DOPPLER2 (1040787), страница 7
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In any practical situation it would obviously be impossible to move the transducer continuously towards the target. Fortunately forward transducer movement can be simulated electronically by comparing the returning echo not with the transmitted signal but rather with a signal at the transmitted frequency minus a Doppler shift offset which is equivalent to the transducer movement. Stationary targets beat with this heterodyned reference to give the offset frequency ¦h while moving targets produce higher or lower frequency beats depending on whether they are moving towards or away from the stationary transducer. A typical system based on the heterodyne principle is shown in Fig. 2.25.
The transducer is driven by the master oscillator either directly for CW operation or via a gating network if pulse-Doppler is required. The offset reference waveform is generated by subtracting the heterodyne frequency wh from the master oscillation w0 in a frequency mixer. The Doppler shifted returns from advancing targets of angular frequency
w¦ ( = 2p¦¦,) or receding targets wr (= 2p¦r) combine with the heterodyne master oscillator in the coherent demodulator. The output components are directionally distinguished Doppler shifts (wh + w¦) and (wh - w¦) situated on either side of the heterodyne frequency.
For the CW case, the received echo R(t) which includes clutter as well as forward and reverse flow components can be expressed in the simple form (which ignores diffraction effects)
R(t) = Acos(w0t+Æc)+ B¦ cos (w0t + w¦t + Ʀ)+ Br cos (w0t - wrt + Ær) (2.54)
where B¦ and Br are the amplitudes of the forward and reverse flow components and Ʀ, Ær take account of their phase. The heterodyned reference signal H(t) output from the frequency mixer can be written
H(t) = cos(w0t + w¦t) (2.55)
The first stage of coherent demodulation involves multiplying the received signal by the reference to give (cf. Eqn (2.51)).
Low-pass filtering removes the high frequency components in the region of 2w0 leaving the low frequency Doppler signal
The echo from the stationary clutter is detected at the heterodyne frequency wh, while the directional Doppler components are located on either side of it as shown in Fig. 2.24b. As mentioned above, the heterodyne frequency must be greater than any encountered Doppler shift. Otherwise signals in the lower sideband would reflect or "fold" about zero frequency producing an ambiguous demodulator output.
The advantage of heterodyne processing is that frequency analysis of the output waveform Dfil(t) provides an immediate display of directional information. However, it is usually necessary to remove large amplitude clutter components using a notch filter precisely tuned to the heterodyne frequency. It is also vital to ensure that the clutter components do not overload the receiver or mixing circuits producing harmonics which cannot then be removed by filtering. These requirements do not generally cause problems and successful instruments using heterodyne demodulation have been described by Cross and Light (1974) and Kato (1966) and are currently being used in a variety of clinical applications (see Chapters 4 to 10).
A final point of interest concerning this method is that the output signal Dfil(t) when broadcast over an audio channel, sounds unfamiliar and is difficult to interpret, probably because Doppler components deviate by only a small fraction from the heterodyne frequency (which is usually located at around 3-6 kHz) A conventional Doppler signal (in the base-band) can range over many octaves. Whatever the cause, the listener usually notices an "indistinct" quality of signal which, without practice, is difficult to analyse by ear. It is, of course, possible to incorporate a non-directional demodulator to provide a more familiar and useful audible output.
2.4f Quadrature-phase Demodulation
The two previously described directional demodulation systems operate in the frequency domain by filtering or shifting the Doppler frequencies in order to identify their upper and lower sidebands. This section will examine the alternative technique known as quadrature-phase demodulation where both the real and imaginary Doppler difference components are detected and then manipulated in a number of different ways to reveal their directional content.
(i) Basic Principles
Quadrature-phase demodulation, as its name implies, involves coherent detection of the received signal in twin channels using quadrature reference signals, that is waveforms of the same frequency but which are separated in phase by p/2 radians (90 degrees). A block diagram of a possible system is shown in Fig. 2.26. The transmitting transducer is driven by the master oscillator waveform either directly for CW operation or via a gate for a pulse-Doppler system. The received signal is split into two and enters the twin coherent demodulation channels. These detectors derive their reference waveform either directly from the master oscillator (the direct channel) or via a p/2 phase shifter (the quadrature channel). The ways in which the two demodulator outputs can be combined to provide directional information will be examined later. Firstly, in order to understand why quadrature demodulation is the first step towards separation of forward and reverse flow. consider the set of waveforms shown in Fig. 2.27. In the top left-hand corner of this illustration there are three waveforms representing: A, the direct channel reference; B , the received ultrasonic signal; and C, the quadrature channel reference. Notice that the received signal B is slightly higher in frequency than the references A and C, indicating that it has been reflected from a target approaching the transducer. Notice also that quadrature reference C leads direct reference A by p/2 radians. Coherent demodulation of the received waveform B using A and C as reference gives the Doppler difference waveforms D and E respectively. It can be seen that these signals are of the same amplitude and frequency but that D leads E by precisely p/2 radians. The corresponding set of waveforms for reverse flow are shown in the bottom half of Fig, 2.27. Waveform G is a received signal which has been Doppler shifted to slightly lower than the reference frequency by a target moving away from the transducer. Coherent demodulation using the direct and quadrature reference waveforms produces Doppler signals which again differ in phase by p/2 radians but this time waveform J from the quadrature channel leads waveform I from the direct channel. Thus following quadrature-phase demodulation, upper and lower Doppler sidebands are distinguished (although not yet separated) by their relative lead-lag relationship: for forward flow the direct channel leads the quadrature channel; for reverse flow the direct channel lags the quadrature channel.
