Bayesian methods are often applied for estimating the event rate from a series of event occurrences. However, the Bayesian posterior distribution requires the computation of the marginal likelihood which generally involves an analytically intractable integration. As an event rate is defined in a very high dimensional space, it is computationally demanding to obtain the Bayesian posterior distribution for the rate. We estimate the rate underlying a sequence of event counts by deriving an approximate Bayesian inference algorithm for the time-varying binomial process. This enables us to calculate the posterior distribution analytically. We also provide a method for estimating the prior hyperparameter, which determines the smoothness of the estimated event rate. Moreover, we provide an efficient method to compute the upper and lower bounds of the marginal likelihood, which evaluate the approximation accuracy. Numerical experiments demonstrate the effectiveness of the proposed method in terms of the estimation accuracy.
It is well known that an nth-order real polynomial D(z)=∑i=0ndizi is Schur stable if its coefficients satisfy the monotonic condition, i.e., dn>dn-1>…>d1>d0>0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for dk than an existing result.
This letter proposes a spread spectrum audio watermarking robust against playback speed modification (PSM) attack which introduces both time-scale modification and pitch shifting. Two important improvements are exploited to achieve this robustness. The first one is selecting an embedding region according to the stable characteristic of the audio energy. The second one is stretching the pseudo-random noise sequence to match the length of the embedding region before embedding and detection. Experimental results show that our method is highly robust to common audio signal processing attacks and synchronization attacks including PSM, cropping, trimming and jittering.
In this letter, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced by shifting particular error-subsequences. In this case, if the identical shifts occur in the corresponding subsequences of each code-path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.