**4.4 Performances**

To satisfy the target performances of frequency resolution and frequency characteristics shown in Table 6, we set up parameters for all the systems, such as the order of the filters and the FFT number. We use the 8th Butterworth filter with cut-off 0.495\**FB*\**fs* and 0.495\**RB*\**fs* for the LPFs of the modulation/demodulation and complex IIR filter systems. We perform 128-point FFT and 256-point inverse-FFT involved in the FFT/IFFT system, and we apply rectangular weight to *WF*Z and *WR*Z .


Delay is estimated at *fs*=4 kHz. (\*1) not including transient response

(\*2) IFFT shift addition pitch is *N*/4.

Table 6. Time-delay of Doppler audio processing


R-add: real-addition, Rmul: real-multiplication, Ovh: over head, C-add: complex-addition, C-mul: complex-multiplication, IFFT shift addition pitch is *N*/4.

Calculation volume is estimated at *fs*=4 kHz.

Table 7. Calculation load of Doppler audio processing

230 Applications of Digital Signal Processing

(a) spectrum of LPF *Hf(z)*

2䞉*RB*

*-fs -fs*/2 0 +*fs*/2 *+fs*

(b) spectrum of LPF *Hr(z)*

2䞉*FB*

*-fs -fs*/2 0 +*fs*/2 *+fs*

*Hf(z)*

*Hr(z)*

we apply rectangular weight to *WF*

(\*2) IFFT shift addition pitch is *N*/4.

modulation/demodulation

FFT/IFFT

**4.4 Performances** 

Power

Power

Fig. 19. Frequency design of the complex IIR filter system

freq.

Z

Delay is estimated at *fs*=4 kHz. (\*1) not including transient response

Table 6. Time-delay of Doppler audio processing

complex IIR C-add: *order*\*8\**fs*

Calculation volume is estimated at *fs*=4 kHz.

C-mul: complex-multiplication, IFFT shift addition pitch is *N*/4.

Table 7. Calculation load of Doppler audio processing

freq.

(c) spectra of complex BPF *Hf(z')* and *Hr(z'')*

*FBC*

freq.

(MFLOPS)

(*order*=8)

5.76 (*N*=128) (*r1*=7,*r2*=8)

(*order*=8)

*fs*\*(48\**order*+24)\*1.2 1.96

(2*fs*\*4/*N*)\**N*\*(12+6\**r1* +12\**r2*)\*1.2

C-mul: *order*\*8\**fs fs*\*(48\**order*)\*1.2 1.84

Power

*Hr(z'') Hf(z')*

*-fs -fs*/2 0 +*fs*/2 *+fs*

*RBC*

To satisfy the target performances of frequency resolution and frequency characteristics shown in Table 6, we set up parameters for all the systems, such as the order of the filters and the FFT number. We use the 8th Butterworth filter with cut-off 0.495\**FB*\**fs* and 0.495\**RB*\**fs* for the LPFs of the modulation/demodulation and complex IIR filter systems. We perform 128-point FFT and 256-point inverse-FFT involved in the FFT/IFFT system, and

 and *WR*

system estimation delay (ms) modulation/demodulation *order*/*fs* (\*1) 2 (*order*=8) FFT/IFFT 0.75\**N*/*fs* (\*2) 24 (*N*=128) complex IIR *order*/*fs* (\*1) 2 (*order*=8)

System calculation component estimation equation load

C-add: *order*\*8\**fs* C-mul: (*order*\*8+6)\**fs*

C-add: *N*\**r1*+4\**N*\**r2* C-mul: *N*\**r1*/2+2\**N*\**r2*

R-add: real-addition, Rmul: real-multiplication, Ovh: over head, C-add: complex-addition,

Ovh: 20%

R-mul: 2*N*\*6 Ovh: 20%

Z . the time-delay from the calculation load itself considered to be zero by sampling, and the estimated values are not affected by the transient response. Since the operation load depends strongly on the hardware-architecture that performs signal processing, we evaluate the frequency of multiplication/addition for 1 s (single-accuracy floating point). The calculation element for every signal processing system, calculation-load estimated formula and operation load per second (*fs*=4 kHz) are shown in Table 7. The estimated results in Tables 6 and 7 show that the complex IIR filter system and the modulation/demodulation systems are fulfilling the time-delay performance goal. Regarding the calculation load, the complex IIR filter system is the smallest, the modulation/demodulation system is slightly larger, and the FFT/IFFT system is the largest, but still small compared with previously reported values. Next, we perform a simulation to check whether we can meet the frequency feature of the performance goal in Table 4. We sweep the frequency of the input IQ-signal and measure the powers of the positive-side and negative-side outputs.

