Theoretical Investigations to Reduce Harmonic Distortions in a Clipping Process
Friedrich Vilbig, Kurt H. Haase · The Journal of the Acoustical Society of America · 1957
To investigate harmonic distortions of clipped speech, the speech waves are replaced by a sum of two sine waves. Infinite clipping of these two frequencies results in a harmonic distortion of 75%. If the audioband is modulated to a higher frequency range, one of the sidebands clipped, and all distortions beyond the single band width suppressed, the distortion drops to 50%. Distortion is further reduced if the original representative sum of the sine waves is differentiated and transformed to a pulse wave with pulse width modulation, the width corresponding to amplitude maximums and minimums. With pulse width modulation of unit amplitude, the advantages of normal clipped speech transmission are retained. On the receiver side the pulse width modulation is transformed to a pulse amplitude modulation with relatively short pulses. The pulse wave, still highly distorted is applied to a storage device (e.g., a magnetic tape or a ladder network of condensers). The picture of the pulses is smoothed and approximates the picture of the original sum of the two sine waves. Essentially, the approximation is the replacement of the original wave by a triangular one. This process, mathematically seen as a sine modulation of an unit triangular curve, reduced harmonic distortions to 12% instead of 75% as in normal infinite clipping.