The invention relates generally to communications, and more particularly to time correlation in communication measurements. Still more particularly, the invention relates to a method and system for frequency domain time correlation.
Time correlation is frequently used in the testing of communication devices, and typically involves synchronizing the timing of the measurement equipment to the timing of the device being tested. The synchronization process also includes accommodation of the frequency errors and noise generated by the device during testing. Once the synchronization process is complete, the measurement equipment can proceed with the testing process.
The frequency-corrected reference signal is then input into correlation 104 via signal line 110. The frequency-corrected reference signal and the measurement signal are correlated to determine how closely the timing of the measurement signal matches the timing of the reference signal. A correlation response is then output on signal line 114.
Time correlation can be performed in the time domain and in the frequency domain. For some applications, performing time correlation in the frequency domain is faster than in the time domain, and the timing of the measurement signal can be calculated once its frequency error is known.
The frequency-corrected reference signal and a measurement signal are then input into correlation 104. Transform 202 converts the time domain data in the measurement signal into frequency domain data. Transform 204 converts the time domain data in the frequency-corrected reference signal into frequency domain data. Multiplication 206 multiplies the two signals and inputs the resulting product data into inverse transform 208. Inverse transform 208 transforms the resulting product data into delay domain data.
Unfortunately, correlation system 200 operates less effectively and efficiently as the size of the frequency errors and noise levels increase. Computational efficiency is reduced when the frequency correction and the correlation process are performed separately. Furthermore, the correlation systems of
In accordance with the invention, a method and system for frequency domain time correlation is provided. Time domain data in a measurement signal and in a reference signal are converted to frequency domain data. The reference signal and the measurement signal are then multiplied and the resulting product data converted to delay domain data. During this process, the frequency of the reference signal is varied. In one embodiment in accordance with the invention, the frequency of the reference signal is adjusted a predetermined number of times and the frequency that produces the strongest correlation selected. In another embodiment in accordance with the invention, the frequency of the reference signal is adjusted until a correlation value for the correlated data matches or exceeds a threshold value. The threshold value provides flexibility in the correlation search by allowing the correlation system to find correlation when the frequency of the reference signal achieves an acceptable equivalence to the frequency of the measurement signal. Embodiments in accordance with the invention, however, are not limited to adjusting the frequency of the reference signal. The frequency of the measurement signal may be adjusted instead of the frequency of the reference signal. Furthermore, the frequency of a signal may be adjusted in integer and fractional amounts.
The invention will best be understood by reference to the following detailed description of embodiments in accordance with the invention when read in conjunction with the accompanying drawings, wherein:
The invention relates to a method and system for frequency domain time correlation. The following description is presented to enable one skilled in the art to make and use the invention, and is provided in the context of a patent application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the generic principles herein may be applied to other embodiments. Thus, the invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the appended claims and with the principles and features described herein.
With reference now to the figures and in particular with reference to
The frequency domain data in the measurement signal and the frequency domain data in the reference signal are then multiplied, as shown in block 304. The resulting product data are then converted to delay domain data at block 306 and the process ends. In this embodiment in accordance with the invention, a strong correlation occurs in the inverse transform output data when the frequency of the reference signal, through frequency variation, matches or nearly matches the frequency of the measurement signal.
Frequency converter 402 receives the frequency domain data in the reference signal and varies the frequency of the signal. Conjugation 404 receives the frequency domain data in the measurement signal and conjugates (i.e. inverts the imaginary parts of) the data values. Multiplier 206 then multiplies the frequency domain data in the reference signal with the conjugate of the frequency domain data in the measurement signal. The resulting product data are input into inverse transform 208, which converts the data into delay domain data. A strong correlation occurs in the inverse transform output data in the
The measurement signal and the reference signal are sampled signals in this embodiment in accordance with the invention. Transforms 202, 204 are implemented as fast Fourier transforms (FFT) while inverse transform 208 is implemented as an inverse fast Fourier transform (IFFT). Multiplier 206 therefore, performs element-by-element vector multiplication, also known as Hadamard multiplication. In other embodiments in accordance with the invention, conversion techniques other than FFTs and IFFTs may be utilized. An example of one such technique is a discrete Fourier transform (DFT) and an inverse discrete Fourier transform (IDFT). The selection of a conversion technique is typically influenced by the specific parameters in each application. Those skilled in the art will recognize the accommodations necessary to adapt the circular correlation that naturally results from this processing to the desired linear correlation. Those skilled in the art will also recognize that, for periodic reference signals, circular correlation may be used to further reduce the computational complexity.
