Digital frequency-domain implementation of arrays

• US 5,671,168 A
• Filed: 07/06/1995
• Issued: 09/23/1997
• Est. Priority Date: 07/06/1995
• Status: Expired due to Fees

• Current Assignee: TECHNION RESEARCH AND DEVELOPMENT FOUNDATION, LTD.
• Original Assignee: TECHNION RESEARCH AND DEVELOPMENT FOUNDATION, LTD.
• Inventors: Liu, Chen, Sideman, Samuel
• Primary Examiner(s): Mai, Tan V.
• Application Number:
  US08/498,846
• Time in Patent Office: 810 Days
• Field of Search: 364/724.18, 364/725-726
• US Class Current: 708/321
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544

Abstract

A method for the digital frequencey domain implementation of receiving arrays. The steps of the method are as follows: a discrete time input signal is transformed into its spectral components and the redundant spectral components are removed. Products of the non-redundant spectral components with a scaled set of acquired weights are computed. From the so-computed products a first set of spectral sums is calculated wherefrom a second set of spectral sums is derived. Thereafter, the first and second sets of spectral sums are converted to the discrete time domain thereby obtaining a discrete time output signal. The invention also provides a system having receiving components operating in accordance with the method. In another embodiment the invention also provides a method and system for the digital frequency domain implementation of transmitting arrays.

Claims

1. A method for the digital frequency domain implementation of receiving arrays which offers improved resolution in both direction and frequency determination without necessitating sampling rates of the received signal much higher than the Nyquist rate, said receiving arrays having receiving elements, each receiving element defining a channel, said method comprising the steps of:

transforming a discrete time input signal in each channel into N spectral components using an N-point discrete Fourier transform;

removing, in each channel, redundant spectral components, whereby only non-redundant spectral components remain in each channel;

deriving for said non-redundant spectral components in each channel a set of weights comprising weights that are scaled both in amplitude and in phase, so that said set of weights corresponds to α

N spectral components, where α

is an integer power of 2;

computing products of said non-redundant spectral components in each channel with said derived scaled weights for each channel;

calculating from the so-computed products a first set of spectral sums;

deriving from said first set of spectral sums a second set of spectral sums; and

converting said first and second sets of spectral sums to the discrete time domain, using an inverse discrete Fourier transform based on a pruned decimation-in-frequency structure fast Fourier transform, thereby obtaining a discrete time output signal.

2. The method of claim 1, wherein the discrete time input signal is obtained by sampling a continuous time signal that is received by the receiving elements of the array.

3. The method of claim 2, wherein the continuous time signal in each channel is sampled at a uniform sampling rate.

4. The method of claim 3, wherein said uniform sampling rate is substantially the Nyquist rate, which is defined as twice the highest frequency component of the spectrum of said continuous time signal.

5. The method of claim 2, wherein the continuous time signal in each channel passes through an anti-aliasing filter before said continuous time signal is sampled.

6. The method of claim 1, wherein the last N/2-1 spectral components in each channel are redundant in the sense that said last N/2-1 spectral components in each channel are obtained by taking the complex conjugate of the first N/2 spectral components in each channel, barring the first spectral component that corresponds to zero frequency.

7. The method of claim 1, wherein the first N/2+1 spectral components in each channel are non-redundant.

8. The method of claim 1, wherein the set of derived weights in each channel of the array is an optimum set of weights which is either deterministic or adaptive, corresponding to N spectral components, for phasing the elements of said array.

9. The method of claim 1, wherein the weights of the set of weights in each channel are scaled both in amplitude and phase so as to correspond to α

N spectral components, where α

is an integer power of 2, whereby effectively increasing the sampling rate of the input signal by a factor of α

.

10. The method of claim 1, wherein the products of the non-redundant spectral components in each channel with the scaled set of acquired weights are formed by multiplying the scaled weights of a given frequency and a given channel by the spectral components of the same frequency and the same given channel.

11. The method of claim 1, wherein said first set of spectral sums is derived by summing separately for each non-redundant spectral component the corresponding products from each channel.

12. The method of claim 1, wherein said second set of spectral sums is obtained from said first set of spectral sums by applying the operation of complex conjugation thereto, whereby the second element of said first set of spectral sums is identified with the last element of said second set of spectral sums, and the last element of said first set of spectral sums is identified with the first element of said second set of spectral sums, and the intermediate elements of the two sets are identified correspondingly.

13. The method of claim 1, wherein said discrete time output signal undergoes the further step of being re-scaled thereby restoring the scaling of the discrete time output signal to that of the input signal.

14. A method for the digital frequency domain implementation of transmitting arrays comprising the steps of:

transforming a discrete time input signal into its spectral components;

removing redundant spectral components;

computing a first set of products, for each channel of the array, of non-redundant spectral components with a scaled set of acquired weights;

deriving from said first set of products a second set of products for each channel of the array; and

converting said first and second sets of products to a discrete time output signal in each channel.

15. The method of claim 14, wherein the discrete time input signal is obtained by sampling a continuous time signal.

16. The method of claim 15, wherein the continuous time signal is sampled at a uniform sampling rate.

17. The method of claim 16, wherein said uniform sampling rate is substantially the Nyquist rate, which is defined as twice the highest frequency component of the spectrum of said continuous time signal.

18. The method of claim 15, wherein the continuous time signal passes through an anti-aliasing filter before being sampled.

19. The method of claim 14, wherein the discrete time input signal is transformed into N spectral components using an N-point discrete Fourier transform.

20. The method of claim 14, wherein the last N/2-1 spectral components in each channel are redundant in the sense that said last N/2-1 spectral components in each channel are obtained by taking the complex conjugate of the first N/2 spectral components in each channel, barring the first spectral component which corresponds to zero frequency.

