This letter analyses the convergence behaviour of the transform domain least mean square (TDLMS) adaptive filtering algorithm which is based on a well known interpretation of the variable stepsize algorithm. With this interpretation, the analysis is considerably simplified. The time varying stepsize is implemented by the modified power estimator to redistribute the spread power after transformation. The main contribution of this letter is the statistical performance analysis in terms of mean and mean squared error of the weight error vector and the decorrelation property of the TDLMS is presented by the lower and upper bound of eigenvalue spread ratio. The theoretical analysis results are validated by Monte Carlo simulation.