Data processing: measuring – calibrating – or testing – Measurement system – Measured signal processing
Reexamination Certificate
1998-08-11
2001-09-18
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Measured signal processing
C702S075000, C702S077000, C702S109000, C702S196000, C324S076190, C324S076210, C375S325000
Reexamination Certificate
active
06292760
ABSTRACT:
BACKGROUND AND SUMMARY OF THE INVENTION
This invention relates in general to the field of test system engineering, and more particularly to a method and system utilizing digital signal processing for measuring non-coherent electrical signals.
BACKGROUND
Test engineering is an important and constantly growing area of engineering practice especially in the field of integrated circuit design. The test engineer is ideally involved in the development cycle of a device from start to finish and provides valuable insight on the performance of the device. Many test and measurement systems rely *on Digital Signal Processing (DSP) to make fast and accurate measurements of electrical signals. Fast measurements are critically important in minimizing the cost of production test of electronic circuits and systems.
Fourier Frequency and Fourier Transforms
The most accurate DSP based test systems rely on coherence between the sampling rate of the test system and the signal under test. In a coherent sampling system, a limited number of samples of the signal under test are collected at regular time intervals. The Fourier frequency F
f
is defined as the sampling rate divided by the number of samples collected. Most common test signals consist of a summation of one or more sine and cosine waves, also known as test tones. If each frequency in such a multitone test signal is an integer multiple of the Fourier frequency, then the test signal is referred to as a coherent signal.
The Discrete Time Fourier Transform (DTFT) is based on a series of correlations between the signal under test and sine/cosine pairs at integer multiples of the Fourier frequency. The results of the correlations are shown in a plot of signal amplitude vs. frequency, and is equivalent to a spectrum analyzer.
The Fast Fourier Transform (FFT) is a mathematically efficient way to perform the full DTFT using many fewer operations, and is therefore an equivalent of a spectrum analyzer that is sensitive to both magnitude and phase. The FFT turns time information into frequency information, if the number of samples N is a power of two. The FFT will allow the evaluation of (N/2)−1 sin/cosine pairs.
Both the DTFT and FFT assume that all signal components are coherent. If they are not, significant errors arise, as described below.
The Fourier transform of a coherent sampled signal results in a spectrum with a very desirable property: each sine or cosine component falls into its own unique mathematical array element. The individual array elements are known as Fourier bins or spectral bins. Since each test frequency falls into a unique spectral bin, it is possible to measure multiple frequencies simultaneously, which significantly reduces test time.
Coherence
One characteristic of a coherent signal is that the endpoints of the signal transition smoothly from one period to the next. In a coherent signal, each frequency component of the output signal falls into its own Fourier spectral bin. If there is a discontinuity in the endpoints, i.e. the signal does not transition smoothly from one period to the next, then the signal is non-coherent. In the case of a non-coherent signal, some of the energy level from each frequency component of the output signal “leaks” or “smears” into the other spectral bins, corrupting the other signal energy levels. For this reason, the FFT normally cannot be used on non-coherent signals without some form of pre-processing, i.e., windowing.
Coherent DSP-based testing results in several distinct disadvantages. First, the test tones must be integer multiples of the Fourier frequency. This restriction limits the frequency resolution of the measurement for a given sampling frequency and number of captured samples. In a coherent measurement system, the frequency resolution can only be increased by collecting more samples of the signal under test. The extra samples require a longer test time, which drives up the cost of test.
Second, coherent testing requires specific numerical ratios between the various sampling frequencies in a mixed analog/digital circuit and the sampling frequencies of the digitizer or digital waveform capture system in the measurement system. Often, these ratios of sampling frequencies cannot be achieved because of architectural restrictions in the measurement system.
Third, the accuracy of a coherent measurement is vulnerable to non-coherent interference tones, such as 60 Hz power hum. Such non-coherent tones are typically generated by external electrical equipment which is not synchronized to the sampling frequency of the measurement system. They can also be generated by parasitic oscillations in the circuit under test. Finally, there are certain types of circuits that generate their own signal frequencies. These signal frequencies cannot be synchronized to the measurement equipment sampling frequencies. In this case, a coherent measurement system cannot be achieved. Coherent and non-coherent multitone signals are illustrated in
FIGS. 3
a
and
3
b,
respectively.
Windowing
In the prior art, a non-coherent signal requires the use of a mathematical window which is applied to the sampled signal before the Fourier transform is computed. Windowing “squeezes” the endpoints of the sampled signal towards zero, in effect forcing coherence (i.e., forcing the endpoints of the signal to wrap smoothly from one period to the next). Windowing is a well known technique in digital signal processing and in test engineering. Windowing is a digital signal processing technique of partitioning a long sequence into smaller subsections by multiplying the long sequence by a shorter sequence of non-zero values. For example, the sequence 8, 3, 6, 4, 1, 0, 4, 2, 3 windowed using the sequence 0, 0, 0.5, 1, 1, 1, 0.5, 0, 0 produces the sequence 0, 0 , 3, 4, 1, 0, 2, 0, 0. this example, both endpoints of the sample are forced to zero, which allows the signal to be tested as if it were truly coherent.
Windowing, however, has a well known side effect in that it introduces substantial error in the measured signal level. The error arises because windowing allows some of the energy at each frequency in the measured signal to spread into adjacent spectral bins. Because the signal energy from each test tone is allowed to spread into many spectral bins, the various test tones become indistinguishable from one another. Also, sine and cosine components of a given tone become mixed together, reducing the accuracy of phase measurements. This problem is most severe in sampled waveforms with a small number of samples, since there are relatively few spectral bins in the resulting Fourier transform. Another problem introduced by windowing is increased noise relative to the signal under test. Increased noise reduces the repeatability of a measurement. Repeatability can only be recovered by averaging or increasing the sample size. Either of these techniques adds a great deal of extra test time.
The presently preferred embodiment provides a means of measuring non-coherent multitone signal amplitudes and phase shifts without sacrificing accuracy and repeatability.
Innovative Method and Apparatus for Measuring Non-Coherent Signals
The preferred embodiment comprises a method and a system of measuring non-coherent single tone or multitone signals using either windowed or non-windowed Fourier transforms. Because the Fourier transform is mathematically equivalent to a series of correlation functions, windowed or non-windowed correlation functions can be used in place of the complete Fourier transform to save calculation time. Frequency resolution is infinite, rather than being limited to an integer multiple of the Fourier frequency F
f
of the sampling system. Furthermore, accuracy can be substantially improved when compared to the windowing process of the prior art.
REFERENCES:
patent: 4417337 (1983-11-01), Favin et al.
patent: 4466108 (1984-08-01), Rhodes
patent: 5995914 (1999-11-01), Cabot
Brady III Wade James
Hoff Marc S.
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
Vo Hien
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