We evaluate simultaneously the frequency features and direction separation performance at this time. The frequency features of the direction separation output according to the three signal processing systems are shown in Fig. 20. A solid line denotes the positive-side component, and a dashed line, the negative-side component. The horizontal axis indicates the frequency range from *-fs* to *+fs*. Moreover, the spectrum image display range corresponding to the frequency range is shown in the bottom rail. The output feature of the Doppler audio at the zero baseline-shift is shown in Figures 20(a), 20(c) and 20(e), and that of +0.4\*fs baseline shift is shown in Figures 20(b), 20(d) and 20(f). From these results, we confirm that the frequency feature in each signal processing system of the Doppler audio corresponds to the baseline-shift of the spectrum image. Here, we consider that owing to the effect of the shift-addition in the Hamming window of the FFT/IFFT system, the component near DC in Figures 20(c) and 20(d) is missing. Since this missing part has a value lower than the typical setting value of cut-off frequency for the high-pass filter (equivalent to HPF in Fig. 11) of the preceding process, we do not encounter any problem. Moreover, we observe that the separation degrees of the positive-side component in Figures 20(b) and 20(f) are insufficient. We consider that the cut-off features (the 8th Butterworth filter is used in the simulation) of the modulation/demodulation and the complex IIR filter systems can be improved by making them steep. However, in the case of using an IIR filter, we should expand the internal bit length (dynamic range), because the increased load is expected to be affected by quantizing noise. For example, although Figures 20(e) and 20(f) are calculated using the single floating point (24-bit mantissa) in the simulation, by increasing cut-off frequency or filter order, mantissa bit length (accuracy) may be insufficient and the calculation load or hardware scale may increase. Although we use the Butterworth filter this time, we can choose the Chebysev filter and acquire a steep cut-off feature. On the other hand, the frequency feature and direction separation performance near cut-off frequency deteriorate with a ripple and rapid phase change.

From the above results, we observe that in choosing the response and calculation load, the complex IIR filter system is the most effective. On the other hand, the FFT/IFFT system is the most effective in choosing the frequency feature, although the response is poor. Since the

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 233

21(f) in addition to the blood flow component, we observe that the clutter component (- 0.08\**fs*) remains on the negative-side under the effect of the filter element. In the negativeside output waveform at the zero baseline-shift in Fig. 21(g), the separation of the clutter component (-0.08\**fs*) is observed on the negative-side. Moreover, in the power spectrum in Fig. 21(h), a clutter component and a DC component are detected. When the baseline shift is +0.4\**fs*, the spectrum image and Doppler audio must generate a negative region larger than a positive region. The positive-side output waveform after the baseline shift in Fig. 21(i) shows the disappearance of the clutter component (+0.24\**fs*). Moreover, we confirm the absence of the blood flow component in the power spectrum shown in Fig. 21(j). We also confirm that a novel blood flow component (-0.76\**fs*), which is an alias component (+0.24\**fs*), is outputted into the negative-side output waveform after the baseline-shift in Fig. 21(k), except for the clutter component (-0.08\**fs*). Moreover, in the power spectrum in Fig. 21(l), we confirm that the blood flow and clutter components are separated on the negative-side.

(a) IQ-input signal (b) spectrum of (a)

0 10 20 30 5040 *-fs*/4 0 *fs*/4 *fs*/2

Power (dB)

Power (dB)

Power (dB)

Power (dB)

Power (dB)

Power (dB)

0 20 40

0 20 40

0 20 40

0 20 40

0 20 40

0 20 40

*-fs*

*-fs*

*-fs*

*-fs*

*-fs*

Freq.

Freq.

Freq.

Freq.

Freq.

Freq.

*-fs*/2 0 *fs*/2 *fs*

*-fs*/2 0 *fs*/2 *fs*

*-fs*/2 0 *fs*/2 *fs*

*-fs*/2 0 *fs*/2 *fs*

*-fs*/2 0 *fs*/2 *fs*

(c) after zero insertion waveform (d) spectrum of (c)

Time (0.5/*fs*)

Time (1/*fs*)

0 10 20 30 5040

0 10 20 30 40 50

0 10 20 30 5040

0 10 20 30 5040

0 10 20 30 40 50

0

2


2

0


1

0


1

0


1

0


1

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

0


(e) forward output (BLS=0) (f) spectrum of (e)

Time (0.5/*fs*)

(g) reverse output (BLS=0) (h) spectrum of (g)

Time (0.5/*fs*)

(i) forward output (BLS=+0.4䞉*fs*) (j) spectrum of (i)

Time (0.5/*fs*)

(k) reverse output (BLS=+0.4䞉*fs*) (l) spectrum of (k)

Time (0.5/*fs*)

Fig. 21. Simulation waveform and spectrum of complex IIR filter system.

response is more important than the frequency feature clinically, and the target performance in Table 4 is fulfilled mostly, we consider the complex IIR filter system to be the best device for the direction separation of the Doppler audio system.

