1. A method for designing a time dependent function k m (t) for a given k-space trajectory k m , where m stands for one or multiple spatial dimension indices x, y, or z, of a magnetic resonance imaging=MRI experiment carried out on an MRI system, the method comprising the steps of: a) determining a gradient magnitude limit G; b) determining a gradient slew rate limit S; c) determining a frequency limit F, the frequency limit being characteristic for gradient hardware of the MRI system and denoting a maximum frequency that can reliably be produced by the gradient hardware; and d) generating the trajectory k m by applying a time varying waveform g m (t) of a gradient magnetic field while obeying the gradient magnitude limit, the gradient slew rate limit, and the gradient hardware frequency limit, wherein no instantaneous frequency of the gradient waveform g m (t) transgresses the frequency limit F, the k-space trajectory k m being a spiral with a rotation angle φ(t), wherein the time dependent function k m (t) comprises the following three domains: a frequency limit domain, in which the instantaneous frequency is close to the frequency limit while the gradient slew rate and gradient amplitude remain below the gradient slew rate and gradient amplitude limits; a slew rate limit domain, in which the gradient slew rate is close to the gradient slew rate limit while the instantaneous frequency and gradient amplitude remain below the frequency and gradient magnitude limits; and an amplitude limit domain, in which the gradient amplitude is close to the gradient amplitude limit while the instantaneous frequency and gradient slew rate remain below the frequency and slew rate limits.