Signal parameterizer

• US 5,034,911 A
• Filed: 01/22/1990
• Issued: 07/23/1991
• Est. Priority Date: 04/11/1988
• Status: Expired due to Fees

• Current Assignee: E-Systems Incorporated (Rtx Corporation)
• Original Assignee: E-Systems Incorporated (Rtx Corporation)
• Inventors: Rachels, Kenneth W.
• Primary Examiner(s): Shaw, Dale M.
• Assistant Examiner(s): Nguyen, Long T.
• Application Number:
  US07/489,711
• Time in Patent Office: 547 Days
• Field of Search: 364/726, 364/725
• US Class Current: 708/403
• CPC Class Codes: G06F 17/14 Fourier, Walsh or analogous domain transformations , e.g. Laplace, Hilbert, Karhunen-Loeve, transforms for correlation function computation G06F17/156; spectrum analysers G01R23/16
• CPC Class Codes: G06F 7/552 Powers or roots , e.g. Pythagorean sums

Abstract

A method and apparatus for parameterizing an input signal as a sum of N unrelated sine waves of various amplitudes, frequencies and phases using a 2N-order difference equation to describe the sine wave sum and converting the problem to a solution of the roots of an N-order polynomial.

Claims

1. Apparatus for parameterizing a digital input signal which is the sum of N unrelated sine wave signals of various frequencies, ω

_m, amplitudes, A_m, and phases B_m where m=1·

·

·

N, said apparatus comprising;

first data storage means for storing samples Y_t ·

·

·

Y_t-(3N-1)h of the digital input signal representing samples at time, t, from the most recent to the oldest sample where h= the time interval between samples,

weighted adder means coupled to the first data storage means for receiving the stored samples and calculating a matrix of row and column component signals, C_nK, by adding selected ones of the stored samples, Y_t ·

·

·

Y_t-(3N-1)h, with a weighting function according to the equation ##EQU27## where n=1·

·

·

N rows, K=1·

·

·

N+1 columns, h= time interval between samples and l= a column between O and K, to obtain the matrix array of signals ##EQU28## a first matrix inverter coupled to the weighted adder means for receiving the C_nK row and column signals and generating signals representing a set of symmetrical polynomials, {σ

^m }, according to the equation ##EQU29## , with each polynomial having coefficients, Z_m, representing the cosines of the N frequency components of the input signal,

a polynomial solver coupled to the first matrix inverter for receiving the signals representing the set of symmetrical polynomials, {σ

^m }, and calculating the roots of each polynomial according to the equation ##EQU30## to obtain signals representing the cosine frequency components, Z_m, where Z_m =cosine ω

_m h and M= the input signal frequency component between 1 and N, and

a function inverter coupled to the polynomial solver for calculating the frequency, ω

_m, of each of the N unknown input sine waves for each of the digital signal samples according to the equation ##EQU31##

2. Apparatus as in claim 1 further comprising:

second data storage means coupled between the polynomial solver and the function inverter for storing the cosine of the frequency components, Z_m and

circuit means coupling the cosine of the frequency components, Z_m, back to the polynomial solver for use in anticipating the calculation of the subsequent frequency component, Z_m +1.

3. Apparatus as in claim 1 further comprising:

first calculator means coupled to the function inverter for receiving the calculated frequencies ω

_m =1/hacosZ_m and generating the functions sin(kω

_m h) and cos(kω

_m h);

second storage means coupled to the first calculator means for storing the functions sin(kω

_m h) and cos(kω

_m h) and solving the equation ##EQU32## a second matrix inverter for receiving the stored sine (kω

_m h), cosine (kω

_m h) signal functions and the stored digital input samples Y_t ·

·

·

Y_t+(3N-1)h and calculating the respective signal amplitude coefficients A₁ ·

·

·

A_n and signal phase coefficients B₁ ·

·

·

B_n ; and

second calculator means coupled to receive the signal amplitude coefficients and the signal phase coefficients from the second matrix inverter for calculating the signal amplitude ##EQU33## and signal phase B_m =arctan 2(B_m, A_m).

4. Apparatus as in claim 3 wherein the second matrix inverter solves the simultaneous equations ##EQU34## to obtain the signal amplitude coefficients A₁ ·

·

·

A_N and the signal phase coefficients B₁ ·

·

·

B_N from which the signal amplitude, A_m, and phase, B_m, can be calculated.

5. Apparatus as in claim 1 wherein said first matrix inverter generates signals representing symmetrical polynomials of the form

6. A device for parameterizing an input signal, Y_t , as a sum of N unrelated sine waves of various amplitudes, A_m, frequencies, ω

_m, and phases, B_m where m=1·

·

·

N, said device comprising;

storage means for digitally sampling the input signal, Y_t, at successive times, t, with constant time intervals, h,

matrix inverter means coupled to the storage means for converting the digital samples of the sine wave sum signals to an N-order polynomial, and

calculator means coupled to the matrix inverter means for solving the roots of the N-order polynomial to enable the determination of the frequency, amplitude and phase of the N unrelated sine wave signals.