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A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discrete-time filter with transfer function $G\left ( z\right )= \frac{2z^{2}-0.5032 \: z}{z^{2}-0.5032 \: z+k}$ so that the impulse response of the continuous-time filter, sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete time-filter. The value of $k$ is _________