**2. Outline of Doppler ultrasound system and conventional analog signalprocessing**

Recently, the diagnostic ultrasound system has been popular in many diagnostic fields, such as cardiac, abdomen, and so on. In Section 2.1, an example of diagnostic image and its principle are introduced. In Section 2.2, the phase shift system that is an example of representation of conventional analog signal-processing is introduced.

### **2.1 Outline of Doppler ultrasound system**

An example of diagnostic image of a carotid artery is shown in Fig. 1. The upper is a tomogram image and bottom is a spectrum Doppler image. This image expresses the time change of the flow velocity in the PWD (Pulse Wave Doppler) range gate set up in the central of a blood vessel in a tomogram. A horizontal axis and a vertical axis are the flow velocities corresponding to Doppler shift frequency and time, respectively.

Signal processing of the ultrasound echo signal is shown in Fig. 2. An ultrasonic wave is transmitted for every cycle of PRF (pulse repetition frequency: *fs*) in the transceiver processing part of Fig. 2(a), and a reflective echo is received. An ultrasonic beam is scanned in the transverse direction, and envelope detection of the received signal is carried out in the range direction. This scanning constitutes the tomogram image.

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 213

flow. Also inside of blood vessel, a blood vessel wall and a transmit-wavelength influence the blood-flow signal. Then, in order to prevent the saturation of the frequency analysis or the Doppler audio processing, a wall-filter is arranged in pre-processing of them. The wallfilter is HPF with high order cut-off property. The details of Spectrum Doppler signal processing are shown in Fig. 2(c). Range gate processing is the integration of *L(t)* in the range direction in the range gate. Wall-filter processing removes a clatter component. The complex IQ-signal *x(t)* after these processing is inputted into the spectrum Doppler display processing and the Doppler audio processing. The former displays the spectrum Doppler as a time-change image of a flow velocity. The latter separates the direction of Doppler signal,

t

t

(a) The outline of signal-processing of ultrasound system

*fp*

*s*/2 0 0 *+*䡂*s*/2 *-*䡂

(b) Spectra od baseband IQ-signal

(c) Spectrum Doppler processing

An analog phase-shift processing system that consists of all-pass filters has been used in the direction separation processing. The outline of it is shown in Fig. 3. This is a processing system that shifts the phase between the IQ-signals of 90 degree, and adds them or subtracts them. Since an all-pass filter has the characteristic that the phase reverses on cut-off frequency, this system shifts the phase in a target frequency range combining all-pass filter

> ( ) exp( ) *<sup>d</sup> xt j t* Z

arrays. If it assumes that the input IQ-signal *x(t)* has a frequency component of

Calc.

Direction Separation

Clutter Doppler R1 R2 R3

*X(t)*

䡂

Wall Filter (HPF) Range Gate FFT/Power

Spectrum Doppler Processing

Envelope detection

Phase detection

*R(t) M(t) L(t)*

Power Power

t

LPF Spectrum

*s*/2 *+*

Spectrum Image Proc.

Audio Proc.

B mode Image Proc.

Doppler Proc.

䡂*s*/2

Display Output

Audio Output

> Z*d* .

(4)

and outputs them as stereo sounds from a right-and-left speaker.

Tx waveform 1/*fs* Rx waveform

T&R Proc.

R1 R2 R3

R2 R3

0

Fig. 2. Doppler ultrasound signal-processing.

**2.2 Conventional analog signal-processing** 

Power

*s*/2 *-*

*+*䡂*s*/2

Probe

Tx Freq. *fp* R1

> *-*䡂

> > *L(t)*

Fig. 1. Example of ultrasound diagnostic image of a carotid artery

Except for Doppler signal processing, as another method of blood-flow or tissue velocity detection, the cross-correlation method using the signal before quadrature-detection processing (*R (t)* in Fig. 2(a)) has been also reported. However, the base-band signal (*L (t)* in Fig. 2(a)) processing after quadrature-detection is the present mainstream, because of its narrow bandwidth and little processing load. All the direction separation systems examined this time are the IQ-signal processing after quadrature-detection. The received signal *R(t)* in a range gate is denoted by a formula (1). Here, a reflective echo signal is assumed to be the amplitude *Ai* , Doppler shift angle-frequency Z*<sup>i</sup>* , and phase I*i* .

$$R(t) = \sum^{i} A\_i \cdot \exp\left(j \cdot \left(\alpha\_p + \alpha\_i\right) \cdot t + j \cdot \phi\_i\right) \tag{1}$$

The mixer output *M(t)* is denoted by a formula (2). Reference angle-frequency of a mixer is set to Z*<sup>p</sup>* (same as probe Tx angle-frequency) here.

