Is periodogram the same as DFT? What is the difference?
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The periodogram (better explanation than the wikipedia) is done by averaging the squared absolute value of the DFT of a signal. If we regard the signal as an stationary stochastic process, the periodogram is an estimator of the spectral density, which is defined as the DFT (not of the signal itself, which is random, but) of the autocorrelation function of the signal.
Now, you might be asking yourself how both things relate: if the periodogram (or the spectral density) of the signal has, say, a peak around 1Khz, does that mean that the signal itself has a peak around 1Khz? Basically, yes. More precisely: that mean that the signal has much energy around that frequency. http://en.wikipedia.org/wiki/Wiener%E2%80%93Khinchin_theorem
Not quite. You can see from the definition that the periodogram is an estimate of the spectral density, thus it is closer to the squared magnitude of the DFT than the DFT itself.