**3.5 Conclusion**

222 Applications of Digital Signal Processing

shift system are filling the target performance of time-delay. It turns out that calculation load is light in order of the phase-shift system, the complex IIR system, and the Hilbert

Ovh: 20% *fs*\*(2\**tap*+1)\*1.2 1.26

C-mul: (*tap*+2)\*2\**fs*, Ovh: 20% *fs*\*(12\**tap*-12)\*1.2 7.32

(MFLOPS)

*fs*\*(12\**tap*-4)\*1.1 6.74

*fs*\*(24\**order*)\*1.1 0.84

12\**N*\**r*\*1.2\*(*fs*\*4/*N*) (FFT shift addition, *N*/4 shift)

> *fs*\*[4\**N*\*(*N*+*order*) +2\*(*N*-1)]\*1.2

(*tap*=128)

(*tap*=128)

(*order*=8)

1.61 (*N*=128, *r*=7)

(*tap*=128)

0.64 (*order*=4,*N*=4)

method calculation component estimation equation load

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

Frequency characteristic and direction separation performance are largely dependent on the filter property that are related to time-delay and calculation load. If the number of filter taps of FIR and the filter order of IIR are reduced, time-delay and calculation load will decrease. But these become the trade-off of frequency resolution and frequency characteristic. The Hilbert transform system frequency characteristic when changing the number of taps is shown in Fig. 9. The frequency characteristic near the Nyquist and near the DC has deteriorated, when the number of taps is short. This is the same also about the taps of the complex FIR system, the modulation/demodulation system and the FFT point number of

In order to compare the direction separation performance, the frequency characteristic simulation is performed. The frequency characteristics of positive-component (solid line: forward) and negative-component (dashed line: reverse) are shown in Fig. 10. The target performance of direction separation is filled except for the phase shift system. The stop-band property near the low frequency and near the Nyquist frequency is good in the Hilbert transform system, the complex FIR system, and the FFT/IFFT system. Exclude near the DC and near the Nyquist frequency, a sufficient separation performance (not less than 30 dB) and frequency characteristic are acquired by the complex IIR system and the modulation/demodulation system. The phase-shift system has generally insufficient

**3.4 Comparison of a frequency characteristic and direction separation** 

R-add: (*tap*+1)\**fs*, R-mul: *tap*\**fs*

C-add: (*tap*-1)\*2+*fs*, C-mul:

C-add: *order*\*4\**fs*, C-mul:

Ovh: 20%, R-mul: *N*\*4

[2\**N*\*(2\**N*+2\**order*)+2]\**fs* R-mul: 4\**N*\*(*N*+*order*)\**fs,* Ovh:

C-mul: complex multiplication, Calculation load is estimated at *fs*=4kHz

C-add: (*tap*-1)\*2\**fs*

*tap*\*2\**fs* Ovh: 10%

*order*\*4\**fs* Ovh: 10%

R-add:

20%

Table 3. Comparison of calculation load

FFT/IFFT C-add: *N*\**r*\*3, C-mul: (*N*\**r*/2)\*3

transform system.

Hilbert transform

complex FIR

complex IIR

 modulation/ demodulation

Phase-shift

the FFT / IFFT system.

We made the target performances of the direction separating process of digital Doppler audio, and evaluated six kinds of digital-signal-processing ideas that were pre-existing or were newly devised. The performances of each processing were evaluated by comparing many responses such as chirp or step and so on. The results are following.


Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 225

frequency range of *–fs/2* to *+fs/2* on the baseline (0Hz) shown in Fig. 12(a). At the time (A) in Fig. 12, the frequency of the spectrum exceeds *+fs/2* and aliasing is induced. The Doppler ultrasound system has an anti-aliasing display function (BLS: baseline-shift) that shifts a baseline to a negative side, as shown in Fig. 12(b), and expands a positive velocity range seemingly. Thus we can measure the peak velocity of blood flow easily. The power spectrum at the zero baseline-shift is shown in Fig. 13(a). The spectrum image at the *-0.25\*fs* baseline-shift and the power spectrum corresponding to the time (A) in Fig. 12 are shown in Fig. 13(b). In the spectrum image, a baseline-shift is easily realized by changing the frequency read-out operation of the spectrum after FFT processing. However, since there is no baseline-shift function in the Doppler audio, a baseline-shift is not realized in spectrum imaging and Doppler audio processing. For example, although a negative-component is lost in the spectrum image shown in Fig. 13(b), since Doppler sound is still in the state shown in Fig. 13(a), it displays a negative-output and does not correspond to the Doppler image.

Baseline

5.0 *fs*

(a) baseline-shift=0 (b) baseline-shift=-0.25䞉*fs*

*+NF* : Nyquist freq. of forward

forward

To solve the problem of the spectrum image and Doppler audio not working together, we examined the signal processing system of the Doppler audio to determine the possible type of baseline-shift. On the other hand, since IQ-signals after quadrature-detection had little merit at a small operation load in narrow-band processing, we examined a realization

Power

*0*

5.1 *fs* 0.1 *fs* 5.0 *fs* 5.0 *fs* 0.1 *fs* 5.1 *fs*

(a) Display area

(b) Display area

**4.2 Anti-aliasing processing of Doppler audio and its target performance** 

reverse forward

Time Freq.

5.0 *fs* 25.0 *fs*

Freq.

(a) baseline-shift=0

(b) baseline-shift=-0.25䞉*fs*

(A)

Time Freq.

*-NF* : Nyquist freq. of reverse

reverse

Fig. 13. Spectrum display area and baseline shift.

Fig. 12. Spectrum Doppler image

(A)

Baseline

5.0 *fs*

75.0 *fs*

3. All the systems fill the frequency characteristic. However, the frequency characteristics near the DC and near the Nyquist region are dependent on the filter characteristics of each processing system.
