Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this letter,  propose an algorithm of the sparse decomposition based on the signal periodic model (SDSPM) to decompose a signal into a series of periodic components and residual or noise. Instead of directly using the complex dictionary, the SDSPM is alternatively performed over two real-valued dictionaries with ighted    $\ell _1$   regularization to yield a complex sparse representation of a signal. The sparse representation is the complex projection coefficient vector of a signal into the complex conjugate subspaces and reveals the periodic structure of the signal. Being different from previous methods with the assumption that the signals are noise free, the proposed method can also perform the decomposition of the noisy signals. Moreover, the block version of the SDSPM is also used to decompose a signal with local or time-varying periodicities. In addition, several examples are presented to illustrate the effectiveness of the proposed method.
['Shiwen Deng', 'Jiqing Han']
I am writing a research paper on a idea Sparse Decomposition for Signal Periodic Model Over Complex Exponential Dictionary
[{"from": "human", "value": "I am writing a research paper on a idea Sparse Decomposition for Signal Periodic Model Over Complex Exponential Dictionary"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this letter,  propose an algorithm of the sparse decomposition based on the signal periodic model (SDSPM) to decompose a signal into a series of periodic components and residual or noise. Instead of directly using the complex dictionary, the SDSPM is alternatively performed over two real-valued dictionaries with ighted    $\\ell _1$   regularization to yield a complex sparse representation of a signal. The sparse representation is the complex projection coefficient vector of a signal into the complex conjugate subspaces and reveals the periodic structure of the signal. Being different from previous methods with the assumption that the signals are noise free, the proposed method can also perform the decomposition of the noisy signals. Moreover, the block version of the SDSPM is also used to decompose a signal with local or time-varying periodicities. In addition, several examples are presented to illustrate the effectiveness of the proposed method."}]