A mass spectrometer having a mass filter which applies a transient voltage profile to accelerate ion packets. The voltage profile is chosen to have a functional form which imparts each ion species with a kinetic energy which is larger the larger the mass-to- charge ratio and a velocity which is smaller the larger the mass-to-charge ratio. The ions are detected in an ion detector which discriminates between different ion species based on their kinetic energy and taking account of the functional form of the voltage profile. Suitable voltage profiles include periodic functions such as sinusoids, triangles and sawtooths, which allow the amplification of drive pulses in the mass filter to be carried out with narrow band amplification stages, which are simple and inexpensive to construct.