On the design of all-pass signals with peak amplitude constraints

In this paper, the problem is discussed of designing a signal other than the standard impulse function to be used to test a digital system of limited dynamic range. The constraints on such a signal are that it must be all-pass, of limited duration (approximately), and peak-amplitude-limited so as to utilize the limited dynamic range of the system as far as possible. Stated another way, the goal is to spread out the energy in the signal as much as possible to reduce its peak amplitude and therefore to be able to pass higher energy signals through the system without clipping them. The class of all-pass signals (obtained as the impulse response of a variable order all-pass filter) was investigated for use as the test signal. The parameters of the all-pass filter of a given order were optimized to give an all-pass signal whose peak amplitude was the smallest possible. Filter orders from first to eighth order were designed and investigated. It was found that reductions in the peak signal level of up to 11.2 dB (relative to the signal level of an equivalent energy impulse) could be obtained for an eighth-order all-pass signal. Interpolated versions of these all-pass signals showed that the peak value of the interpolated waveform was only on the order of 6 dB. Thus, the use of an all-pass signal, rather than the standard impulse, for testing a digital system can result in about 1 bit extra dynamic range.