When the input signal to an FFT algorithm has many samples equal to

$0$ it is possible to prune the FFT tree to achieve computational saving. Consider an $8-$pt

case where only x$[0]$ and x$[1]$ are non$-$zero and the remaining six samples are all $0.$

Determine which of the two radix$-2$ methods is preferred in this scenario and determine

the computational savings the preferred pruned radix$-2$ method provides relative to the

other pruned radix$-2$ method.