Fig. 20. Frequency characterization of Doppler audio output

#### **4.5 Implementation of complex IIR filter system 4.5.1 Signal processing simulation**

We examine the possibility of using the complex IIR filter system in signal processing simulation. The input signal is conceived to be for the actual venous blood model. The model consists of a noise component (white noise), a blood vessel wall component (clutter: low frequency high power), and a blood flow component. The powers and frequencies of these components are shown in Table 8. The input and output waveforms and power spectra of the processing blocks in the complex IIR filter system are shown in Fig. 21. The amplitude of the left-hand-side waveform is normalized by clutter amplitude to be 2. Moreover, 256-point FFT with a Hanning window is applied to the calculation of the righthand-side power spectrum. Figures 21(a) and 21(c) show the input and output waveforms of zero insertion processing, respectively. A solid line denotes the I-component, and a dashed line, the Q-component. Figures 21(e) and 21(g) show the Doppler audio outputs of both directions at the zero baseline-shift. A solid line denotes the real component, and a dashed line, the imaginary component. Figures 21(i) and 21(k) show the Doppler audio outputs of both directions at the +0.4\**fs* baseline-shift. A solid line denotes the real-component, and a dashed line, the imaginary-component. Figures 21(b), 21(d), 21(f), 21(h), 21(i) and 21(l) show power spectra corresponding to the waveforms in the time domain. The aliasing spectra of blood flow and clutter are observed in Fig. 21(d) for a zero insertion processing output. Moreover, the approximately –20 dB DC component is observed at the center of the spectra. This DC component, which is not removed using the Hanning window, does not affect the latter complex band-pass filter processing. From the positive-side output waveform at the zero baseline-shift shown in Fig. 21(e), we confirm that the blood flow component of +0.24\**fs* frequency is separated on the positive-side. Moreover, in the power spectrum shown in Fig. 232 Applications of Digital Signal Processing

response is more important than the frequency feature clinically, and the target performance in Table 4 is fulfilled mostly, we consider the complex IIR filter system to be the best device

Power (dB)

reverse

reverse

reverse

Frequency(*fs*)

forward

forward

Frequency(*fs*)

Frequency(*fs*)

forward

forward

4.0 *fs*

(a) mod./demod. system: BLS=0 (b) mod./demod. System: BLS=+0.4䞉*fs*

Power (dB)

> Power (dB)

(c) FFT/IFFT system: BLS=0 (d) FFT/IFFT system: BLS=+0.4䞉*fs*

(e) complex IIR system: BLS=0 (f) complex IIR system: BLS=+0.4䞉*fs*

We examine the possibility of using the complex IIR filter system in signal processing simulation. The input signal is conceived to be for the actual venous blood model. The model consists of a noise component (white noise), a blood vessel wall component (clutter: low frequency high power), and a blood flow component. The powers and frequencies of these components are shown in Table 8. The input and output waveforms and power spectra of the processing blocks in the complex IIR filter system are shown in Fig. 21. The amplitude of the left-hand-side waveform is normalized by clutter amplitude to be 2. Moreover, 256-point FFT with a Hanning window is applied to the calculation of the righthand-side power spectrum. Figures 21(a) and 21(c) show the input and output waveforms of zero insertion processing, respectively. A solid line denotes the I-component, and a dashed line, the Q-component. Figures 21(e) and 21(g) show the Doppler audio outputs of both directions at the zero baseline-shift. A solid line denotes the real component, and a dashed line, the imaginary component. Figures 21(i) and 21(k) show the Doppler audio outputs of both directions at the +0.4\**fs* baseline-shift. A solid line denotes the real-component, and a dashed line, the imaginary-component. Figures 21(b), 21(d), 21(f), 21(h), 21(i) and 21(l) show power spectra corresponding to the waveforms in the time domain. The aliasing spectra of blood flow and clutter are observed in Fig. 21(d) for a zero insertion processing output. Moreover, the approximately –20 dB DC component is observed at the center of the spectra. This DC component, which is not removed using the Hanning window, does not affect the latter complex band-pass filter processing. From the positive-side output waveform at the zero baseline-shift shown in Fig. 21(e), we confirm that the blood flow component of +0.24\**fs* frequency is separated on the positive-side. Moreover, in the power spectrum shown in Fig.

