Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
1998-06-30
2001-03-27
Hoff, Marc S. (Department: 2757)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C702S075000, C708S405000, C708S406000
Reexamination Certificate
active
06208946
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to a high-speed Fourier transform apparatus preferably used in test instruments such as network analyzers and spectrum analyzers, and more particularly, to a high-speed Fourier transform apparatus which performs a discrete Fourier transform in a parallel fashion.
BACKGROUND OF THE INVENTION
Fourier transform technology, for example FFT (Fast Fourier Transform), is widely used in test instruments such as network analyzers and spectrum analyzers as a means for analyzing the response of a device, the frequency spectrum of an incoming signal and the like. For example, such a Fourier transform process is performed on time domain data that is obtained by measuring an incoming signal in a predetermined time interval. Such test instruments convert the time domain data to frequency domain data and analyze the frequency components in the frequency domain or obtain the frequency spectrum of the incoming signal.
Alternatively, frequency domain data may be converted to time domain data through a Fourier transform process (or an inverse Fourier transform process). For example, in measuring a communication device such as a filter or other device under test (DUT), a network analyzer provides a frequency swept signal to the DUT and measures a resultant frequency domain signal in a predetermined frequency step. Based on the measured data, the network analyzer calculates and displays various parameters including transfer functions, reflection coefficients, phase shifts, group delay, Smith chart, etc., of the DUT.
The network analyzer may further be used to obtain a time domain response, such as a time domain reflectometry (TDR), of the DUT. In such a situation, for example, the frequency domain data indicating the transfer function of the DUT may be inverse Fourier transformed into time domain data. Prior to the inverse transform, a window function may be provided to the transfer function in the frequency domain. Consequently, it is possible to analyze a time domain response of the DUT, such as an impulse response without actually applying an impulse to the DUT.
Generally, such a Fourier transform method is based on what is called a discrete Fourier transform where a DUT response is measured in terms of discrete harmonics determined by a sequence of equally spaced samples. A discrete Fourier transform generally requires a large number of calculations. In particular, for N measured data points, N
2
transform coefficients are calculated. Consequently, for large data sets, the discrete transform process may take a long time to complete the calculation.
To address this issue, a high speed Fourier transform method, the so-called Fast Fourier Transform or FFT, was developed by J. W. Cooly and J. W. Tukey. FFT is an algorithm, typically implemented on a computer, used to reduce the number of calculations required to obtain a DFT. In essence, an FFT algorithm reduces the number of calculations of a typical DFT by eliminating redundant operations when dealing with Fourier series. As a result, according to the FFT, the number of operations required is represented by N log
2
N where N is the number of data samples to be transformed. Thus, the FFT requires significantly fewer calculations than that required in the DFT, and for large data arrays, the FFT is considerably faster than the conventional DFT.
There are some drawbacks to FFT methods. First is that the FFT requires the number N of a transform array to be equal to a power of 2, which may prove restrictive for some applications. More importantly however, in general it is very difficult to initiate the FFT transform until all of the N sampled data are taken. Thus, an overall time required for the Fourier transform operation is represented by T
MES
+T
FFT
as shown in
FIG. 8
, where T
MES
is a measuring time for obtaining all of the sampled data and T
FFT
is a Fourier transformation time by the FFT algorithm.
There is another type of Fourier transform process called Chirp Z transform, which is an improved version of FFT, that can perform Fourier transform with higher resolution than that of FFT. Another advantage of the Chirp Z transform is that the number of data samples need not be equal to a power of 2. This Fourier transform method is described by Rabiner and Gold in “Theory and Application of Digital Signal Processing”, pages 393-398, 1975. As far as a transformation time is concerned, since the Chirp Z transform process typically carries out the FFT process three times, a transformation time of 3T
FFT
must be added to the measuring time T
MES
as shown in FIG.
9
. In other words, the Chirp Z transform requires a longer Fourier transformation time than that required in the traditional FFT process.
SUMMARY OF THE INVENTION
Therefore, it is an object of the present invention to provide a high-speed Fourier transform method and apparatus that is able to overcome the drawbacks in the conventional Fourier transform technology.
It is another object of the present invention to provide a high speed Fourier transform apparatus and method which is able to complete a Fourier transform by a shorter time than that required in the conventional FFT process when including a measuring time T
MES
.
It is a further object of the present invention to provide a high speed Fourier transform apparatus and method wherein a discrete Fourier transform process is carried out in a real time fashion while obtaining sampled data.
It is a further object of the present invention to provide a high speed Fourier transform apparatus and method wherein a discrete Fourier transform process is carried out in a parallel fashion for each term in Fourier equation.
It is a further object of the present invention to provide a network analyzer using the high speed Fourier transform method wherein a discrete Fourier transform process is carried out in a parallel fashion for each term in Fourier equation.
The high speed Fourier transform method and apparatus of the present invention is basically a parallel discrete Fourier transform newly developed by the applicant of the present invention. The high speed Fourier transform of the present invention is based on the fact that the same order of terms in a plurality of Fourier equations can be determined independently from the other terms based on sampled data corresponding to the order of the terms. An overall Fourier transform is a sum of all of the terms in the equations. The present invention also takes into consideration the recent increases in operational speeds of digital processing devices.
The high speed Fourier transform apparatus comprises a discrete Fourier transform means for calculating corresponding terms in a plurality of Fourier equations upon acquisition of a portion of sampled data. The terms correspond to a sequence of sampled data counting from the start of measurement operation. The apparatus also comprises a calculation result file that stores the results of calculation corresponding to the terms in the plurality of Fourier equations. The apparatus further comprises an adder for adding the calculation results in the calculation result file in such a way to complete each and all of the plurality of discrete Fourier equations.
In accordance with the invention, a sweep frequency signal is applied to a device to be tested. An output signal level of the device under test is measured for each of N predetermined frequency intervals in the frequency sweep. Measuring the signal levels N times by this procedure produces N samples of frequency data. The discrete Fourier transform process of the present invention is carried out for same-order terms of N Fourier equations upon acquisition of a corresponding order of sampled data by the above measurement process. The order of sampled data may be defined with reference to the number of measurements from the start of the measurement process. The calculation process for the same terms in the Fourier equations is performed in real time upon obtaining the sampled data and before obtaining the next sampled data. Thus for each measured da
Arakawa Norio
Konno Hiroyuki
Advantest Corp.
Bui Bryan
Hoff Marc S.
Muramatsu & Associates
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