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Changed the title because it's now apparent that LTSPICE itself is really part of the question.
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What's the junk at the end of anmy FFT in LTSPICE?

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What's the junk at the end of an FFT?

Why do FFTs have junk on the high frequency end? Suppose I go to simulate this circuit in LTSPICE:

schematic

simulate this circuit – Schematic created using CircuitLab

Where the LTSPICE sine and simulation parameters are:

SINE(0 1 1K 0 0 0 1000)
.tran 1 startup

Then I ask LTSPICE to give me an FFT with no window and 1,000,000 points: FFT

What's all the junk at the end for? I would expect only one spike at 1KHz, not an additional one at 3KHz, etc. Does this happen to all FFTs? What controls the spikes that you get after your fundamental?