Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
  • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
  • G06F7/544—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices for evaluating functions by calculation
  • G06F7/552—Powers or roots, e.g. Pythagorean sums
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F2207/00—Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F2207/552—Indexing scheme relating to groups G06F7/552 - G06F7/5525
  • G06F2207/5523—Calculates a power, e.g. the square, of a number or a function, e.g. polynomials

Definitions

• Frequency analysis of a waveform is a basic technique in signal processing since certain information carried by a signal can be very di fficult or impossible to extract otherwise than in the frequency domain.
• the range of applications of frequency analysis is very wide, and includes, for exampl e, sonar, radar and image processing.
• the Di screte Fourier Transform is used to compute the frequency domain matrix [X k ] from the time domain series [x n ] according to the equation for an N-point DFT:
• x n is the value of the n th (complex) waveform sample and X k is the amplitude of the k th frequency component.
• the expression (1) and hence also the present invention, is not limited to applications in frequency analysis, but the primary use of the expression is to perform a DFT.
• the DFT may be calculated by various methods, but digital techniques are preferable where hi gh precision is requi red.
• the necessary hardware is simplified greatly if the DFT is calculated by a recursive prime radix transform, as described by T.E. Curtis and J.E.Wickenden in I .E.E. Proceedings Vol .130, Part F, No.5, pages 424-425. Equation (1) may be written in the recursi ve form:
• N which is the transform length
• N which is the transform length
• the transform wi ll be calculated for all k between 0 and N-1.
• An object of this invention is to remove the condition that N be relatively prime to k.
• a processor for computing a value X k from a series of input data x o ..x n ..x N-1 for selected values of k in the range 0 ⁇ k ⁇ N
• Q is any non-zero integer containing no prime factors common to N that are not common to all values of k
• the processor being arranged to calculate and store sequential current values, each current value being the sum o a product component and a sum component, the sum component being he sum of a group of selected data, the number in each group, whi may be one, being derived by multiplying together those prime factors of N which are common to k, and the product component being the product of W Q and the preceding current value, the arrangement being such that a value of X k is obtained for any non-zero Integral value of N.
• the processor may include a kernel arranged to calculate the current values, an accumulator arranged to operate concurrently with the kernel to sum Input data, and a selector adapted to select data to be loaded into the kernel from raw input data and summed data from the accumulator.
• a processor is arranged to compute a value X k from a series of input data x o ..x n ..x N _ 1 for selected values of k in the range 0 ⁇ k ⁇ N
• a processor is arranged to compute a value X k from a series of input data x o ..x n ..x N-1 for selected values of k in the range 0 ⁇ k ⁇ N where
• FIG. 3 is a block diagram of the elements of the processor.
• the powers of W have been written modulo N i.e. as the remainder after dividing by N.
• the rate at which the power of W increases down the W column matrix is equal to Q.
• N is not prime and consequently powers of W occur more than once in rows of the W matrix, so it cannot be re-expressed directly in the simple recursive form of Figures 1c-e.
• Figure 3 shows the computing structure. This could be in software or analogue or digital hardware but for convenience of description it will be treated as digital hardware.
• the kernel constitutes the means for computing the terms W Q X and the final expressions for X k .
• the kernel and accumulator operate concurrently.
• the input data x n are time samples of some signal which is to be analysed in the frequency domain, for example Doppler signals from a radar or vibration from an engine.
• the corresponding frequency components X n are normally computed for all of 0 k N although a subset only may be required in certain applications.
• N and k are chosen by the user according to the application in hand.
• Q is also chosen by the user. Its value is always modulo N, and must not be zero or contain any prime factors common to N that are not also common to each and every value taken by k. (Illegal values of Q do not allow a solution to the recursive form equation (2), since the powers of W required in the direct form, equation (1), cannot be generated).
• the accumulator 1 operates to Load, Sum or Hold.
• the Load operation is used when it is necessary to reinitialise the accumulator, i.e. at the start of each X k computation sequence.
• the current input value x n at A is loaded and held.
• 'Sum' adds the next x n to the stored value.
• 'Hold' simply holds the current stored value, with no loading.
• the data x n are input under the control of some control means (not shown) in the order required for the values of N, k and Q in use.
• the selector 2 operates to select Zero, Accumulate or Raw for the input to the kernel 3. If Accumulate is selected the total from the accumulator 1 is fed into the kernel. If Raw is selected, the Raw input value x n is read off path 4, which is a bypass around the accumulator.
• the facility for selecting Raw data enables parallel processing to take place, as will be described below.
• the kernel 3 also requires reinitialising before the start of each X n computation sequence, and this is achieved by a 'Load' operation. Otherwise, the kernel Computes i.e. multiplies the value it holds (which will initially be zero) by W Q and adds the value selected by the Selector. The sum thus formed provides the new stored value.
• the accumulator is reinitialised (to zero) then loads the first input value, x 5 .
• the accumulator adds the next input x 3 to the stored value x 5 and so on as shown.
• Steps 13 to 18 the accumulator continues to load and sum the Input data x n , but now the selector selects Raw, that is the data loaded Into the kernel is the raw data x n from the bypass path 4.
• This accumulation is completed at Step 18, as the computation of X 1 is completed by the kernel.
• the accumulator 'Holds' its value until Step 19 when it is loaded Into the reinitialised kernel and can be output directly at D as X Q .
• This parallel computation of X 0 and X 1 Increases the speed of computation.

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• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Engineering & Computer Science (AREA)
• Computational Mathematics (AREA)
• Mathematical Analysis (AREA)
• Pure & Applied Mathematics (AREA)
• Theoretical Computer Science (AREA)
• Computing Systems (AREA)
• Mathematical Optimization (AREA)
• General Engineering & Computer Science (AREA)
• Complex Calculations (AREA)

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• 1986
  • 1986-05-07 GB GB868611124A patent/GB8611124D0/en active Pending
• 1987
  • 1987-05-06 WO PCT/GB1987/000297 patent/WO1987007053A1/en not_active Application Discontinuation
  • 1987-05-06 JP JP50286487A patent/JPH01500779A/ja active Pending
  • 1987-05-06 EP EP19870902646 patent/EP0273921A1/en not_active Withdrawn
  • 1987-05-06 GB GB08710679A patent/GB2191316A/en not_active Withdrawn

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