Frequency converter 402 varies the frequency of the reference signal by rotating the data in the reference signal in this embodiment in accordance with the invention. For example, the reference signal transform data may include four data values [D1, D2, D3, D4]. The data values become [D4, D1, D2, D3] when the data are rotated up one position. Rotation of the data values varies the frequency of the reference signal by integer values in this embodiment. A reference signal may include any number of data values in other embodiments in accordance with the invention.
Furthermore, the frequency of the reference signal may be varied in any desired sequence. For example, the frequency may be varied by ±1, ±2, ±3, etc., or by ±2, ±4, ±6, etc. In this embodiment in accordance with the invention, the frequency of the reference signal is shifted sequentially over the entire range of frequencies correlation system 400 accommodates. For each frequency in the frequency range, the reference data are rotated accordingly, multiplied with the conjugate of the frequency domain data in the measurement signal, and input into the inverse transform 208. The resulting correlation data are then examined for each frequency. The data containing the strongest correlation represents a match or near match between the timing of the measurement signal and the timing of the reference signal in the
Those skilled in the art will appreciate that the frequency of the reference signal may be varied differently in other embodiments in accordance with the invention. For example, the frequency domain data in a signal may be shifted in an ordered pattern over a limited range of frequencies. The pattern is typically governed by the specific parameters in each application.
Other embodiments in accordance with the invention may also eliminate conjugation 404 by utilizing convolution with time reversal with the measurement signal. Convolution with time reversal is equivalent to conjugation. In these other embodiments, the transformed time-reversed measurement signal is input directly into multiplier 206, where the reference signal transform is multiplied element-by-element with the time reversed measurement signal transform. The resulting product data are then input into inverse transform 208.
Referring now to
Next, the reference signal is read out of memory and the frequency of the signal varied, as shown in block 506. The frequency domain data in the measurement signal and the frequency domain data in the reference signal are then multiplied, as shown in block 508. The resulting product data are converted to delay domain data at block 510 and the process ends. A strong correlation occurs in the inverse transform output data in this embodiment in accordance with the invention when the frequency of the reference signal, through frequency variation, matches or nearly matches the frequency of the measurement signal.
A reference signal is input into transform 204 to convert the time domain data in the signal into frequency domain data. The transformed reference signal is then stored in storage 602. In this embodiment in accordance with the invention, the reference signal does not vary and therefore can be pre-computed and transformed into frequency domain data prior to being stored in memory. Multiple transformed reference signals may be stored in storage 602 in other embodiments in accordance with the invention.
A measurement signal is input into transform 202 to convert the time domain data in the signal into frequency domain data. Conjugation 404 receives the frequency domain data in the measurement signal and conjugates the transform data. The conjugate of the measurement signal is then stored in storage 604.
Frequency converter 402 reads the frequency domain data out of storage 602 and varies the frequency of the signal. Multiplier 206 then multiplies the frequency domain data in the reference signal with the conjugate of the frequency domain data in the measurement signal. The resulting product data are input into inverse transform 208, which converts the data into delay domain data. In the
Referring now to
A determination is made at block 704 as to whether the frequency of the reference signal is to be adjusted by a fractional amount. If not, the unadjusted reference signal is selected and its frequency varied by an integer amount, as shown in blocks 706 and 708. The reference signal and the measurement signal are then multiplied at block 710. The resulting product data are converted to delay domain data and the process ends.
Returning to block 704, if the frequency of a reference signal is to be adjusted by a fractional amount, the process passes to block 714 where a reference signal corresponding to the fractional adjustment is selected. A determination is then made as to whether the frequency of the selected reference signal is to be adjusted by an integer amount. If not, the process passes to block 710 and continues through block 712. If the frequency of the selected reference signal is to be adjusted by an integer amount, the process passes to block 708 where the frequency is adjusted by the integer amount. The process then continues through blocks 710 and 712.
