Short time transient events are extremely challenging to represent in the transform domain employed by common transform-based codecs used in applications such audio compression. These short-time events last for a duration that is much shorter than a typical data window, and consequently have power distributed throughout the transform domain. Accurate representation of these events in the transform domain requires higher bitrates than usually available. A common solution is to use window switching, where smaller windows are used for short time transient events, but this has a negative impact on the bitrate as well. In this paper, we show that with certain simplifying assumptions, transient reconstruction can be reduced to a tractable problem that is performed in the frequency domain, so that the transient event can be easily mixed in with the representation of the non-transient events. A closed form frequency domain representation for the phase of a transient event is introduced, and it is shown that this can be done in an iterative way that allows for increasingly complex transient structures back in the time domain.
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