Abstract:
One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with num...Show MoreMetadata
Abstract:
One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-the-art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.
Published in: IEEE Transactions on Signal Processing ( Volume: 63, Issue: 20, October 2015)
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- IEEE Keywords
- Index Terms
- Complex Sinusoid ,
- White Noise ,
- Asymptotic Distribution ,
- Frequency Estimation ,
- Theoretical Derivation ,
- Weighted Least Squares ,
- Least-squares Optimization ,
- Accurate Estimation ,
- Least-squares ,
- Computational Complexity ,
- Theoretical Analysis ,
- Data Matrix ,
- Additive Noise ,
- Singular Value ,
- Singular Value Decomposition ,
- Linear Prediction ,
- Iterative Procedure ,
- Singular Vectors ,
- Cramer-Rao Lower Bound ,
- Mean Square Error Performance ,
- Unitary Transformation ,
- Prime Number ,
- Left Singular Vectors
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Complex Sinusoid ,
- White Noise ,
- Asymptotic Distribution ,
- Frequency Estimation ,
- Theoretical Derivation ,
- Weighted Least Squares ,
- Least-squares Optimization ,
- Accurate Estimation ,
- Least-squares ,
- Computational Complexity ,
- Theoretical Analysis ,
- Data Matrix ,
- Additive Noise ,
- Singular Value ,
- Singular Value Decomposition ,
- Linear Prediction ,
- Iterative Procedure ,
- Singular Vectors ,
- Cramer-Rao Lower Bound ,
- Mean Square Error Performance ,
- Unitary Transformation ,
- Prime Number ,
- Left Singular Vectors
- Author Keywords