A random phase signal will also have random phase differences between two independent random phases. A phase
increment across a time increment is in fact a phase-rate, or frequency. A phase-rate change is in fact a frequency-hop.
By controlling the phase-rate, that is the characteristics of the phase increments, we can control the spectrum of the
random-phase waveform. Spectrum precision and sharpness is enhanced by holding a frequency for some ‘chip’ length.
For digitally generated phase samples, this means that the chip length needs to be many samples. This is a time-bandwidth
issue. The definition of ‘many’ will depend on the sharpness desired, but often several tens’ of samples will
be adequate. To shape the Energy Spectral Density (ESD) of a random-phase signal, we need to control the average
energy at various phase-rates. This can be done with either or a combination of 1) Controlling the likelihood of specific
phase increments, and/or 2) Controlling the duration of a specific phase increment chip length. For range-Doppler
images, it is the 2-dimensional Impulse Response (IPR) that is of principal concern. This will tend to average out the
random effects of any single pulse.