Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
2001-06-12
2004-08-10
Hoff, Marc S (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C704S205000, C381S101000
Reexamination Certificate
active
06775629
ABSTRACT:
FIELD OF THE INVENTION
The invention relates generally to the field of signal analysis, and more particularly, to a system and method for detecting the frequency, amplitude and/or phase of one or more tones comprised within an input signal.
DESCRIPTION OF THE RELATED ART
In many applications, it is necessary or desirable to precisely locate one or more tones comprised in a signal. This need arises in many fields including telecommunications, radar, sonar, networking, measurement, and various other applications. Prior art techniques for detecting tones in a signal generally may not produce accurate results and/or may suffer from slow performance.
The discrete Fourier transform (DFT) is a popular tool for analyzing signals. However, before an input signal is transformed, it is quite often windowed with a windowing function. (It is noted that the action of capturing a finite-length sequence of samples of the input signal automatically implies a rectangular windowing.) The frequency transform F(n) of the windowed input signal will typically exhibit multiple scaled and shifted versions of transform function W, i.e., the transform of the window function. Each sinusoidal component of the input signal expresses itself as a pair of such shifted versions, one version shifted up to the frequency f
j
of the sinusoidal component, and the other shifted down to frequency −f
j
. The positive frequency version is referred to herein as a positive frequency image, and the negative frequency version is referred to herein as a negative frequency image. When a sinusoidal component frequency f
j
is small compared to the sample rate, the positive frequency image and the negative frequency image for the sinusoidal component may overlap in frequency space. Similarly, when a sinusoidal component frequency f
j
is close to one-half the sample rate, the positive frequency image and the negative frequency image for the sinusoidal component may overlap. Furthermore, when two sinusoidal components have frequencies that are close together, their positive images and negative images may overlap.
Prior art techniques for tone estimation quite often focus on identifying the peaks in the magnitude spectrum |F(n)|. The peaks roughly determine the frequency of the corresponding tones. However, because of the cross-interaction of the images from other tones, or the negative frequency image from the same tone, the peak of a positive frequency image may be perturbed away from a purely scaled and frequency-shifted version of the template function W. Thus, parameter estimation techniques which compute parameters for a given tone based only on transform array values (i.e. DFT values) in the vicinity of a corresponding image peak may not produce accurate results. Therefore, there exists a substantial need for a system and method which could estimate tone parameters from the transform array with increased accuracy.
SUMMARY OF THE INVENTION
The present invention comprises various embodiments of a system and a method for estimating signal parameters (e.g., one or more of frequency, amplitude and/or phase) of one or more tones present in an input signal. More particularly, one embodiment of the invention comprises a system and method for estimating parameters for a tone based on a frequency transform F(n) of the input signal. The input signal may be windowed with a window function w(n) and transformed into the frequency domain.
The tone in the input signal may express itself in the frequency domain as an additive combination of two spectra, one centered at the tone frequency and the other at the negative of the tone frequency. These two spectra are referred to herein as the positive frequency image and the negative frequency image respectively. A tone in the input signal may also be affected by spectra (e.g., positive or negative images) from other tones present in the signal.
The method may comprise first receiving samples of the input signal, wherein the input signal includes the tone. A frequency transform of the samples may then be generated, e.g., a Fourier transform of the samples. The method may then identify a frequency location proximate to an amplitude peak in the frequency transform, wherein the amplitude peak corresponds to the tone. Two or more frequency bins may then be selected proximate to the identified frequency location in the frequency transform. The method preferably selects one or more frequency bins located on either side of the frequency location of the amplitude peak. In other words, the method may select one or more bins located on one side of the amplitude peak and one or more bins located on the other side of the amplitude peak.
The method may then determine a tone frequency value that minimizes a difference between two or more expressions, e.g., at least a first expression and a second expression. Stated another way, the method may select a tone frequency value that makes a plurality of expressions most nearly equal.
Each of the plurality of expressions may comprise a sum of one or more numerator terms divided by a sum of one or more denominator terms, wherein:
1) each of the plurality of expressions includes a tone frequency variable;
2) each numerator term and each denominator term corresponds to one of the frequency bins; and
3) a ratio of each numerator term and its corresponding denominator term represent a complex amplitude of the tone at a respective bin.
Thus, for example, the plurality of expressions may comprise a first expression and a second expression having the above characteristics.
In each expression, the tone frequency variable may represent a correct tone frequency value of the tone. The first expression may be approximately equivalent to the second expression when the correct tone frequency value is used for the tone frequency variable in the first and second complex expressions.
The step of determining a tone frequency value may comprise computing a plurality of differences between the first expression and the second expression for different respective tone frequency values of the tone frequency variable, and then selecting the tone frequency value that produces a smallest difference. The method may compute the plurality of differences by performing a Newton-Rhapson root finding method.
The expressions may be real expressions or complex expressions. Where the expressions are complex expressions, the method may involve minimizing a difference between an amplitude of the first complex expression and an amplitude of the second complex expression.
In the preferred embodiment, the first expression and the second expression have the form:
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F(n) is the nth value of the single sided scaled FFT spectrum; and
W represents a window function, wherein the window function is shifted by a value of the tone frequency variable f
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When the frequency transform of the samples comprises generating a power spectrum of the samples, the first expression and the second expression have the form:
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Cerna Michael
Rao Yong
Baran Mary Catherine
Hoff Marc S
Hood Jeffrey C.
Meyertons Hood Kivlin Kowert & Goetzel P.C.
National Instruments Corporation
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