1. The problem statement, all variables and given/known data Match each discrete-time signal with its DFT: 2. Relevant equations 3. The attempt at a solution I am mainly confused about Signal 7 and Signal 8. Signal 1 is the discrete equivalent to a constant function, therefore its DFT is an impulse (Dirac ##\delta##), so it corresponds to DFT 3. DFT of an impulse is a constant. Therefore Signal 6 corresponds to DFT 5. Signal 2 is a sampled version of a full period of a cosine. So we expect ##X(1)## and ##X(-1)## to be nonzero (##X(-1)## really is ##X(N-1)=X(25)##). Therefore Signal 2 corresponds to DFT8. By similar arguments, Signal 4 has exactly 2 cycles of a cosine and corresponds to DFT2. And Signal 3 has one and a half periods of a cosine, as we do not have complete periods we should expect spectral leakage, so signal 3 corresponds to DFT4 (the main peaks are around 1 & 2 plus negative frequencies). Likewise, Signal 5 corresponds to DFT7. Here is a summary of the results so far: Only Signals 7 & 8 and DFT 6 & 1 are left: What do signals 7 and 8 represent? Is Signal 7 an undersampled cosine? How do we go about matching them with their corresponding DFTs? Any explanation would be greatly appreciated.