \frac{ \sum_{i=1}^{M_{k}} [W_{k}^{P} x(i)]^{2} }{ M_{k} } \right\} \,\mathrm{dB}, \qquad k=1,2,\dots,N$$


You probably also want to use siunitx for units, so \,\mathrm{dB} can better become \si{\decibel}, which is even much clearer, isn't it?

The fraction appears to be quite crowded, though; better set the denominator in front of the summation:

\documentclass{article}
\usepackage{amsmath}
\usepackage{siunitx}

\begin{document}

$$E_{k}=10\log_{10} \biggl\{ \frac{1}{M_{k}} \sum_{i=1}^{M_{k}} [W_{k}^{P} x(i)]^{2} \biggr\} \si{\decibel}, \qquad k=1,2,\dots,N$$

\end{document}