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 i...