display area display area

BLS=0 BLS=

reverse forward reverse

for the direction separation of the Doppler audio system.

reverse

reverse

reverse

forward

forward

forward

Fig. 20. Frequency characterization of Doppler audio output

**4.5 Implementation of complex IIR filter system** 

**4.5.1 Signal processing simulation** 

Frequency(*fs*)

Frequency(*fs*)

Frequency(*fs*)

Power (dB)

Power (dB)

Power (dB)

21(f) in addition to the blood flow component, we observe that the clutter component (- 0.08\**fs*) remains on the negative-side under the effect of the filter element. In the negativeside output waveform at the zero baseline-shift in Fig. 21(g), the separation of the clutter component (-0.08\**fs*) is observed on the negative-side. Moreover, in the power spectrum in Fig. 21(h), a clutter component and a DC component are detected. When the baseline shift is +0.4\**fs*, the spectrum image and Doppler audio must generate a negative region larger than a positive region. The positive-side output waveform after the baseline shift in Fig. 21(i) shows the disappearance of the clutter component (+0.24\**fs*). Moreover, we confirm the absence of the blood flow component in the power spectrum shown in Fig. 21(j). We also confirm that a novel blood flow component (-0.76\**fs*), which is an alias component (+0.24\**fs*), is outputted into the negative-side output waveform after the baseline-shift in Fig. 21(k), except for the clutter component (-0.08\**fs*). Moreover, in the power spectrum in Fig. 21(l), we confirm that the blood flow and clutter components are separated on the negative-side.

Fig. 21. Simulation waveform and spectrum of complex IIR filter system.

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 235

First, we defined the target performance of Doppler audio processing and selected three signal-processing systems. We developed processing algorithms and compared their performances. Consequently, we confirmed that the complex IIR band-pass filter system has an excellent response and a low calculation load. Next, we performed functional and performance analyses by simulation with the data collected using a Doppler signal model and a phantom. Conventionally, although in the anti-aliasing process unique to a Doppler ultrasound system, the image and audio did not correspond, since it was applied only to a

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Table 8. Components of simulation input model

#### **4.5.2 Implementation**

On the basis of the Doppler IQ-signal of the carotid artery collected with the actual Doppler ultrasound system, an example of anti-aliasing signal processing of the Doppler audio is shown in Fig. 22. We use a string phantom (Mark 4 Doppler Phantom: JJ&A Instrument Company) and the ultrasonic diagnosis equipment (SSA-770A: Toshiba Medical Systems Corporation) for generating and collecting the Doppler signal. We use PLT-604AT (6.0 MHz linear probe) at PRF=4 kHz equivalent to *fs*. We collect the IQ-data in PWD mode. Moreover, we set cut-off frequency at an HPF of 200 Hz for clutter removal. The output waveforms of both sides of the Doppler audio and spectrum image obtained from the IQdata are shown in Fig. 22. In this figure, in the vicinity of 0.9 s, the baseline-shift is switched into -0.4\**fs* from 0. At the zero baseline-shift, we observe aliasing in the spectrum image shown in Fig. 22(a) and a negative-side output in Fig. 22(c). However, we confirm that the positive-side display range of the spectrum image expands after a baseline-shift and is interlocked with the Doppler audio. Although it is not observed in Fig. 22, the characteristic of the band-pass filter changes immediately after a baseline-shift. We will continue to examine the transient response of the Doppler audio under this effect and to consider implementation technologies, such as muting.

Fig. 22. Doppler spectrum display and audio output waveform

#### **4.6 Conclusion**

We developed the direction separation system of a Doppler audio interlocked with the antialiasing processing of a spectrum image using a complex IIR band-pass filter system.

First, we defined the target performance of Doppler audio processing and selected three signal-processing systems. We developed processing algorithms and compared their performances. Consequently, we confirmed that the complex IIR band-pass filter system has an excellent response and a low calculation load. Next, we performed functional and performance analyses by simulation with the data collected using a Doppler signal model and a phantom. Conventionally, although in the anti-aliasing process unique to a Doppler ultrasound system, the image and audio did not correspond, since it was applied only to a spectrum image, we could solve this problem by this signal processing.
