Estimating a plurality of tones in an input signal

Details Estimating a plurality of tones in an input signal Estimating a plurality of tones in an input signal

2002-01-03

2004-04-13

Hoff, Marc S. (Department: 2857)

Data processing: measuring, calibrating, or testing

Measurement system in a specific environment

Electrical signal parameter measurement system

C073S182000

Reexamination Certificate

active

06721673

ABSTRACT:

FIELD OF THE INVENTION
The invention relates generally to the field of signal analysis, and more particularly, to detecting the frequency, amplitude and/or phase of a plurality of tones comprised within an input signal.
DESCRIPTION OF THE RELATED ART
In many applications, it is necessary or desirable to precisely locate multiple 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 can estimate tone parameters from the transform array for a plurality of tones 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 a plurality of tones present in an input signal. More particularly, a system and method are described for estimating parameters for each of a plurality of tones based on a frequency transform F(n) of the input signal, where the input signal may be windowed with a window function w(n) and transformed into the frequency domain.
In one embodiment, the method may include first receiving the input signal. For example, samples of the input signal may be received, where the samples include the plurality of tones.
One or more signal parameter estimates characterizing each of the plurality of tones may be determined based on the received samples. In one embodiment, the one or more signal parameter estimates characterizing each of the plurality of tones may comprise a knowledge base of the signal parameter estimates, and the method may further include storing a copy of the knowledge base, as a prior knowledge base.
Then, the method may generate a refined estimate of the one or more signal parameters of each respective tone of the plurality of tones, updating the one or more signal parameter estimates accordingly, where the refined estimates are generated in an iterative fashion. In other words, refined estimates of the parameters for each tone may be generated in an iterative fashion, where each successive iteration produces a more refined estimate of parameters for each tone. Updating the one or more signal parameter estimates with the refined estimate of the one or more signal parameters of the respective tone may include updating the knowledge base with the refined estimate of the one or more signal parameters of the tone, where, after updating the estimates for each tone, the knowledge base is comprised of the refined estimates for each tone.
In one embodiment, iteratively generating the refined estimate of the signal parameters of each of the respective tones may include: for each respective tone of the plurality of tones, generating a refined estimate of the one or more signal parameters of the respective tone, and updating the one or more signal parameter estimates (e.g., the knowledge base) with the refined estimate. The generating and updating for each respective tone may be performed one or more times to produce final one or more signal parameter estimates for each of the plurality of tones. In one embodiment, performing the generating and updating one or more times may include performing the generating and updating for each respective tone in an iterative manner until one or more of 1) the number of iterations exceeds a threshold number of iterations, and 2) the difference between values of the one or more signal parameters of the knowledge base and values of the one or more signal parameters of the prior knowledge base is less than a threshold value.
In one embodiment, generating a refined estimate of the one or more signal parameters of each respective tone may include: for each respective tone of the plurality of tones, iteratively applying a single tone estimation method to the respective tone, thereby generating a refined estimate of the one or more signal parameters of the respective tone, and updating said one or more signal parameter estimates with the refined estimate of the one or more signal parameters of the respective tone.
Finally, the method may include storing and/or outputting the final one or more signal parameter estimates for each of the plurality of tones in response to iteratively generating the refined estimates.
In one embodiment of the invention the method may estimate parameters for the plurality of tones based on a frequency transform F(n), e.g., a Fourier transform of the samples of the input signal. The input signal may be windowed with a window function w(n) and transformed into the frequency domain. In a preferred embodiment, the window function is a cosine-based window function. Each tone in the input signal may express itself in the frequency domain as an additive combination of two or more spectra, e.g., 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.
Thus, in one embodiment, the method may include generating a frequency transform of the samples, where the frequency transform includes frequency response data for the plurality of tones. In this embodiment, generating a refined estimate of the one or more signal parameters of each respective tone may include: for each respective tone of the plurality of tones, generating modified frequency response data for the respective tone which operates to remove effects of other tones of the plurality of tones from the frequency response data of the respective tone, using the one or more signal parameter estimates of each of the other tone

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