Why does a spike lasting a millisecond contain frequencies far above 1 kHz? · Lobeworks/17

Because a sharp shape is never one frequency.

Why does a spike lasting a millisecond contain frequencies far above 1 kHz?

Because a sharp shape is never one frequency. By Fourier, any waveform is a sum of sine waves, and the faster it changes the higher the sines it needs; a spike rises in a fraction of its millisecond, so its sum reaches several kilohertz. That is why the spike band of a probe runs to about 10 kHz and is sampled at 30 kHz: cutting at 1 kHz would round every spike into a different shape and blur the footprints spike sorting depends on.