Suppose that we have used the Parks–McClellan algorithm to design a causal FIR linear-ph...

Suppose that we have used the Parks–McClellan algorithm to design a causal FIR linear-phase lowpass filter. The system function of this system is denoted H(z). The length of the impulse response is 25 samples, i.e., h[n] = 0 for n < 0 and for n > 24, and h[0] ≠ 0. The desired response and weighting function used were

In each case below, determine whether the statement is true or false or that insufficient information is given. Justify your conclusions.

(a) h[n + 12] = h[12 − n] or h[n + 12] = −h[12 − n] for −∞ < n < ∞.

(b) The system has a stable and causal inverse.

(c) We know that H(−1) = 0.

(d) The maximum weighted approximation error is the same in all approximation bands.

(e) If z₀ is a zero of H(z), then 1/z₀ is a pole of H(z).

( f ) The system can be implemented by a network (flow graph) that has no feedback paths.

(g) The group delay is equal to 24 for 0 < ω < π.

(h) If the coefficients of the system function are quantized to 10 bits each, the system is still optimum in the Chebyshev sense for the original desired response and weighting function.

(i) If the coefficients of the system function are quantized to 10 bits each, the system is still guaranteed to be a linear-phase filter.

(j) If the coefficients of the system function are quantized to 10 bits each, the system may become unstable.