Revolutionary new knowledge about auditory perception!

Leonhard is presenting a new analysis model for analysing sound. The new model is patent pending and is called Auditory Perceptual Pulse Analysis (APPA) because the model is based on mathematical and physical phenomena that correspond very much to how the human ear perceive sound. The phenomena are among other things a result of the behaviour of transient response of a system. The response reacts in practise as a pulse and in the model the pulse is analysed in auditory frequency channels. The outputs of the channels are oscillating pulses. The time period of the oscillations is very important for the sound picture. It would be very tempting to make a Fourier analysis but damped oscillations are broad spectred with more than one frequency.

Problems by Using Short Time Fourier Analysis or FFT in Speech Recognition (Analysis)

  • The dynamic behavior of the speech signal is very important in speech recognition. Speech consists of transient components (damped sines) and not steady state components.

  • By voiced speech the speech signal is periodic that gives a discrete spectrum which is easy to detect in an FFT, but during periods the signal also has a dynamic behavior.

  • In these cases, it is nearly impossible to tell in a spectrum what frequency components in a spectrum that are created from the dynamic behavior and how the dynamics behavior is.

  • Interference analysis has much better relation to the physically behavior of the signal (oscillations and instantaneous energy).

Interference Modulation – Sines


Interference Modulation – Speech




  • Oscillagram look like spectrum – with frequency axis in Hz and amplitude axis

  • However, the frequency axis is not sine or cosine but oscillation. Oscillation is definite by the period between the crossover and the RMS value of amplitude in the crossover period.


  • The Oscillagram is calculated over a timeframe and the amplitude is calculated as the mean RMS of all the crossover amplitudes as function of crossover period (Hz).

For more detailed information about APPA contact Frank U. Leonhard on: