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Figure 38 Time Series and Doppler Power Spectrum Example
7.3.2 Frequency Domain Processing- Doppler Power Spectrum
The Doppler power spectrum (also known as Doppler spectrum) is the easiest way to
visualize the meteorological information content of the time series.
The Doppler power spectrum is obtained by taking the magnitude squared of the input time
series, that is, for a continuous time series,
� � = � � �
2
Here
S
denotes the power spectrum as a function of frequency ω, and
f
denotes the Fourier
transform of the continuous complex time series s(t) . The Doppler power spectrum is real-
valued since it is the magnitude squared of the complex Fourier transform of s(t) .
In practice, a pulsed radar operates with discrete rather than continuous time series. That is,
there is an
I
and
Q
value for each range bin for each pulse. In this case we use the discrete
Fourier transform or DFT to calculate the discrete power spectrum.
When we have
2n input time series samples (for example, 16, 32, 64, 128, ...), we use the fast
Fourier transform algorithm (FFT), which is significantly faster than the full DFT.
The DFT has the form:
Chapter 7 – Processing Algorithms
185