Image Processing Reference
In-Depth Information
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.
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
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