Multiple reference signals are input into transform 204 to convert the time domain data in the signals into frequency domain data. Each reference signal corresponds to a different fractional frequency adjustment, including zero. The transformed reference signals are then stored in storage 602. In this embodiment in accordance with the invention, the fractional amounts represent zero, a ¼, a ½, and a ¾ adjustment to the frequency. Other embodiments in accordance with the invention may utilize different fractional amounts, such as, for example, one-third adjustments or one-eighth adjustments.
A measurement signal is input into transform 202 to convert the time domain data in the signal into frequency domain data. Conjugation 404 receives the frequency domain data in the measurement signal and conjugates the data. The conjugate of the measurement signal is then stored in storage 604. Frequency converter 402 reads the frequency domain data of a reference signal out of storage 602 and varies the frequency of the signal. If the frequency will be adjusted by a fractional amount, the frequency converter 402 selects the reference signal that corresponds to the fractional adjustment. If the frequency is not adjusted by a fractional amount, the zero adjustment reference signal is selected. If the frequency is also adjusted by an integer amount, the frequency converter 402 rotates the frequency domain data values to vary the frequency by the integer amount.
For example, when the adjustment value is 0.5, frequency converter 402 reads the reference signal corresponding to the 0.5 adjustment from storage 602. When the adjustment value is an integer and fractional amount, such as 2.5, frequency converter 402 reads a reference signal that corresponds to the fractional adjustment from storage 602. Frequency converter 402 then varies the 0.5 reference signal by the integer amount 2. In this embodiment in accordance with the invention, frequency converter 402 would vary the 0.5 reference signal by 2 by rotating the data values in the reference signal as described in conjunction with
Multiplier 206 then multiplies the frequency domain data in the reference signal with the conjugate of the frequency domain data in the measurement signal. The resulting product data are input into inverse transform 208, which converts the data into delay domain data. A strong correlation occurs in the inverse transform output data in the
Referring now to
In this embodiment in accordance with the invention, the frequency of the measurement signal typically clusters around a particular nominal frequency, i.e., within a certain tolerance around the nominal frequency. The nominal frequency and the tolerance value are usually specific to an application. The nominal frequency is utilized in the
The frequency domain data in the measurement signal and the frequency domain data in the nominal frequency signal are then multiplied (block 904). Next, the resulting product data are converted to delay domain data and stored in a memory, as shown in blocks 906 and 908. The nominal frequency is then adjusted at block 910. In this embodiment in accordance with the invention, the nominal frequency is adjusted by a tolerance value. The value of the tolerance value is dependent on the application being measured.
Next, the adjusted nominal frequency signal and the measurement signal are multiplied and the resulting product data converted to delay domain data (blocks 912 and 914). The delay domain data is stored in memory, as shown in block 916. A determination is then made at block 918 as to whether the desired number of frequency adjustments has been performed. If not, the process returns to block 910 and repeats until the desired number of frequency adjustments has occurred.
When all of the frequency adjustments have occurred, the results are compared and the frequency and delay that produce the strongest or maximum correlation are selected (block 920). A strong correlation occurs in the inverse transform output data in this embodiment in accordance with the invention when the frequency of the reference signal, through frequency variation, matches (or nearly matches) the frequency of the measurement signal.
A signal having a nominal frequency is used as an initial reference signal and is input into transform 204. The nominal frequency signal is based on the application, and provides a preference as to where the search for a frequency match begins. Transform 204 converts the time domain data in the nominal frequency signal to frequency domain data. The frequency domain data in the nominal frequency signal are then input into frequency converter 402. Frequency converter 402 does not vary the nominal frequency initially in this embodiment in accordance with the invention, so the nominal frequency signal is input into multiplier 206.
A measurement signal is input into transform 202 and conjugation 404. Multiplier 206 then multiplies the frequency domain data in the nominal frequency signal with the conjugate of the frequency domain data in the measurement signal. The resulting product data are input into inverse transform 208, which converts the data into delay domain data.
After the data in the nominal frequency signal and the measurement signal are correlated, the frequency adjuster 1002 adjusts the nominal frequency pursuant to a search algorithm in this embodiment in accordance with the invention. The frequency adjuster 1002 inputs the adjustment value or amount into frequency converter 402. Frequency converter 402 then varies the nominal frequency according to the adjustment value. The adjustment value includes integer adjustments in the
In the
Referring now to
A signal having a nominal frequency is used as an initial reference signal, as shown in block 1102. Next, the frequency domain data in the measurement signal and the frequency domain data in the nominal frequency signal are multiplied, as shown in block 1104. The resulting product data are then converted to delay domain data (block 1106).
