**4.1 Anti-aliasing display and conventional problem**

The Doppler ultrasound system extracts the blood flow component used in the quadraturedetection of the Doppler signal from the blood (mainly an erythrocyte), which moves inside a blood vessel, and removes a reflective signal from tissue, such as a blood vessel wall with a high-pass filter, and transforms the Doppler component into an image and sound. The Doppler ultrasound system is shown in Fig. 11. The signal obtained after HPF processing is divided into two lines. Spectrum image processing generates a Doppler signal as a spectrum time change image corresponding to blood velocity, and Doppler audio processing outputs direction separation signals as stereo sound from the right-and-left speakers.

Fig. 11. Doppler ultrasound system.

Because the Doppler signal contains phase information, the signal includes both positiveside (forward) and negative-side (reverse) frequency components. If sampling frequency is set to be *fs*, the detection of a Doppler frequency component corresponding to the frequency range of *-fs/2* to *+fs/2* is possible. A spectrum image is shown in Fig. 12. The horizontal axis corresponds to time. The vertical axis corresponds to the velocity derived from Doppler shift frequency, and luminosity corresponds to the spectrum intensity of each time. Since a spectrum image is a power spectrum generated by complex FFT processing, it has the

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.

Fig. 12. Spectrum Doppler image

224 Applications of Digital Signal Processing

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

The direction separation system of the foregoing section is developed further, and the Doppler audio technology exceeding the Nyquist frequency is examined. Some directionseparation systems for a Doppler audio that is interlocked with the baseline-shift of a spectrum image are investigated. First, section 4.1 explains a problem peculiar to the Doppler audio corresponding to the Doppler display processing. In section 4.2 we defined the target performance of anti-aliasing Doppler audio processing selected three kinds of signal-processing systems. In section 4.3 the various systems of the modulation/demodulation system, the FFT/IFFT system and the complex IIR Filter system are explained. Next, in section 4.4 the signal-processing algorithms are compared with the target performances. It was confirmed that the complex IIR band-pass filter system has an excellent response and a low calculation load. Finally, in section 4.5 using the blood-flow data collected from Doppler phantom, we performed functional and performance analyses

The Doppler ultrasound system extracts the blood flow component used in the quadraturedetection of the Doppler signal from the blood (mainly an erythrocyte), which moves inside a blood vessel, and removes a reflective signal from tissue, such as a blood vessel wall with a high-pass filter, and transforms the Doppler component into an image and sound. The Doppler ultrasound system is shown in Fig. 11. The signal obtained after HPF processing is divided into two lines. Spectrum image processing generates a Doppler signal as a spectrum time change image corresponding to blood velocity, and Doppler audio processing outputs

B-Mode Image Processing

Because the Doppler signal contains phase information, the signal includes both positiveside (forward) and negative-side (reverse) frequency components. If sampling frequency is set to be *fs*, the detection of a Doppler frequency component corresponding to the frequency range of *-fs/2* to *+fs/2* is possible. A spectrum image is shown in Fig. 12. The horizontal axis corresponds to time. The vertical axis corresponds to the velocity derived from Doppler shift frequency, and luminosity corresponds to the spectrum intensity of each time. Since a spectrum image is a power spectrum generated by complex FFT processing, it has the

Spectrum Image Proc. Doppler Audio Proc. Display

Left Speaker Right Speaker

direction separation signals as stereo sound from the right-and-left speakers.

HPF

Quadrature detection

each processing system.

by simulation shown in Fig. 22.

**4. Signal processing for Doppler audio anti-aliasing** 

**4.1 Anti-aliasing display and conventional problem** 

Tx/Rx Processing

Probe

Fig. 11. Doppler ultrasound system.

