3) Im z-plane Re 1/2 2/3 Unit Circle Pole-zero map and ROC (shaded area) of a filter is given above. a) Is the filter causal or not? Explain why. b) Is the filter stable or not? Explain why. c) Is the...

Please answer D) E) F) and G) SUBPARTS. Please answer the question step by step and please care to explain the question in detailed with your own sentence and explain why you used that formula, calculations etc asap. Thanks in advance.

Extracted text: 3) Im z-plane Re 1/2 2/3 Unit Circle Pole-zero map and ROC (shaded area) of a filter is given above. a) Is the filter causal or not? Explain why. b) Is the filter stable or not? Explain why. c) Is the filter IIR or FIR? Explain why. d) If the filter has unity gain, find its z-transform, H(z). e) Find the filter's impulse response, h[n]. f) If a pole at z= - 2 and a zero at z-0 are added to the original filter above, draw pole-zero map and ROC of the new filter which is causal. g) Is the new filter in (f) stable or not? Explain why? h) How would you change the original filter from IIR to FIR (if the original filter is IIR) or from FIR to IIR (if the original filter is FIR) considering the z-transform in (d)? Explain your proposal/example. If make the original filter left-sided with the same poles and zeros, plot its ROC. i) j) you Is the filter in (i) stable and causal? Explain why.