Proceedings with Extended Abstracts (single PDF file) - Radio ...

frequency response. This calculation gives the curves of Figure 3 for two of the B 6 - values ofFigure 2. It shows that higher resolution requires a larger bandwidth. In this case the -6 dBbandwidth for a 500 m pulse (B 6 -=1.04) is 240 kHz, while for the B 6 -=0.55 case, the -6 dBbandwidth is only 152 kHz.Figure 3. Frequency response of system using 500 m long pulse, with two differentB6- products. The box shows the -6 dB points of the matched filter.The Nyquist criterion states that if we want to be able to fully reconstruct this signal, weneed to sample at a rate at least twice the highest frequency in the signal. The choice of themaximum frequency is arbitrary so if one uses the -6 dB frequencies, then this means that thesampling needs to be done at 2*240 kHz, or 480 kHz, or once every 2.1 s (312.5 m). Note thatmany times in the radar community, sampling in range at intervals less than one pulse length isreferred to as “over-sampling”. Many meteorological radars set the sampling equal to the pulselength so that the samples are independent. However, if one uses a Nyquist criterion to determinesample spacing with the goal of accurately reproducing the signal as a function of time, or theprofile as a function of range, then it would not be unreasonable to use 2 or more samples perpulse length.When looking at time series from a single height, it is useful to examine the Dopplerspectrum of the time series. This spectral representation shows how the signal varies asfrequency, or the reciprocal of time. This is the method used by the AL to obtain the wind speedsat each height in order to produce the data in Figure 1. Another time series available from theradar is the range series, showing the atmospheric profile of the received signal. We usuallyconvert the time delay from the radar to the echoing volume to distance from the radar, but it isstill a time series. In a manner analogous to time series spectra, a spatial frequency could bedefined, as the reciprocal of range instead of time. Here we choose not to do this, but to discussspatial frequencies in units of reciprocal length. For example, the 3.3 s long pulse requires a 240kHz bandwidth between the -6 dB points. The reciprocal of 240 kHz is 4.17 s, which has areciprocal scale length of 625 m. This means that spatial features of 625 m or shorter (higherfrequencies) have been attenuated in the signal by more than 0.25 (-6 dB). If we look at the sameatmosphere with a B 6 -=0.55 and a 500 m long pulse, the reciprocal scale length is 987 m,reflecting the fact that the receive bandwidth is narrower.The time and frequency domains tell us similar information. In the time domain, wherethe system response is specified by the resolution, we learn about the ranges that contribute tothe data in a sample. In the frequency domain, the reciprocal lengths define the size of thestructures that contribute to the data at a given range. The frequency domain also gives usinformation about how we need to sample our data in range in order to accurately reproduce thedata.Why do we want to be able to accurately reconstruct the range profile of the radar signal?The simple answer is to improve the accuracy and precision of the instrument. If we want to264