Analyse und Resynthese digitaler Audiosignale durch lineare Zeit-Frequenz-Transformationen

The Shorttime-Fourier-Transform, the Wavelet-Transform and the less known Bounded-Q-Transform are discussed with respect to the analysis and the resynthesis of digital audio signals. All of these linear time-frequency-transformations are two-dimensional. They can be used to plot a one-dimensional time signal as a time-frequency-picture. The Shorttime-Fourier-Transform uses the Fourier-Transform, transforming short pieces of the signal. It can be easily computed with the Fast-Fourier-Transform. The signal representation, however, depends on the length of the signal-pieces and is less suitable for audio signals, because of the equal spaced frequency resolution and the fact that most of the audio signal's energy is found in the low frequency range. The Wavelet-Transform partitions the frequency axis logarithmically with a high frequency resolution at the lower frequencies and a lower resolution at high frequencies. But the cost of computing the Wavelet-Transform as a graphical signal representation is very high, and also the burden of data that has to be stored for the resynthesis. The Bounded-Q-Transform links the less computational expense of the Shorttime-Fourier-Transform with a somewhat logarithmic frequency partitioning. This transform has been implemented in Objective-C on a NeXT-computer. This program was used to analyse audio signals, to change the time-frequency-representation graphically and to resynthesize audio signals from the changed data.