This can be derived from basic Fourier transform properties. To derive an equation for velocity resolution we start with the fact that the scaled (by $\alpha$) rectangular window function forms a Fourier pair with the sinc function. With this understanding we can calculate a velocity resolution by calculating the minimum distance in frequency our windowing function can be spaced before we can no longer discriminate between the two copies. Specifically we will have "copies" of our windowing function spectra centered at the frequency of our target. Using the multiplication property of the Fourier transform (multiplication in time is equivalent to convolution in frequency) we realize that windowing has the effect of "smearing" the spectrum of our target. Since we only are able to collect coherent samples over the CPI we've effectively multiplied (in time) our signal by a rectangular windowing function. The key to understanding velocity resolution for pulsed radar is that coherent processing interval (CPI - the total amount of time spanned by slow time samples) acts as a rectangular windowing function on your slow time samples.Ī target moving at a constant velocity sampled for an infinite number of slow time samples would be represented by a impulse (delta) at a frequency defined by the equation below. If we want to derive a 1 m resolution raster from the LiDAR data, we overlay a 1m by 1m grid over the LiDAR data points. As mentioned elsewhere, if your target does not maintain a constant radial velocity throughout the CPI, this will result is some spectral spreading across your FFT bins.ĭoppler frequency for a target is calculated by taking the FFT over the slow time for the range bin the target is in. LiDAR Light Detection and Ranging (LiDAR) is a remote sensing method that works on the principle of radar, but uses light in the form of pulsed laser to measure variable distances to the earth. The number of pulses you integrate is referred to as the Coherent Processing Interval (CPI). Note that at a fixed PRF you will also have blind velocities. PRF needs to be low enough to allow the pulse to propagate to the target range and back, or else you will suffer from pulse ambiguities.
The PRF needs to be high enough to sample the Doppler frequency bandwidth of interest. There are design constraints on the Pulse Repetition Frequency (PRF).
You can increase the resolution by coherently integrating multiple pulses. This assumes the radial velocity of the target is relatively constant for the pulse - usually this is not too bad an assumption The length of the pulse then determines the Doppler resolution for that single pulse. If you are using a FFT to to determine the Doppler shift, this assumes that you're transmitting a sinusoidal pulse. It is determined by the Radar system parameters. The Doppler frequency resolution is not determined by any characteristic of the moving target.
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