Let the signal, 

\(x\left( t \right) = \mathop \sum \nolimits_{k = - \infty }^\infty {\left( { - 1} \right)^k}\delta \left( {t - \frac{k}{{2000}}} \right)\)

is passed through an LTI system with frequency response H(ω) given as:

\(H\left( \omega \right) = \left\{ {\begin{array}{*{20}{c}} {1\;\;;\;\;\left| \omega \right| < a}\\ {\;0\;\;\;otherwise} \end{array}} \right.\)

For the number of sinusoids in the output to be 3. The Nyquist sampling frequency of the output is _________ kHz