A computer-implemented method of audio processing, the method comprising: receiving a first transform domain signal, wherein the first transform domain signal is a hybrid complex transform domain signal having a plurality of bands, wherein at least one of the plurality of bands has a plurality of sub-bands, wherein the first transform domain signal has a first plurality of harmonics; generating an upsampled transform domain signal by upsampling the first transform domain signal, wherein the upsampled signal is a complex-valued time domain signal; generating a second transform domain signal based on the upsampled first transform domain signal by: generating a second plurality of harmonics to the upsampled first transform domain signal according to a non-linear process, wherein the second transform domain signal has the second plurality of harmonics that differs from the first plurality of harmonics; and performing loudness expansion or compression on the second plurality of harmonics, wherein the second transform domain signal is a complex-valued signal having an imaginary part; filtering the second transform domain signal to split the second transform domain signal into a plurality of sub-bands and generate a third transform domain signal, wherein the third transform domain signal has a plurality of bands, wherein at least one of the plurality of bands has the plurality of sub-bands; and generating a fourth transform domain signal by mixing the third transform domain signal with a delayed version of the first transform domain signal, wherein a given sub-band of the third transform domain signal is mixed with a corresponding sub-band of the delayed version of the first transform domain signal. receiving a first transform domain signal, wherein the first transform domain signal is a hybrid complex transform domain signal having a plurality of bands, wherein at least one of the plurality of bands has a plurality of sub-bands, wherein the first transform domain signal has a first plurality of harmonics; generating an upsampled transform domain signal by upsampling the first transform domain signal, wherein the upsampled signal is a complex-valued time domain signal; generating a second transform domain signal based on the upsampled first transform domain signal by: generating a second plurality of harmonics to the upsampled first transform domain signal according to a non-linear process, wherein the second transform domain signal has the second plurality of harmonics that differs from the first plurality of harmonics; and performing loudness expansion or compression on the second plurality of harmonics, wherein the second transform domain signal is a complex-valued signal having an imaginary part; filtering the second transform domain signal to split the second transform domain signal into a plurality of sub-bands and generate a third transform domain signal, wherein the third transform domain signal has a plurality of bands, wherein at least one of the plurality of bands has the plurality of sub-bands; and generating a fourth transform domain signal by mixing the third transform domain signal with a delayed version of the first transform domain signal, wherein a given sub-band of the third transform domain signal is mixed with a corresponding sub-band of the delayed version of the first transform domain signal. generating a second plurality of harmonics to the upsampled first transform domain signal according to a non-linear process, wherein the second transform domain signal has the second plurality of harmonics that differs from the first plurality of harmonics; and performing loudness expansion or compression on the second plurality of harmonics, wherein the second transform domain signal is a complex-valued signal having an imaginary part; filtering the second transform domain signal to split the second transform domain signal into a plurality of sub-bands and generate a third transform domain signal, wherein the third transform domain signal has a plurality of bands, wherein at least one of the plurality of bands has the plurality of sub-bands; and generating a fourth transform domain signal by mixing the third transform domain signal with a delayed version of the first transform domain signal, wherein a given sub-band of the third transform domain signal is mixed with a corresponding sub-band of the delayed version of the first transform domain signal.