Determine whether the following statements are true or false. Briefly justify your answer.

1.   Determine whether the following statements are true or false. Briefly justify your answer.

(a)   A Type 1 linear-phase FIR filter does not have a mandatory zero at z = 1 and therefore is not suitable for highpass filter design.

(b)  A rectangular window has a larger main lobe width and higher sidelobe level than a Blackmanwindow (suppose both have the same window duration).

(c)   For a given transfer function, there exists only a finite number of equivalent structures realizing the same transfer function.

(d)  If a digital filter has a pole at z = 1, then it cannot be an FIR filter.

(e)  The ROC of a causal transfer function H(z) cannot be a disk, i.e., it cannot be expressed as |z| < a for some non-negative constant a.

(f)    For any LTI system with a rational transfer function H(z), we can always find a minimum-phase system Hmin(z) that has an identical magnitude response as that of H(z).

(g)   Bilinear transform is not suitable for designing a differentiator H(ejω) = jω.

(h)  Window-based FIR filter design is unable to provide different ripple sizes in the passband and stopband of a filter.