A determination is then made at block 1108 as to whether a correlation value for the correlated data matches or exceeds a correlation threshold value. A correlation threshold value allows the correlation system to detect correlation with an acceptable, but less than perfect, match between the frequency of the measurement signal and the frequency of the reference signal. When a correlation threshold value is set to zero, the correlation search will stop after the nominal frequency correlation. When the correlation threshold value is set to a value approaching one, the correlation search will stop when the frequency of the reference signal matches the frequency of the measurement signal. When the correlation threshold value is set to an appropriate value between zero and one, the correlation search will stop when the frequency of the reference signal reaches an acceptable, but not perfect, equivalence or closeness to the frequency of the measurement signal, which results in a useable correlation. The value of a correlation threshold value depends on the specific parameters in each application.
Returning to block 1108, if the correlation threshold value is matched or exceeded, the process ends. Otherwise the process passes to block 1110, where the nominal frequency is adjusted. The adjustment amount includes integer adjustments in the
Next, the frequency domain data in the adjusted signal and the frequency domain data in the measurement signal are multiplied and the resulting product data converted to delay domain data (blocks 1112 and 1114). A determination is then made at block 1116 as to whether a correlation value for the correlated data matches or exceeds a correlation threshold value. If the correlation threshold value is matched or exceeded, the process ends. If, not, the process returns to block 1110, where the frequency is adjusted again. The process continues through blocks 1110 to 1116 until the correlation threshold value is matched or exceeded.
In this embodiment in accordance with the invention, the side lobe responses 1202 in the correlated signal increase in magnitude when the frequency of the reference signal approaches Fm. And as the frequency of the reference signal moves away from Fm, the side lobe responses 1202 in the correlated signal decrease in magnitude. The side lobe responses 1202, and possibly the peak response 1204, are compared with a correlation threshold value in this embodiment in accordance with the invention.
As discussed in conjunction with
When the correlation threshold value is set properly, an acceptable correlation may often be found at an offset nearer the nominal frequency than the actual frequency of the measurement signal, allowing the frequency search to terminate before the frequency of the measurement signal is matched by the search. Thus, the use of a correlation threshold value can result in a faster correlation process in those applications where a match is not required. In certain situations, however, the side lobe responses 1202 may generate false detections. Those skilled in the art will recognize that to avoid false detections, further analysis with known techniques may be required to confirm the main lobe has been located. Furthermore, the side lobe responses 1202 may be mitigated through the use of window functions applied to the reference signal.
Referring now to
A signal having a nominal frequency is used as an initial reference signal and is input into transform 204. The nominal frequency is based on the application, and provides a preference as to where the search for a frequency match begins. Transform 204 converts the time domain data in the nominal frequency signal to frequency domain data. The frequency domain data in the nominal frequency signal are then input into frequency converter 402. In this embodiment in accordance with the invention, frequency converter 402 does not vary the nominal frequency initially, so the nominal frequency signal is input into multiplier 206.
A measurement signal is input into transform 202 and conjugation 404. Multiplier 206 then multiplies the frequency domain data in the nominal frequency signal with the conjugate of the frequency domain data in the measurement signal. The resulting product data are input into inverse transform 208, which converts the data into delay domain data.
Frequency adjuster and analyzer 1302 analyzes the correlated data output from inverse transform 208 to determine whether a correlation value for the correlated data matches or exceeds a correlation threshold value. The correlation threshold value is input into frequency adjuster and analyzer 1302 via signal line 1304. If the correlation value for the correlated data does not match or exceed the correlation threshold value, the frequency adjuster and analyzer 1302 transmits the adjustment value or amount to frequency converter 402, which in turn varies the frequency according to the adjustment value. In this embodiment in accordance with the invention, frequency adjuster and analyzer 1302 adjusts the frequency pursuant to a search algorithm. As discussed in conjunction with
The process of adjusting the frequency of the nominal frequency signal continues until the correlation value of the correlated data output from inverse transform 208 matches or exceeds the correlation threshold value. In the
Embodiments in accordance with the invention, however, are not limited to adjusting the frequency of the reference signal. Other embodiments in accordance with the invention can adjust the frequency of the measurement signal.
As with the