Quote:
Originally Posted by TweakHead
I can't? I just did. I've made the seemingly trivial task of placing a 30,5Hz inside a second time frame for you and - once again - that gives you 30 complete cycles and a half. Do yourself a favour and open it in an audio editor software and check for yourself.
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No you didin't. Watch this (most important part starts around 3:07):
This demonstrates that if sine is tuned to frequency that can't exist in the window - the impossible sine frequency doesn't magically emerge from the spectrum. Rather the signal consists of many different allowed frequencies. That is also called spectral leakage. 30.5hz frequency can not exist in a one second window, rather such wave would contain different allowed frequencies of 30hz, 31hz, and maybe other frequencies...
Do you understand that half a cycle sine wave IS NOT a sine wave anymore? This is where your confusion seems to stem from. Sinewave has to start and end at the same phase, if it doesn't - it's not a sine wave. And that is what the FFT shows (it's a collection of different sine waves).