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

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

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 227

sides correspond to the baseline-shift shown in Table 5. *FB* and *RB* indicate the bandwidths on the positive (forward) and negative (reverse) sides, whereas *FBC* and *RBC*, the center frequencies on the same sides, respectively. These are normalized using *fs*. Although five stages were used from the baseline shift range of -0.5 to +0.5 in this example, a small setup is

The block diagram of the modulation/demodulation system is shown in Fig. 14. The IQsignal is modulated with two sets of quadrature modulators. Thereby, the frequency of the signal induces a *+FBC* shift on the positive-side and a *–RCB* shift on the negative-side. Next, Nyquist frequency is doubled by zero insertion, and applying band limitations on the positive and negative sides demodulates signals. The input signal (equivalent to (A) in Fig. 12) with the aliasing spectrum in Fig. 15(a) is modulated, and the spectra indicating the *+FBC*, and *-RCB* shifts of the frequency of the signal are shown in Figures 15(b) and 15(c), respectively. A positive-side component and a negative-side component are extracted by carrying out a baseline-shift and applying a band limitation using the bandwidths of r*FB* and r*RB* in the passage regions of *LPF1 (z)* and *LPF2 (z).* The spectra of the *LPF1 (z)* and *LPF2 (z)* outputs are shown in Figures 15(d) and 15(e). Since sampling frequency has doubled after an LPF output, the direction separations on the positive and negative sides that shift the frequencies of *-FBC/2* and *+RCB/2* by demodulation, and are denoted by *BPF1 (z)* and *BPF2 (z)* in Fig. 15(f) are realizable. Although the spectrum in Fig. 15 (equivalent to the aliasing (A) in Fig. 12) is outputted to the negative side for the Nyquist frequency *fs/2*, it can extract the positive-side component beyond the Nyquist frequency in Fig. 15( f). The operation was changed and performed in the calculation example shown in Table 7. For response improvement, we did not use a FIR filter for LPF but the 8th IIR filter with an

> Zero Insertion

> Zero Insertion

×

×

*exp(-ʌ* 䞉 *FBC*䞉*j)*

*exp(+ʌ* 䞉 *RBC*䞉*j)*

> Band Width Center Freq. Table

Fig. 14. Block diagram of the modulation/demodulation system

Complex

Complex *LPF2(z)*

D

<sup>2</sup>䞉*fs exp(-<sup>ʌ</sup>*

IQ-Inpu Forward Signal t

2䞉*fs*

*LPF1(z) Real(Forward)*

×

*exp(+ʌ* 䞉 *FBC/2* 䞉*j)*

×

䞉 *RBC/2* 䞉*j)*

*Real(Reverse)* Reverse Signal

possible with the actual Doppler ultrasound system.

**4.3 Three kinds of digital signal-processing ideas 4.3.1 The modulation/demodulation system** 

equivalent performance.

BLS

method based on the IQ-signals. The Hilbert transform, complex FIR filter, phase-shift, complex IIR filter, FFT/IFFT and modulation/demodulation systems also indicated that the direction separation system of the Doppler audio does not allow a baseline-shift. Among these systems, the Hilbert transform and phase-shift systems enable direction separation by addition and subtraction between signals with a 180-degree phase-difference. Since an input IQ-signal has a 90-degree phase difference, these systems give a phase-difference of 90 degree between channels with a filter. Since the phase-difference of an IQ-signal stops being 90 degree when sampling frequency is doubled as a countermeasure, in the Hilbert transform and phase-shift systems, which make the phase-difference between channels a simple 90 degree, direction separation is difficult. Moreover, the complex FIR filter system involves the same pre-processing step as that in the complex IIR filter system, and anti-alias processing becomes possible. However, since the length of a FIR coefficient sequence doubles, the operation load increases. On the other hand, the FFT/IFFT system can reduce the operation load by diverting the FFT output of spectrum Doppler imaging processing. When the FFT output is diverted, the returning anti-alias processing can be performed only by inverse-FFT and shift-addition. The modulation/demodulation and the complex IIR filter systems mainly involve the multiplication of modulation/demodulation and IIR filter processing. Thus, their calculation processing is easy, and the increase in calculation load by anti-aliasing processing is small. As mentioned above, from the viewpoints of calculation load reduction and anti-alias processing feasibility, we chose and examined the following three systems: the modulation/demodulation, the FFT/IFFT, and the complex IIR systems. When evaluating these systems, we showed the same target performance required as that of the Doppler ultrasound system in Table 4. The items 1 to 4 (time-delay, direction separation, frequency characteristic, frequency resolution) are same as table 1.


Table 4. Target specification of Doppler audio processing.


Notes: Baseline shift, *FB*, *FBC*, *RB* and *RBC* are normalized by *fs*.