21. The method of claim 14, wherein the first N/2 spectral components are non-redundant.

22. The method of claim 14, wherein the set of acquired weights in each channel of the array is an optimum set of weights which is either deterministic or adaptive, corresponding to N spectral components, for phasing the elements of said array.

23. The method of claim 14, wherein the weights of the set of weights in each channel are scaled both in amplitude and phase so as to correspond to α

N spectral components, where α

is an integer power of 2, whereby effectively increasing the sampling rate of the input signal by a factor of α

.

24. The method of claim 14, wherein the first set of products of the non-redundant spectral components with the scaled set of acquired weights are formed by multiplying, for each value of frequency, the spectral components by weights corresponding to the same frequency, for each channel of the array.

25. The method of claim 14, wherein said second set of products is acquired from said first set of products, for each channel of the array, by applying the operation of complex conjugation thereto, whereby the second element of said first set of products is identified with the last element of said second set of products, and the last element of said first set of products is identified with the first element of said second set of products, and the intermediate elements of the two sets are identified correspondingly.

26. The method of claim 14, wherein said first and second sets of products, for each channel, are transformed into the discrete time domain using an inverse discrete Fourier transform based on a pruned decimation-in-frequency structure fast Fourier transform.

27. The method of claim 14, wherein said discrete time output signal, in each channel, undergoes the further step of being re-scaled thereby restoring the scaling of the discrete time output signal, for each channel, to that of the input signal.

28. A system for the digital frequency domain implementation of receiving arrays which offers improved resolution in both direction and frequency determination without necessitating sampling rates of the received signal much higher than the Nyquist rate, said receiving arrays having receiving elements, each receiving element defining a channel, said system comprising:

spectral transforming means for transforming a discrete time input signal in each channel into N spectral components using an N-point discrete Fourier transform;

spectrum filtering means responsive to said spectral components and capable of passing, in each channel, non-redundant spectral components only;

computational means for deriving for said non-redundant spectral components in each channel a set of weights comprising weights that are scaled both in amplitude and in phase, so that said set of weights corresponds to α

N spectral components, where α

is an integer power of 2;

computational means for computing products of said non-redundant spectral components in each channel with said scaled weights for each channel;

summing means for calculating from the said computed products a first set of spectral sums;

computational means for deriving from said first set of spectral sums a second set of spectral sums; and

processor means for converting said first and second sets of spectral sums to the discrete time domain, using an inverse Fourier transform based on a pruned decimination-in-frequency structure fast Fourier transform, thereby obtaining a discrete time output signal.

29. The system of claim 28, further including an analog to digital processor for converting a continuous time input signal to said discrete time input signal.

30. The system of claim 28, wherein said spectral transforming means is based on an N-point digital Fourier transform.

31. The system of claim 28, wherein said spectrum filtering means is a processor which accepts an input array of spectral components and outputs only part of the input array.

32. The system of claim 28, wherein said means for deriving said second set of spectral sums from said first set of spectral sums is a processor based on applying the operation of complex conjugation to said first set of spectral sums.

33. The system of claim 28, wherein said processor means for converting said first and second sets of spectral sums to said discrete time output signal is based on a pruned decimation-in-frequency structure fast Fourier transform.

34. The system of claim 28, wherein said processor means for converting said first and second sets of spectral sums to said discrete time output signal is followed by a further processor for scaling up said discrete time output signal in order to restore the scaling of said discrete time output signal to that of the input signal.

35. The system of claim 28, wherein said further processor for scaling up said discrete time output signal is followed by a digital to analog processor in order to convert said discrete time signal having original sampling rate and scaling to a continuous time output signal.

36. A system for the digital frequency domain implementation of transmitting arrays comprising:

spectral transforming means for transforming a discrete time input signal into its spectral components;

spectrum filtering means responsive to said spectral components and capable of passing non-redundant spectral components only;

computational means for computing a first set of products, for each channel of the array, of said non-redundant spectral components with a scaled set of acquired weights;

means for deriving from said first set of products a second set of products for each channel of the array; and

processor means for converting said first and second sets of products to a discrete time domain output signal in each channel of the array.

37. The system of claim 36, further including an analog to digital processor for converting a continuous time input signal to said discrete time input signal.

38. The system of claim 37, wherein said analog to digital processor is preceded by an anti-aliasing filter.

39. The system of claim 36, wherein said spectral transforming means is based on an N-point digital Fourier transform.

40. The system of claim 36, wherein said spectrum filtering means is a processor which accepts an input array of spectral components and outputs only part of the input array.

41. The system of claim 36, wherein said means for deriving said second set of products from said first set of products is a processor based on applying the operation of complex conjugation to said first set of products.

42. The system of claim 36, wherein said processor means for converting said first and second sets of products to said discrete time output signals is based on a pruned decimation-in-frequency structure fast Fourier transform.

43. The system of claim 36, wherein said processor means for converting said first and second sets of products to said discrete time output signals is followed by a further processor for scaling up said discrete time output signals in order to restore the scaling of said discrete time output signals to that of the input signal.

44. The system of claim 36, wherein said further processor for scaling up said discrete time output signals is followed by a digital to analog processor in order to convert said discrete time signals having original scaling to continuous time output signals.

45. The system of claim 36, wherein said digital to analog processor is followed by a transducer for transmitting said continuous time output signals to a neighboring medium.

46. The system of claim 36, wherein said transducer is an antenna and said continuous time output signals are electromagnetic signals.

47. The system of claim 36, wherein said transducer is associated with at least one of a microphone, a hydrophone, or a geophone and said continuous time output signals are acoustic signals.