Frequency Doppler

A phase modulation can also be expressed as frequency modulation. The corresponding frequency deviation is the time derivative of the modulated phase angle (Pm t). According to the basic relationships Afrequency deviation Af(f) with respect to the carrier frequency fg, commonly known as the Doppler frequency shift... 

Computation of this function results in a three-dimensional plot for which one axis is time delay (or range), the second is Doppler frequency or radial velocity and the third is the output power of the matched filter (usually normalised to unity). The extent of the ambiguity function peak in the Tr and the fd dimensions determines the range and Doppler resolutions respectively. As we are using the directly received signal only we term this self-ambiguity as there is no inclusion of any system geometry dependence on the transmitter and receiver locations. 

Figure 19. Effect of earth rotation on Doppler frequency.

After some simplification, we obtain the modified Doppler frequency to... 

Micro-Doppler analyses can also be used for people identification. In that case, it is possible to detect Doppler frequency modulation caused by heartbeats, breathing and body motion (walk, run, head turns etc.). 

Figure 12. Simulated Doppler signature of human walk - x-axis time, y-axis Doppler frequency.

The effect of DP-2) is to produce a virtual pulse whose length is the width of the central lobe. Of course, this is never completely perfect since it does have side-lobes, but waveforms have been described for which the performance in this respect is excellent. DP-3) means that the Doppler frequency shift is being sampled at a discrete set of time points. If the sampling rate is faster than the Nyquist of the Doppler frequency shift, then the Doppler can be unambiguously extracted. 

One might ask why Moyal s Identity does not cause problems here. Of course it does. Whatever the sampling rate, there are Doppler frequencies that are ambiguous and correspond to side-lobes in the overall... 

Doppler ultrasonic flowmeters depend upon the reflection of a continuous ultrasonic wave (frequency 0.5-10 MHz) from particulate matter (scatterers) contained in the fluid. Hence they may be used to monitor the rate of flow of dirty liquids. The transducer involved can act both as transmitter and receiver and is generally of the clamp-on type (Fig. 6.4). If the scatterers can be assumed to be moving at the velocity of the liquid, then the volumetric rate of flow Q is related to the Doppler frequency shift AtoD by ... 

An interesting modification of this technique is the fibre-optic dynamic anemometer (FODA)143. A length of fibre-optic cable carries the laser beam to the interior of the dispersion. Back-scattered light, with its Doppler frequency shift, is returned to the detector along with reflected light and, again, the resulting beat frequency pattern is analysed. Since only a very small volume around... 

Devices such as ultrasonic flow equipment use the Doppler frequency shift of ultrasonic signals reflected from discontinuities in the fluid stream to obtain flow measurements. These discontinuities can be suspended solids, bubbles, or interfaces generated by turbulent eddies in the flow stream. The sensor is mounted on the outside of the pipe, and an ultrasonic beam from a piezoelectric crystal is transmitted through the pipe wall into the fluid at an angle to the flow stream. Signals reflected off flow disturbances are detected by a second piezoelectric crystal located in the same sensor. Transmitted and reflected signals are compared in an electrical circuit, and the corresponding frequency shift is proportional to the flow velocity. 

Uses Doppler frequency shift of ultrasonic signals reflected off discontinuities in fluid... 

The first-order Doppler frequency shift, Av, of a wave emitted by a source moving at a velocity, v, is given by the following expression... 

Doppler frequency of the signal, respectively. For any given experimental condition, a number of measurements were made and stored. These stored parameters were then analyzed using the same programmable calculating oscilloscope to give both a statistical analysis (arithmetic mean and standard deviation) and a representation of the data in the form of a histogram. 

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