GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

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