This problem concerns a discrete-time filter with a real-valued impulse response h[n]. Determine whether the following statement is true or false:
Statement: If the group delay of the filter is a constant for 0 < ω < π, then the impulse response must have the property that either
h[n] = h[M − n]
or
h[n] = −h[M − n],
where M is an integer.
If the statement is true, show why it is true. If it is false, provide a counterexample.
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