Radio Science Bulletin 313 - June 2005 - URSI

Figure 5a. A time-domainrepresentation of a linearlyfrequency-modulated waveformfor n = 800 andµ = 0.01 f c .steepness of the edges and the waviness of the in-bandspectrum are functions of the number, n, of half cycles. Bothn (the duration of the signal) and µ (the modulation factor)determine the width of the occupied frequency band. Sincebandwidth provides a measure of the spectral occupancy,one expects the value of an appropriately defined bandwidthto be closely related to the width of the rectangular part ofthe spectrum. For the example depicted in Figure 5, thismeans that the calculated bandwidth is close to 2 f c ,fl≅ fc, and fh≅ 3 fc. With the exception of B RMS , thebandwidth definitions under consideration roughly satisfythis expectation, since f l and f h of Table 6 differ from theexpected values by less than ± 0.17 f c (by less than ± 0.04 f cfor B 3dB and B 10dB ). As a result of the sharp gradients atthe spectral edges, B RMS significantly overestimates theoccupied band, by a factor of two.The linear frequency-modulated waveform is ofinterest in the context of this article because theapproximately rectangular form of the spectrum creates aspecial classification problem if B 90EB is used. That is, onecannot uniquely determine a frequency band, althoughB 90EB is well defined. In the example ( n = 800 andµ = 0.01 f c ), at least two pairs of high and low frequencies,{ 1.06,2.84 } and { 1.16,2.94 }, satisfy the requirement that90% of the signal energy lies between them for the minimalwidth of 1.78 f c ( = B90EB). The pair { fl,f h } cannot beuniquely defined, since at least two intervals exist thatcontain 90% of the signal energy and have the identicalminimal width.Figure 5b. A frequency-domainrepresentation of a linearlyfrequency-modulated waveform forn = 800 and µ = 0.01 f c .24TheRadio Science Bulletin No 313 (June, 2005)