Performance Analysis for Subband Identification

The so-called subband identification method has been introduced recently as an alternative method for identification of finite-impulse response systems with large tap sizes. It is known that this method can be more numerically efficient than the classical system identification method. However, no results are available to quantify its advantages. This paper offers a rigorous study of the performance of the subband method. More precisely, we aim to compare the performance of the subband identification method with the classical (fullband) identification method. The comparison is done in terms of the asymptotic residual error, asymptotic convergence rate, and computational cost when the identification is carried out using the prediction error method, and the optimization is done using the least-squares method. It is shown that by properly choosing the filterbanks, the number of parameters in each subband, the number of subbands, and the downsampling factor, the two identification methods can have compatible asymptotic residual errors and convergence rate. However, for applications where a high order model is required, the subband method is more numerically efficient.We study two types of subband identification schemes: one using critical sampling and another one using oversampling. The former is simpler to use and easier to understand, whereas the latter involves more design problems but offers further computational savings.