1. The problem statement, all variables and given/known data I am trying to match each of the following 28-point discrete-time signals with its DFT: Set #1: Set #2: 2. Relevant equations 3. The attempt at a solution Set #1 We have already established (here) that: ##Signal 1 \leftrightarrow DFT3## ##Signal 4 \leftrightarrow DFT2## Now, Signal 3 looks like Signal 4. The only difference is that the temporal sample spacing has been increased. So, instead of having a single central peak in the DFT, we now have two peaks (at 7 and 21). Why? Likewise, Signal 2 looks like Signal 1, except it was sampled at twice the sampling interval. So, why does increasing the sample spacing create an additional frequency peak in each case? Set #2: These signals look like rectangular pulses (but none of them are a full period of a periodic rectangular signal). The DFT of a rectangular pulse is samples of the sinc function. DFT1 & 3 look like sincs, but I am not sure how to interpret DFT2. Clearly, each signal has a different average value. For instance, Signal 3 should have the highest DC value because it has more samples at 1 than the other two signals. But the axes of the DFTs are not labeled. So, how else can I match these? Any suggestions would be greatly appreciated.