An Analysis of Clipped Speech

The application of infinite clipping to speech has only a small influence on intelligibility. The reason for this is that clipping the original speech‐spectrum only causes tolerable distortion. Since the mathematical analysis for many frequencies becomes involved to a high degree of difficulties, the theoretical investigation was restricted to 2 frequencies, a cosαt+b cosβt e.g., representing 2 harmonics of the pitch frequency. The clipping is considered to be a rectification of a rectangular curve i=f(x) where i=0 for −π<x<0 and i=A for 0<x<+π. Only the range −π⋯0⋯π is used. The resulting amplitudes are expressed as infinite sum of a product of 2 Bessel functions. The results of this calculation are confirmed by an experimental analysis. Highest distortions appear for a=b. Considering $α = (α+β/2) + (α−β/2)$ and $β = (α+β/2) − (α−β/2)$⁠, the 2 unclipped frequencies represent 2 sideband frequencies of a suppressed carrier frequency, (α+β/2). By infinite clipping, the frequencies $n(α+β/2)±(α−β/2)$ are the most important ones in amplitude, where n=1, 3, 5 ⋯. Thus, speech clipping, as applied to vowels, causes distortions mostly of frequencies above 3000 cps. e.g. n=3 or higher. But if the clipped speech is put through a 3000‐cps low‐pass filter, the difference between original speech and clipped speech is not very important. Since α and β and all distortion frequencies are harmonics of the pitch frequency, the good intelligibility of clipped speech is quite reasonable. An experimental analysis of several vowels and consonants has proven this theory.