A band-limited continuous signal has $X(f)=1-|f|/200$ for $|f|\leq200$ Hz and zero otherwise. It is uniformly impulse-sampled at 600 Hz, giving spectrum Xₛ(f). Find Xₛ(600)/Xₛ(500) to one decimal place.
Sampling creates replicas every six hundred hertz, with a common scaling factor. At six hundred, the replica centered there contributes X(0)=1. At five hundred it contributes X(−100)=0.5. The other replicas contribute zero because the original support is ±200 Hz. The common scale cancels, giving 1/0.5=2.0.
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