Table 5. Frequency shift and bandwidth table of baseline-shift

#### **Baseline-shift range:**

The baseline-shift range is considered to be *-0.5\*fs* to *+0.5\*fs* to enable range expansion on the positive and negative sides to twice the Nyquist frequency range. The ranges of both sides correspond to the baseline-shift shown in Table 5. *FB* and *RB* indicate the bandwidths on the positive (forward) and negative (reverse) sides, whereas *FBC* and *RBC*, the center frequencies on the same sides, respectively. These are normalized using *fs*. Although five stages were used from the baseline shift range of -0.5 to +0.5 in this example, a small setup is possible with the actual Doppler ultrasound system.

#### **4.3 Three kinds of digital signal-processing ideas 4.3.1 The modulation/demodulation system**

226 Applications of Digital Signal Processing

method based on the IQ-signals. The Hilbert transform, complex FIR filter, phase-shift, complex IIR filter, FFT/IFFT and modulation/demodulation systems also indicated that the direction separation system of the Doppler audio does not allow a baseline-shift. Among these systems, the Hilbert transform and phase-shift systems enable direction separation by addition and subtraction between signals with a 180-degree phase-difference. Since an input IQ-signal has a 90-degree phase difference, these systems give a phase-difference of 90 degree between channels with a filter. Since the phase-difference of an IQ-signal stops being 90 degree when sampling frequency is doubled as a countermeasure, in the Hilbert transform and phase-shift systems, which make the phase-difference between channels a simple 90 degree, direction separation is difficult. Moreover, the complex FIR filter system involves the same pre-processing step as that in the complex IIR filter system, and anti-alias processing becomes possible. However, since the length of a FIR coefficient sequence doubles, the operation load increases. On the other hand, the FFT/IFFT system can reduce the operation load by diverting the FFT output of spectrum Doppler imaging processing. When the FFT output is diverted, the returning anti-alias processing can be performed only by inverse-FFT and shift-addition. The modulation/demodulation and the complex IIR filter systems mainly involve the multiplication of modulation/demodulation and IIR filter processing. Thus, their calculation processing is easy, and the increase in calculation load by anti-aliasing processing is small. As mentioned above, from the viewpoints of calculation load reduction and anti-alias processing feasibility, we chose and examined the following three systems: the modulation/demodulation, the FFT/IFFT, and the complex IIR systems. When evaluating these systems, we showed the same target performance required as that of the Doppler ultrasound system in Table 4. The items 1 to 4 (time-delay, direction separation,

frequency characteristic, frequency resolution) are same as table 1.

1. time-delay bellow 20ms (*fs*=4KHz)

5. baseline-shift range -*fs*/2 to +*fs*/2 (-0.5 to 0.5)

3. frequency characterization -*fs*/128 to –127\**fs*/128, *fs*/128 to 127\**fs*/128

baseline-shift -0.5 -0.25 0 0.25 0.5 *FB*: band-width of forward 4/8 3/8 2/8 1/8 0 *FBC*: center freq. of forward 4/16 3/16 2/16 1/16 0 *RB*: band-width of reverse 0 1/8 2/8 3/8 4/8 *RBC*: center freq. of reverse 0 -1/16 -2/16 -3/16 -4/16

The baseline-shift range is considered to be *-0.5\*fs* to *+0.5\*fs* to enable range expansion on the positive and negative sides to twice the Nyquist frequency range. The ranges of both

flat as possible

item target

4. frequency resolution *fs*/100

2. direction separation above 30dB

Table 4. Target specification of Doppler audio processing.

Notes: Baseline shift, *FB*, *FBC*, *RB* and *RBC* are normalized by *fs*. Table 5. Frequency shift and bandwidth table of baseline-shift

