Tham khảo tài liệu 'fourier transforms in radar and signal processing_5', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Interpolation for Delayed Waveform Time Series 97 Figure Flat waveform oversampled. flat part of the waveform with constant value unity has been sampled at an oversampling rate of q 3. We see that at the sample points the weight value is 5 3 but the contributions from the interpolating sinc functions from nearby sample points are negative bringing the value down to the correct level. The weights given by for oversampling factors of 2 and 3 are shown in Figure for comparison with the values for the minimum sampling rate q 1 plotted in Figure . The same set of delays has been taken. These plots show that the weight for the tap nearest the interpolation point taken to be the center tap here can be greater than unity that the weight magnitudes do not necessarily fall monotonically as we move away from this point and that much the same number of taps is required above a given weight level such as 30 dB. At first this last point might seem unexpected there is no significant benefit from using the wider spectral gate that is possible with oversampling. However the relatively slow falling off of the tap weight values is a result of the relatively slowly decaying interpolating sinc function and this in turn is the result of using the rectangular gate with its sharp discontinuous edges. This is the case whether we have oversampling or not. The solution if fewer taps are to be required is to use a smoother spectral gating function and this is the subject of the next section. Three Spectral Gates Trapezoidal The first example of a spectral gate without the sharp step discontinuity of the rect function is given by a trapezoidal function Figure . As illustrated 98 Fourier Transforms in Radar and Signal Processing Figure FIR interpolation weights with oversampling. rect ỹợfl l lfl-DF rect f q- 1 F Figure Trapezoidal spectral gate. Interpolation for Delayed Waveform Time Series 99 in this figure and also in Section this symmetrical trapezoidal
