Apparatus for generating an encoded audio or image signal in the presence of transients, comprising: a window sequence controller for generating a window sequence information for windowing an audio or image signal, the window sequence information indicating a first window function for generating a first frame of spectral values, a second window function and at least one third window function for generating a second frame of spectral values having a first and a second portion, wherein the first window function, the second window function and the one or more third window functions overlap within a multi-overlap region; a preprocessor for windowing a second block of samples corresponding to the second window function and the one or more third window functions using an auxiliary window function to obtain a second block of windowed samples, and for preprocessing the second block of windowed samples using a folding-in operation of a portion of the second block overlapping with a first block into the multi-overlap portion to obtain a preprocessed second block of windowed samples having a modified multi-overlap portion; a spectrum converter for applying an aliasing-introducing transform to the first block of samples using the first window function to obtain the first frame of spectral values, for applying another aliasing-introducing transform to a first portion of the preprocessed second block of windowed samples using the second window function to obtain a first portion of spectral values of the second frame and for applying another one or more aliasing-introducing transforms to a second portion of the preprocessed second block of windowed samples using the one or more third window functions to obtain a second portion of spectral values of the second frame; and a processor for processing the first frame and the second frame to obtain encoded frames of the audio or image signal. a window sequence controller for generating a window sequence information for windowing an audio or image signal, the window sequence information indicating a first window function for generating a first frame of spectral values, a second window function and at least one third window function for generating a second frame of spectral values having a first and a second portion, wherein the first window function, the second window function and the one or more third window functions overlap within a multi-overlap region; a preprocessor for windowing a second block of samples corresponding to the second window function and the one or more third window functions using an auxiliary window function to obtain a second block of windowed samples, and for preprocessing the second block of windowed samples using a folding-in operation of a portion of the second block overlapping with a first block into the multi-overlap portion to obtain a preprocessed second block of windowed samples having a modified multi-overlap portion; a spectrum converter for applying an aliasing-introducing transform to the first block of samples using the first window function to obtain the first frame of spectral values, for applying another aliasing-introducing transform to a first portion of the preprocessed second block of windowed samples using the second window function to obtain a first portion of spectral values of the second frame and for applying another one or more aliasing-introducing transforms to a second portion of the preprocessed second block of windowed samples using the one or more third window functions to obtain a second portion of spectral values of the second frame; and a processor for processing the first frame and the second frame to obtain encoded frames of the audio or image signal.