Adaptive Time Domain Noise Cancellation for EMP Measurements

A direct adaptive time domain noise cancellation technique has been developed and applied to measured fast EM transient response data. The filter perfor­ mance is determined by processing data and transforming the residual signal and error terms into the frequency domain. When applied to actual data, the range of usable data is extended to higher frequencies, and a direct estimate of the signal-to-noise ratio as a function of frequency is obtained. The use of the noise cancellation process not only extends the useful range in the frequency domain, but additionally provides the upper frequency limit for use of measured responses. I . INTRODUCTION Adaptive noise cancellation techniques have been applied to a wide variety of processes. The simplest technique conceptually is known as the Widrow LMS [1], [2] (Least Mean Square) technique. The procedure has been widely applied with the notable absence of applications to fast transient electromagnetic pulse data where the potential benefits are significant. The primary differences between previous applica­ tions and those presented in this paper relate to the bandwidth of the signal, the environment-induced noise, the measurement noise, and the concatenation of time segments into a single signal record. The objective here is to develop a robust algorithm which will handle data with widely varying properties as opposed to the development of a statistically robust signal processing procedure. Section II of this paper describes the measurement process and illustrates the range of data types requiring processing. Section III presents a brief derivation of the LMS filter with some heuristic arguments considered for the algorithms selected for investigation. Section IV consists of plots of the test signals used for the study, along with plots of the filtered signals and noise signals in the frequency domain. Section V presents the conclusions obtained from the filter study. II. MEASUREMENT PROCESS AND NOISE CHARACTERISTICS The measurement process and equipment is illustra­ ted in Figure 1 . The probe balun and fiber optic transmitter are usually exposed to the incident field resulting in a transient environment-induced noise signal. Examples of this noise signal are presented in Figure 2. The data in Figure 2 was obtained with a terminated balun and represents signal coupled directly to the exposed instrumentation system. The coupling of a derivative effect is clearly discernable in Figures 2a and 2b. Figure 2c is an identical setup with a 36 dB attenuation of the fiber optic transmitter output. The power spectrum density of the signals is presented in Figure 3The second source of noise occurs in the digitiza­ tion process. This process is usually carried out by three or four separate digitizers with intensity and sweep speed settings appropriate for the particular portion of the waveform being recorded. Free running digitizer output is illustrated in Figure 4. In this case, the digitizer is effectively recording the output Figure 1. Hardware c o n f ig u ra t io n f o r s ig n a l a c q u i s i t i o n ^ T in r r T r jr m m n f r r r n n 11 j 111 n iT u ^ T T n rm T ji nrrm T|TnTTTTTg *.M_C4 _3_ ! 5 -a .M .p j.1 H i i i i j 11 i i m i 11 j 11111 n 11 j i i i m n 11 m i 111 [ t [ 111 i 11 n R ^ H fm T r jn T n n n jT i 11 n i n j 111 m ir r j m tT rm j t n r m r r | i n i r m g ^ T r r r r m j m m w i j n 1111111 j 11 n 11111 fn n r r r n Im T T rrT T jn m n T n e a _ jL jiiu i. i. [ i m i.L i i i |.i u u u u | il u ±llu Jj .li l u iu Ji l i i m u 111111 u F i g u r e 2 . E n v i r o n m e n t n o i s e 376 CH2116-2/85/0000-376 $1.00 © 1985 IEEE