Velocity

For a Doppler power spectrum that is symmetric about its mean velocity, the velocity is obtained directly from the argument of the autocorrelation at the first lag, that is,

V = \frac{λ}{4 π τ_{s}} θ_{1} w h e r e θ_{1} = \arg {R_{1}}

ʎ is the radar wavelength, Ʈ_sis the sampling time (1/PRF). θ₁ is constrained to be on the interval [-π, π]. When θ₁= ± π, then V =± V_u where the unambiguous velocity is ,

V_{u} = \frac{λ}{4 τ_{s}}

If the absolute value of the true velocity of the scatterers is greater than V_u, then the velocity calculated by RVP10 is folded into the interval [- V_u, V_u] , which is called the Nyquist interval. Folding is usually easily recognized on a color display by a discontinuous jump in velocities. For example, if the true velocity is:

V_u+ ΔV

then the velocity calculated by the RVP10 is:

 - V_u+ ΔV

which is 2V_u away from the true mean velocity.

For 8-bit outputs, rather than calculating the absolute velocity in scientific units, RVP10 calculates the mean velocity for the normalized Nyquist interval [-1,1], that is, the output values are,

V' = \frac{θ_{1}}{π}

For example, an output value of -0.5 corresponds to a mean velocity of - V_u/2. The normalized velocity V' is more efficient use of the limited number of bits.