**Baseline-shift range:** 

The block diagram of the modulation/demodulation system is shown in Fig. 14. The IQsignal is modulated with two sets of quadrature modulators. Thereby, the frequency of the signal induces a *+FBC* shift on the positive-side and a *–RCB* shift on the negative-side. Next, Nyquist frequency is doubled by zero insertion, and applying band limitations on the positive and negative sides demodulates signals. The input signal (equivalent to (A) in Fig. 12) with the aliasing spectrum in Fig. 15(a) is modulated, and the spectra indicating the *+FBC*, and *-RCB* shifts of the frequency of the signal are shown in Figures 15(b) and 15(c), respectively. A positive-side component and a negative-side component are extracted by carrying out a baseline-shift and applying a band limitation using the bandwidths of r*FB* and r*RB* in the passage regions of *LPF1 (z)* and *LPF2 (z).* The spectra of the *LPF1 (z)* and *LPF2 (z)* outputs are shown in Figures 15(d) and 15(e). Since sampling frequency has doubled after an LPF output, the direction separations on the positive and negative sides that shift the frequencies of *-FBC/2* and *+RCB/2* by demodulation, and are denoted by *BPF1 (z)* and *BPF2 (z)* in Fig. 15(f) are realizable. Although the spectrum in Fig. 15 (equivalent to the aliasing (A) in Fig. 12) is outputted to the negative side for the Nyquist frequency *fs/2*, it can extract the positive-side component beyond the Nyquist frequency in Fig. 15( f). The operation was changed and performed in the calculation example shown in Table 7. For response improvement, we did not use a FIR filter for LPF but the 8th IIR filter with an equivalent performance.

Fig. 14. Block diagram of the modulation/demodulation system

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 229

audio is expanded, and the positive-side component in Fig. 17 (b) and the negative-side component in Fig. 17 (c) are obtained. In the calculation example shown in Table 7, we perform 128-point FFT and 256-point inverse-FFT. Moreover, we perform the shiftaddition of 32 time series data to which the Hamming window is applied after inverse-FFT.

Power

*fs*

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

*RB FB*

**4.3.3 The complex IIR filter system** 

response of direction separation.

BLS

Zero Insertion

Center Freq. Table

Fig. 18. Block diagram of the complex IIR filter system

IQ-Input *X*

BLS *fs*

Fig. 17. Frequency design of the FFT/IFFT system

freq.

*WF(Ȧ)*

*FB*

Power

Power

(b) IFFT forward component extracted by *WF(*

freq.

䃨*)*

(a) spectrum of IQ-input (c) IFFT reverse component extracted by *WF(Ȧ)*

The signal processing block diagram of the complex IIR filter system is shown in Fig. 18. Zero insertion is carried out with a pre-treatment, and Nyquist frequency is increased. Next, two complex band-pass filters separate both components directly. The frequency characteristics of the transfer functions *Hf (z)* and *Hr (z)* with the bandwidths of *FB* and *RB* (one side bandwidth) for LPF are shown in Figures 19(a) and 19(b). On the basis of the Fourier transform shift theory, the frequency shifts (*FBC* and *RBC*) are applied to *z*  operators, and a transfer function of LPF changes to the positive-side and a negative-side band-pass filters. Operator *z* is transformed to *z z j FBC* ' exp( ) and *z z j RBC* '' exp( ) . The frequency characteristics of the complex band-pass filters *Hf (z')* and *Hr (z'')* enable the *+FBC* and *-RBC* frequency shifts are shown in Fig. 19(c). In the calculation example shown in Table 7, we use the 8th Butterworth filter by considering the

> Complex BPF *Hf(z')*

*Real(Forward)*

Reverse Signal

Forward Signal

Complex BPF *Hr(z'')*

*Real(Reverse)* Band Width

2䞉*fs*

2䞉*fs*

*RB*

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

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

*WR(Ȧ)*

*RBC FBC* freq.

Fig. 15. Frequency design of the modulation/demodulation system

#### **4.3.2 The FFT/IFFT system**

The block diagram of the FFT/IFFT system is shown in Fig. 16. Two sets of filters corresponding to the baseline-shift separate the IQ-signal after FFT processing. These filters are realized by applying *WF*Z and *WR*Z with the characteristics of *FB*, *RB*, *FBC*, and *RBC* shown in Table 6. Next, the separated spectra are returned to the time domain signals by inverse-FFT. Since the frequency range expands on the basis of the baseline-shift, we perform twice-point inverse-FFT. Further shift in time waveform after inverse-FFT is carried out, and a continuous output is obtained. The power spectrum of the IQ-signal after FFT is shown in Fig. 17(a). When the baseline-shift is terminated, the spectrum in the figure (equivalent to the aliasing (A) in Fig. 12) is observed on the negative-side. However, by operating the read-out address of FFT, the positive display range is expanded and observed on the positive-side. Similarly, by carrying out inverse-FFT processing with *WF* Zand

*WR* Zwith a frequency twice that of sampling ( 2 *fs* ), the frequency range of the Doppler

Fig. 16. Block diagram of the FFT/IFFT system

audio is expanded, and the positive-side component in Fig. 17 (b) and the negative-side component in Fig. 17 (c) are obtained. In the calculation example shown in Table 7, we perform 128-point FFT and 256-point inverse-FFT. Moreover, we perform the shiftaddition of 32 time series data to which the Hamming window is applied after inverse-FFT.

