A1.1 Introduction

In this appendix, the output of the matched filter for the classical stepped frequency technique is derived. This is required to determine the various properties of the waveform, which affect its applications in target recognition. Initially, in this and the following section, the properties of a basic pulse are presented (Figure A.1). The frequency transform of a pulse on a carrier frequency, f _c, of width, ? ?, is:

Figure A.1: Time and frequency domain representations of a sinusoidal signal of frequency, f _C, modulated by a pulse of duration ? ?: (a) time and (b) spectrum

where F( f, f _c) is the frequency transform of time domain signal.

This frequency domain signal is:

The power spectrum of a pulse of duration ? ? and frequency f _c is the square of Equation (A.2):

which is now defined to be a function = { F( f ? f _c)} ².

A1.2 Auto-correlation function of a single pulse

The output of the matched filter is the auto-correlation ^[1] of the time domain signal:

where C(t) is the waveform's auto-correlation function, F _sig ( ?)* is the complex conjugate of the signal and F _sig( t + ?) is the signal shifted in time by t (Figure A.2).

Figure A.2: The auto-correlation function of a pulse of width ?: (a) pulse and (b)...