ASA: Advanced Signal Processor
Artium's ASA is the most advanced signal processor available for LDV and PDI applications. It is a Fourier transform based signal processor with several innovations to ensure optimum performance. The optical signal collected by the PDI optics is converted to a voltage using a PMT/pre-amplification system. The signal is then high-pass filtered and amplified before being fed to the ASA analog section. Within the analog section, the signal is mixed with a software selectable variable quadrature mixer. The quadrature mixer outputs are low-pass filtered to improve signal SNR. The quadrature outputs of the analog section are sampled and digitized at a software selectable sampling rate. The digitized signal is then applied to the phase domain burst detector. The Phase Burst Detector (PBD) output is combined with the analog burst detector output and then used as an input to the adaptive sampling circuitry. The sampled data for each Doppler burst is then packed into a single data packet. The data packets are stamped with other relevant information (time of arrival, transit time and external input data) and transferred to the computer via a high-speed PCI interface card.
The Fourier Transform Method
Artium uses Fourier analysis to measure signal frequency. Therefore, we sample the signal at a rate, or sampling frequency (fs) that is slightly higher than the Nyquist rate. The Nyquist rate is the frequency that is twice the maximum signal frequency. The paper, Aliasing (Olshausen, 2000), explains why there is no need to sample at a rate higher than the Nyquist rate to avoid aliasing. The frequency of the sampled signal is then measured using the Fourier transform method. The paper by Rife and Boorstyn shows the Fourier transform method provides the best frequency and phase measurement accuracy results. At signal SNR of 0 dB. the frequency measurement accuracy is proportional to 1/(N)^3 where N is the number of samples within the signal transit time (T). To attain this resolution, we compute the Fourier transform over N^3 frequencies that covers the range -fs/2 to fs/2. For LDV applications, it is sufficient to have a frequency measurement resolution of 0.1%. Therefore, there is no need to compute the Fourier transform over more than (64*N) frequencies (to attain a frequency resolution of better than 1/(64*N)).
Artium’s signal processor bandwidth is 150 MHz (10 MHz to 160 MHz). Therefore, the maximum sampling frequency required is 300 MHz. We use a maximum sampling frequency of 320 MHz to ensure that signals with a frequency of 160 MHz are processed properly. Sampling at a higher rate is not necessary. The user has the option of increasing the sampling frequency to 400 MHz, if there is a need to increase the processor frequency bandwidth to 190 MHz (i.e., processing signals over the range 10 MHz to 200 MHz).
Comparing the Fourier Transform Method
Manufacturers of similar instrumentation employ “counter” techniques to measure the signal frequency. For example, if the counter clock (sometimes incorrectly referred to as sampling frequency) = fs and the transit time is T, then there are a maximum of N counts (where N=1/(T*fs)) within the transit time T. Therefore, the frequency measurement resolution does not exceed 1/N =1/(T*fs). This measurement resolution is only possible with signal SNR higher than 10 dB. For lower SNR, the frequency measurement will be further compromised due to the presence of extra zero crossings generated by the noise (a well-known problem with counting methods).
To demonstrate the superiority of the Fourier transform method over the counter technique, consider a Doppler signal with a transit time T of 50 ns. For a sampling frequency (fs) of 400 MHz, the number of samples is given by (T*fs) = 20 samples. Therefore, the frequency resolution attained with Artium processor is given by 1/(64*20) ~ 0.12%. However, the frequency resolution attained with a counter-technique processor is given by 1/(20) = 4%.
We have to emphasize that the counter-technique processor is based on an obsolete method for frequency and phase measurements. The auto-correlation method is used only to improve the signal SNR before using the counter (for frequency and phase measurements). Autocorrelation offers only limited advantage in improving the signal SNR. However, counter-technique processors still suffer from the well-known drawback of generating biased results due to the counting of extra zero crossings introduced as the signal crosses zero.
It should be pointed out that Artium is the only company that executes the Fourier analysis (or Fourier method) as outlined by Rife and Boorstyn; using quadrature signals (the real part R(t) and its Hilbert transom Q(t) to form the complex signal R(t) + i Q(t) where i is the square root of -1) to compute the signal Fourier transform. Competitive processors use only the real part of the signal.
One of the key advantages in using quadrature sampling, is its ability to detect when the signal frequency is at or around the Nyquist rate. Note that when R or Q is staying flat (or has gaps), the other signal is changing or oscillating at the Nyquist rate. That is why the FFT algorithm is able to measure the signal frequency accurately. This result cannot be achieved using only R sampled data (as it is the case with our competitive instrumentation). More crucially, phase measurement will be compromised if only the real part of the signal is used. In addition, using only the real signal R, the phase measurement accuracy is dependent on the number of cycles within the signal record. US Patent 5,808,895