4please provide full answer

a) Z -transform is mainly used for analysis of discrete signal and discrete LTI system. i) Given x(n) =3(-4)"u(n) - 2 (1)"u(n) + (2)"u(-n -1), find X(z) and determine the Region of Convergence (ROC) for this input sequences. State the causality and the stability of this system. [10 marks] ii) By using partial fraction expansion method, determine the input sequence x (n) for: 1 - 32-1 X(Z) = 1 2-147 -2 [5 marks] b) Given the raw electromyography (EMG) signal with a sampling frequency of 1000 Hz. The signal below 20 Hz needs to be removed during the analysis process. By focusing on the cut-off frequency and the selective type of filter, design the filter system. [5 marks]\f