Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An exact analysis is presented for the LMS algorithm with tonal reference signals in the presence of frequency mismatch. First, the time-varying linear system describing the LMS algorithm is converted into a time-invariant linear system. Then, a necessary and sufficient condition about the step sizes for convergence of the algorithm is derived using the Lyapunov function method and a transient behavior is analyzed. Finally, the effects of observation noise and frequency mismatch are examined without any approximations. The validity of the obtained results is shown by simulations.
['Hideaki Sakai', 'Yoichi Hinamoto']
I am writing a research paper on a idea An exact analysis of the LMS algorithm with tonal reference signals in the presence of frequency mismatch
[{"from": "human", "value": "I am writing a research paper on a idea An exact analysis of the LMS algorithm with tonal reference signals in the presence of frequency mismatch"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An exact analysis is presented for the LMS algorithm with tonal reference signals in the presence of frequency mismatch. First, the time-varying linear system describing the LMS algorithm is converted into a time-invariant linear system. Then, a necessary and sufficient condition about the step sizes for convergence of the algorithm is derived using the Lyapunov function method and a transient behavior is analyzed. Finally, the effects of observation noise and frequency mismatch are examined without any approximations. The validity of the obtained results is shown by simulations."}]