In order to understand how this lead-lag relationship occurs, think of the received signal B from the advancing target as being a sine wave at the transmitted frequency which, because of its slightly higher frequency content, appears to travel from left to right past the reference waveforms A and C. Because the direct channel reference lags behind the quadrature channel reference, the received Doppler shifted signal moves into phase with the direct channel p/2 radians before it encounters a similar phase situation in the quadrature channel. Thus the direct demodulated signal leads the quadrature demodulated signal by p/2. Similarly, for reverse flow, the received echo G can be thought of as being a sinusoid at the transmitted frequency which because of its slightly lower frequency content appears to travel from right to left relative to the reference signals F and H. This time, therefore, the (leading) quadrature reference is encountered first and so the quadrature Doppler difference waveform also leads the direct channel output.
(ii) Analysis
The following mathematical description of quadrature-phase demodulation shows that the process effectively extracts both real and imaginary components of the Doppler vector.
The received signal R(t) can be written in the now familiar form
R(t) = Acos(w0t+Æc)+ B¦ cos (w0t + w¦t + Ʀ)+ Br cos (w0t - wrt + Ær) (2.58)
Coherent demodulation of R(t) by reference waveforms cos w0t to give the direct channel D(t) and cos(w0t+p/2) = sin w0t to give the quadrature channel Q(t), leads to
Ignoring the stationary clutter component and expressing the detected Doppler difference outputs in terms of cosine waves reveals the expected lead-lag relationships which were illustrated in Fig. 2.27, viz.
Forward flow in the quadrature‚ channel lags forward flow in the direct channel by p/2: reverse flow in the quadrature channel leads reverse flow in the direct channel by p/2.
Quadrature demodulation provides the basis for directional Doppler systems. The sections below outline the three ways in which the outputs D(t)and Q(t) can be manipulated to indicate flow direction. The three processing methods are illustrated in Fig. 2.28.
(iii) Time Domain Processing
It has been shown in Eqn (2.59) that after quadrature demodulation, the forward and reverse flow waveform can be distinguished by their relative lead-lag relationship. McLeod (l964, 1967) uses this property as the basis for a direction-sensing Doppler system. The device, shown schematically in Fig. 2.28a, incorporates a logic system to monitor the phase angle between D(t) and Q(t) and then, depending on the lead-lag conditions. switches one of the demodulated Doppler channels (in this case D(t)) through to either the forward or reverse Flow channel. In their comprehensive review of directional Doppler systems, Coghlan and Taylor (1976) label this technique "time domain" processing because the directional information is retrieved directly from the demodulation channels.
This system usually suffers from switching artefacts and, because of the design principles, can only operate under conditions of monodirectional flow. If simultaneous reverse and forward flow signals are received then the lead-lag relationship is ambiguous and the flow direction cannot be resolved. In spite of this, commercial instruments based on this principle have become popular in recent years and are in wide clinical use. Operators of such instruments should be aware of the limitations mentioned above in order to avoid incorrect and misleading flow recordings.
(iv) Phase Domain Processing
The quadrature Doppler outputs can also be processed in the phase domain to give a more powerful method of separating forward and reverse flow channels. In addition, when the Doppler outputs are manipulated in the phase domain, the original purpose of quadrature-phase demodulation becomes more apparent and sensible. Refer once again to Fig. 2.27 which shows the direct and quadrature channel waveforms for both forward and reverse flow. Remember also that in any practical situation the positive and negative Doppler shifts would be combined in the returning signal rather than being separated as shown in the illustration. Consider now the effect of advancing by p/2 the phase of the quadrature-channel demodulated waveform only. (For notational purposes the resulting waveform will be termed Qp/2(t).) For forward Flow Qp/2(t) is shown as waveform K and for reverse flow as waveform L. The direct channel outputs D(t) have been redrawn as waveforms D and t above K and L for phase comparison. Notice that for forward flow the two waveforms D and k have now come into phase whereas for reverse flow waveforms I and L are precisely in antiphase. Thus summing D(t) and Qp/2(t) would double the amplitude of the forward flow component while completely canceling the reverse flow component. In other words, only the upper Doppler sideband would emerge from such a processing system. Alternatively shifting the direct channel by p/2 radians (to give Dp/2(t)) and adding it to Q(t) gives a double-amplitude reverse flow component while completely eliminating the forward flow component.
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