Fig. 17. Frequency design of the FFT/IFFT system

## **4.3.3 The complex IIR filter system**

228 Applications of Digital Signal Processing

*FBC*

Power

(b) spectrum of forward modulation

*RBC* Power

Power

*BPF2(z) BPF1(z)*

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

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

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

*RBC*

The block diagram of the FFT/IFFT system is shown in Fig. 16. Two sets of filters corresponding to the baseline-shift separate the IQ-signal after FFT processing. These filters

*RBC* shown in Table 6. Next, the separated spectra are returned to the time domain signals by inverse-FFT. Since the frequency range expands on the basis of the baseline-shift, we perform twice-point inverse-FFT. Further shift in time waveform after inverse-FFT is carried out, and a continuous output is obtained. The power spectrum of the IQ-signal after FFT is shown in Fig. 17(a). When the baseline-shift is terminated, the spectrum in the figure (equivalent to the aliasing (A) in Fig. 12) is observed on the negative-side. However, by operating the read-out address of FFT, the positive display range is expanded and observed on the positive-side. Similarly, by carrying out inverse-FFT processing with *WF* 

with a frequency twice that of sampling ( 2 *fs* ), the frequency range of the Doppler

2䞉*fs*

Complex IFFT

Complex IFFT

2䞉*fs*

IQ-Input Signal

FD Filter WF(Ȧ) WR(Ȧ)

Shift Adder

Shift Adder *Forward*

*Reverse* Signal

Z

*FBC*

freq.

 with the characteristics of *FB*, *RB*, *FBC*, and

Z

and

freq.

freq.

(f) spectrum of demodulation

(a) spectrum of IQ-input

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

*LPF2(z)* Power (d) spectrum of complex LPF1

**4.3.2 The FFT/IFFT system** 

are realized by applying *WF*

*WR* Z

(e) spectrum of complex LPF2

Fig. 15. Frequency design of the modulation/demodulation system

Z

Complex FFT

Band Width Center Freq. Table

*fs*

BLS

Fig. 16. Block diagram of the FFT/IFFT system

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

2䞉*RB*

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

0

2䞉*FB*

Power

freq.

freq.

 and *WR*

freq.

(c) spectrum of reverse modulation *LPF1(z)* Power

The signal processing block diagram of the complex IIR filter system is shown in Fig. 18. Zero insertion is carried out with a pre-treatment, and Nyquist frequency is increased. Next, two complex band-pass filters separate both components directly. The frequency characteristics of the transfer functions *Hf (z)* and *Hr (z)* with the bandwidths of *FB* and *RB* (one side bandwidth) for LPF are shown in Figures 19(a) and 19(b). On the basis of the Fourier transform shift theory, the frequency shifts (*FBC* and *RBC*) are applied to *z*  operators, and a transfer function of LPF changes to the positive-side and a negative-side band-pass filters. Operator *z* is transformed to *z z j FBC* ' exp( ) and *z z j RBC* '' exp( ) . The frequency characteristics of the complex band-pass filters *Hf (z')* and *Hr (z'')* enable the *+FBC* and *-RBC* frequency shifts are shown in Fig. 19(c). In the calculation example shown in Table 7, we use the 8th Butterworth filter by considering the response of direction separation.

Fig. 18. Block diagram of the complex IIR filter system

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 231

First, the time-delays theoretically determined from the above-mentioned parameters and calculation loads are shown in Tables 6 and 7, respectively. Since the signal processing input is sampled using *fs*, delay time increases with a decrease in *fs*. Table 6 shows the time-delay calculation result for a typical *fs*=4 kHz diagnostic operation. Moreover, we simply estimate 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.

deteriorate with a ripple and rapid phase change.

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

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

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