3.1 Introduction

In this chapter we consider the spectra of pulses and pulse trains. Signals used in radar, sonar, and radio and telephone communications often turn out to be combinations of certain quite simple basic waveforms or of variations on them. For example, the rectangular pulse is an almost universal feature of radar waveforms, and although the perfect pulse is a mathematical idealization, it is often closely realized in practice, and the approximation is good enough for an analysis based on the idealization to give very useful results (which in some cases are obtained very simply).

One reason for studying the spectrum of a pulse, or pulse train, can be to investigate the interference that the pulse transmission will generate outside the frequency band allocated. The sharp-edged rectangular pulse is particularly poor in this respect, producing quite high interference levels at frequencies several times the radar bandwidth away from the radar operating frequency. The interference levels can be lowered quite considerably by reducing the sharp, vertical edges in various ways. Giving the edges a constant finite slope so that the pulse becomes trapezoidal produces a considerable improvement, as shown in Section 3.2. The triangular pulse (Section 3.3) is a limiting case of the trapezoidal with the flat top reduced to zero. The asymmetric trapezoidal pulse (with sides of different magnitude slope) is considered in Section 3.4. While the practical use of such a pulse is not obvious, this is an interesting exercise in the use of the rules-and-pairs method, showing...