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Fourier Transforms in Radar And Signal Processing_4

Tham khảo tài liệu 'fourier transforms in radar and signal processing_4', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Pulse Spectra 53 spectral power factors in both linear and logarithmic form multiplying the original pulse spectrum in the two cases sinc2 2ft for the rectangular pulse and 1 1 2pfrý2 for the stray capacitance. The power spectrum of the smoothed pulse is that of the spectrum of the original pulse multiplied by one of these spectra. Assuming the smoothing impulse response is fairly short compared with the pulse length the spectrum of the pulse will be mainly within the main lobe of the impulse response spectrum. We see that the side-lobe pattern of the pulse will be considerably reduced by the smoothing e.g. by about 10 dB at 0.4 t from center frequency . We also see that the rect pulse of width 2t gives a response fairly close to the stray capacitance filter with time constant t. 3.7 General Rounded Trapezoidal Pulse Here we consider the problem of rounding the four corners of a trapezoidal pulse over different time intervals. This may not be a particularly likely problem to arise in practice in connection with radar but the solution to this awkward case is interesting and illuminating and could be of use in some other application. The problem of the asymmetrical trapezoidal pulse was solved in Section 3.4 by forming the pulse from the difference of two step-functions each of which was convolved with a rectangular pulse to form a rising edge. By using different-width rectangular pulses we were able to obtain different slopes for the front and back edges of the pulse. In this case we extend this principle by expressing the convolving rect pulses themselves as the difference of two step functions. The finite rising edge can then be seen to be the difference of two infinite rising edges as shown in Figure 3.14. Each of these which we call Ramp functions is produced by the convolution of two unit step functions as shown in Figure 3.15 and defined in 3.20 below. We define the Ramp function illustrated in Figure 3.15 by Ramp t - T h t h t - T 3.20 so that f 0 for t 0 .