Stepped FM acoustic signal design

The linear Frequency Modulated (LFM) signal is a means of providing a broadband signal with a short time duration. One of its main uses is in active sonar, where it provides enhanced target range resolution and improved performance against reverberation. Its generation can be simplified by approximating it using a so-called Stepped Frequency Modulated (SFM) signal, where the pulse is made up of a set of contiguous single frequency pulses. In its simplest form, the frequency of these pulses increases (or decreases) in a linear manner along the time history of the pulse. This paper presents a technique for designing a SFM pulse that best emulates its LFM counterpart in its detection performance. It is shown that if the time-bandwidth product of the LFM is BT, the number of pulses in the SFM that best emulates the LFM is equal to the nearest integer to the square root of BT. Values of N smaller than this reduce the detection performance and values larger than this provide no improvement in detection performa...