A.1 Introduction

The width of the spectrum of a simple pulsed radar signal is largely determined by the pulse shape. Simple means that there is no intrapulse FM or phase modulation for pulse compression purposes. Spectrum width is conventionally measured at the half power points, while pulse duration is measured at the half voltage points.

A.2 Rectangular Pulses

For a rectangular pulse, the power spectrum has a sin ² x/ x ² shape. In this case, the 3-dB points are 2.78 units apart, while the first nulls (which occur at x = ?) are 2 ? units apart. Therefore, the ratio of the width between the first nulls to the 3-dB spectrum width is 2.27. This means that the null-to-null spectrum width is 2.27 times the 3-dB bandwidth.

It should be noted that the peaks of the spectrum sidebands decrease in proportion to 1/ f ² for frequencies separated by f from the carrier. The first nulls occur at a frequency of plus and minus the reciprocal of the pulse duration away from the carrier frequency. Therefore, the null-to-null spectrum width = 2/PD and the 3-dB spectrum width = 0.88/PD.

A.3 Trapezoidal Pulses: Equal Rise and Fall Times

A trapezoidal pulse with equal rise and fall times can be thought of as a narrow pulse of width ? convolved with a wider pulse of width T. This produces a total rise time of the composite pulse of ? (this...