$$\begin{split} M(t) &= R(t) \cdot \exp\left(j \cdot o\_p \cdot t\right) \\ &= \frac{1}{2} \sum\_{i}^{i} A\_i \cdot \exp\left(j \cdot \left(2 \cdot o\_p + o\_i\right) \cdot t + j \cdot \phi\_i\right) + \frac{1}{2} \sum\_{i}^{i} A\_i \cdot \exp\left(j \cdot o\_i \cdot t + j \cdot \phi\_i\right) \end{split} \tag{2}$$

The LPF output *L(t),* high frequency component is removed is denoted by a formula (3).

$$L(t) = \frac{1}{2} \sum^{i} A\_i \cdot \exp\left(j \cdot o\_i \cdot t + j \cdot \phi\_i\right) \tag{3}$$

In Fig. 2(a) (R1), (R2), and (R3) show the position of the blood-vessel-wall upper part, the inside of a blood vessel, and the blood-vessel-wall lower part, respectively. Fig. 2(b) shows typical spectra of quadrature-detection output *L(t),* when a range gate is set in each position. A vertical axis shows power and the horizontal axis shows frequency, respectively. Since the sampling is interlocked with PRF of transmission, the vertical axis has a frequency range of r *fs* / 2 . *L(t)* is mainly constituted from the low frequency component caused by the clatter (strong echo from tissue) and middle to high frequency component caused by weak blood212 Applications of Digital Signal Processing

Except for Doppler signal processing, as another method of blood-flow or tissue velocity detection, the cross-correlation method using the signal before quadrature-detection processing (*R (t)* in Fig. 2(a)) has been also reported. However, the base-band signal (*L (t)* in Fig. 2(a)) processing after quadrature-detection is the present mainstream, because of its narrow bandwidth and little processing load. All the direction separation systems examined this time are the IQ-signal processing after quadrature-detection. The received signal *R(t)* in a range gate is denoted by a formula (1). Here, a reflective echo signal is assumed to be the

Z

*Rt A j t j <sup>i</sup>* Z*p* Z

The mixer output *M(t)* is denoted by a formula (2). Reference angle-frequency of a mixer is

*<sup>i</sup>* , and phase

 

Z I

¦ ¦ (2)

*i p i i i ii*

*A j tj A j tj*

 <sup>1</sup> ( ) exp <sup>2</sup>

In Fig. 2(a) (R1), (R2), and (R3) show the position of the blood-vessel-wall upper part, the inside of a blood vessel, and the blood-vessel-wall lower part, respectively. Fig. 2(b) shows typical spectra of quadrature-detection output *L(t),* when a range gate is set in each position. A vertical axis shows power and the horizontal axis shows frequency, respectively. Since the sampling is interlocked with PRF of transmission, the vertical axis has a frequency range of r *fs* / 2 . *L(t)* is mainly constituted from the low frequency component caused by the clatter (strong echo from tissue) and middle to high frequency component caused by weak blood-

*Lt A j t j* ¦ *i ii*

The LPF output *L(t),* high frequency component is removed is denoted by a formula (3).

 I I*i* .

 I*i i* ¦ (1)

Z

 I

(3)

Fig. 1. Example of ultrasound diagnostic image of a carotid artery

( ) exp   *<sup>i</sup>*

 

Z

*p i i*

> Z

1 1 exp 2 exp 2 2

Z

*i*

*<sup>p</sup>* (same as probe Tx angle-frequency) here.

amplitude *Ai* , Doppler shift angle-frequency

( ) ( ) exp

*Mt Rt j t*

set to Z flow. Also inside of blood vessel, a blood vessel wall and a transmit-wavelength influence the blood-flow signal. Then, in order to prevent the saturation of the frequency analysis or the Doppler audio processing, a wall-filter is arranged in pre-processing of them. The wallfilter is HPF with high order cut-off property. The details of Spectrum Doppler signal processing are shown in Fig. 2(c). Range gate processing is the integration of *L(t)* in the range direction in the range gate. Wall-filter processing removes a clatter component. The complex IQ-signal *x(t)* after these processing is inputted into the spectrum Doppler display processing and the Doppler audio processing. The former displays the spectrum Doppler as a time-change image of a flow velocity. The latter separates the direction of Doppler signal, and outputs them as stereo sounds from a right-and-left speaker.

(a) The outline of signal-processing of ultrasound system

(b) Spectra od baseband IQ-signal

(c) Spectrum Doppler processing

Fig. 2. Doppler ultrasound signal-processing.
