*Coherent Doppler Lidar for Wind Sensing DOI: http://dx.doi.org/10.5772/intechopen.91811*

corresponding power spectra are accumulated over 10 k laser shots. Power

*Spatial Variability in Environmental Science - Patterns, Processes, and Analyses*

1 ffiffiffi *T* p ð *T*

*FT*ð Þ¼ *w*

*PSD w*ð Þ¼ *lim*

The normalized Fourier transform of a time domain signals*f(t)* can be expressed as:

0

*T*!∞

Eq. (29) shows that the squared modulus of the Fourier transform is the power spectrum. Therefore, we program the FPGA to calculate the square modulus of the output of the FFT block. Our ADC vendor provided us with an FPGA logic design that streams digitally converted signals (sampled at 400 MHz rate) across the PCI express bus to the host PC. This logic design accepts an external trigger signal to start data acquisition. A 20 kHz signal synchronized with laser pulses is used to trigger the data acquisition process. The ADC card operates in a frame mode in which it acquires a frame of incoming data every time it receives an external trigger's interrupt. A frame size of 8192 samples is chosen, which corresponds to approximately 3.1 km. Xilinx Fast Fourier Transform 7.1 circuit block is used in a pipelined-streaming-io mode to calculate FFT for a vector of 128 samples of time gated scattered signals (corresponding to a 48 m spatial resolution). Logic circuits that calculate the modules of the FFT complex output are also implemented and

Once accumulated power spectra are streamed from the FPGA across the PCI express bus, data post processing is carried out on the host PC to estimate various parameters such as radial wind velocity, backscattered signal strength, and velocity statistics. Data archiving and visualization are also carried out on the host PC.

vector is obtained from the mean-frequency *Δf* (Hz) of the Doppler lidar signal as:

*<sup>v</sup>* <sup>¼</sup> <sup>λ</sup> 2

*vmax* <sup>¼</sup> <sup>λ</sup>

The main parameter of interest in Doppler wind measurement is the mean frequency shift of the backscattered signal, because it is directly proportional to the mean velocity of moving aerosol particles within the atmosphere [20, 21]. Doppler frequency shift can be estimated by finding the centroid of the discrete power spectrum of the backscattered signal after removing the amplifier gain shape [22]. One easily calculated method of finding this frequency from a discrete power spectrum is to find the frequency of the highest power, i.e. the frequency

.

where λ (m) is the laser wavelength. As a result, the maximum radial velocity

The Doppler lidar estimate of the radial component *v* (m.s�<sup>1</sup>

*f t*ð Þ *e*

*E FT*ð Þ *w* 2 � � � � h i

�*iwt dt* (28)

(29)

) of the velocity

Δ*f* (30)

<sup>2</sup> *<sup>f</sup>* max, (31)

spectrum can be calculated using the FFT as follows:

The discrete spectral density can then be found as:

integrated with this design.

**4.4 Host computer signal processing**

that can be measured is given by:

**14**

which is approximately 30 m s�<sup>1</sup>

corresponding to the peak power [23]. If the backscattered signal's mean frequency shift and the frequency corresponding to the peak power do not coincide, the velocity estimate can be off by as much as one-half of a frequency resolution.
