In this paper, we introduce a new local frequency-based detector for improved resolvability of closely-spaced exponential signals. The frequency resolution problem is defined as a hypothesis-testing problem in the frequency domain, and a corresponding detector, based on the generalized likelihood ratio test is constructed. We derive a theoretical resolution limit in terms of the signal-to-noise ratio, the observable-data length, and the probabilities of detection and false-alarm. Experimental results validate the theoretical results and demonstrate the effectiveness of the proposed detector over a time-based detector.

In this paper, we extend the cross-multiplicative transfer function (CMTF) approach for improved system identification in the short- time Fourier transform (STFT) domain. The proposed algorithm adaptively controls the number of cross-terms in the CMTF approximation to achieve the minimum mean-square error (mmse) at each iteration. A small number of cross-terms is initially used to achieve fast convergence, and as the adaptation process proceeds, the algorithm gradually increases this number to enhance the steady-state performance. When compared to the conventional multiplicative transfer function (MTF) approach, the resulting algorithm achieves a substantial improvement in steady-state performance, without compromising for slower convergence. Experimental results validate the theoretical derivations and demonstrate the advantage of the proposed approach to acoustic echo cancellation.

In this paper, we introduce cross-multiplicative transfer function (CMTF) approximation for modeling linear systems in the short-time Fourier transform (STFT) domain. We assume that the transfer function can be represented by cross-multiplicative terms between distinct subbands. We investigate the influence of cross-terms on a system identifier implemented in the STFT domain and derive analytical relations between the noise level, data length, and number of cross-multiplicative terms, which are useful for system identification. As more data becomes available or as the noise level decreases, additional cross-terms should be considered and estimated to attain the minimal mean-square error (mse). A substantial improvement in performance is then achieved over the conventional multiplicative transfer function (MTF) approximation. Furthermore, we derive explicit expressions for the transient and steady-state mse performances obtained by adaptively estimating the cross-terms. As more cross-terms are estimated, a lower steady-state mse is achieved, but the algorithm then suffers from slower convergence. Experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach as applied to acoustic echo cancellation.

The multiplicative transfer function (MTF) approximation is widely used for modeling a linear time invariant system in the short-time Fourier transform (STFT) domain. It relies on the assumption of a long analysis window compared with the length of the system impulse response. In this paper, we investigate the influence of the analysis window length on the performance of a system identifier that utilizes the MTF approximation. We derive analytic expressions for the minimum mean-square error (MMSE) in the STFT domain and show that the system identification performance does not necessarily improve by increasing the length of the analysis window. The optimal window length, that achieves the MMSE, depends on the signal-to-noise ratio and the length of the input signal. The theoretical analysis is supported by simulation results

In this paper, we investigate the influence of crossband filters on a system identifier implemented in the short-time Fourier transform (STFT) domain. We derive analytical relations between the number of crossband filters, which are useful for system identification in the STFT domain, and the power and length of the input signal. We show that increasing the number of crossband filters not necessarily implies a lower steady-state mean-square error (mse) in subbands. The number of useful crossband filters depends on the power ratio between the input signal and the additive noise signal. Furthermore, it depends on the effective length of input signal employed for system identification, which is restricted to enable tracking capability of the algorithm during time variations in the system. As the power of input signal increases or as the time variations in the system become slower, a larger number of crossband filters may be utilized. The proposed subband approach is compared to the conventional fullband approach and to the commonly used subband approach that relies on multiplicative transfer function (MTF) approximation. The comparison is carried out in terms of mse performance and computational complexity. Experimental results verify the theoretical derivations and demonstrate the relations between the number of useful crossband filters and the power and length of the input signal