# Bandwidth-limited pulse

Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is determined by its complex spectral components, which include not just their relative intensities, but also the relative positions (spectral phase) of these spectral components. For different pulse shapes, the minimum duration-bandwidth product is different. The duration-bandwidth product is minimal for zero phase-modulation. For example, ${\displaystyle \mathrm {sech^{2}} }$ pulses have a minimum duration-bandwidth product of 0.315 while gaussian pulses have a minimum value of 0.441.