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In the previous chapter, we showed how the eigenvalue decomposition of the speech correlation matrix can be exploited in the derivation of different types of optimal filtering matrices for the general problem of speech enhancement. This chapter attempts to show the same results but with the joint diagonalization of the speech and noise correlation matrices. We will see that there are some subtle differences between these two approaches with many more possibilities with joint diagonalization, suggesting that this tool is very natural to use in this problem.

In this chapter, we study the multichannel speech enhancement problem in the frequency domain. By exploiting the structure of the speech subspace, we can easily estimate all convolved speech signals at the microphones with a simple complex filter. As a result, binaural noise reduction with this approach is straightforward since we can choose any two signals from the estimated convolved speech signals, which contain all the necessary spatial information for the localization of the desired source signal.

So far, all the chapters have been dealing with the derivation of optimal filters for speech enhancement from a subspace perspective. In this chapter, we present evaluations of the time-domain versions of these filters for both single-channel as well as multichannel scenarios. First, we evaluate the single-channel scenario, where we consider both the case where the rank of the correlation matrix of the desired signal is less than the filter length and the case where it is full rank. Then, we proceed to evaluate the time-domain multichannel filters.

In all previous chapters, we showed the importance of the speech subspace; so it is extremely important in practice to find good ways to estimate it. One very promising possibility is the Bayesian approach based on the Stiefel manifold and the Bingham distribution. This chapter explores this avenue. We would like to point out that all the ideas presented in the following are borrowed from [1] but adapted to our specific problem of speech enhancement.

In this chapter, we study the general speech enhancement problem by considering the diagonalization of the speech correlation matrix in the context of the classical linear filtering technique. The entire problem is formulated as a function of the speech subspace. We define the most fundamental performance measures in this scenario. We then derive the well-known conventional filtering matrices for noise reduction and show how the nullspace of the speech correlation matrix is exploited in some of these approaches such as the MVDR and LCMV filtering.

Recently, two optimal filter designs for fundamental frequency estimation have been proposed with the first being based on a filterbank and the second on a single filter. The two designs are related in a simple manner and are shown to result in the same residual when used for cancelling out the harmonics of periodic signals. We propose to use this residual for estimating the number of harmonics by combining a noise variance estimate with an order dependent penalty term. This leads to a joint estimator of the fundamental frequency and the order based on the same criterion. Via Monte Carlo simulations, the estimator is demonstrated to have good performance in terms of the percentage of correctly estimated orders.

For music information retrieval tasks, a nearest neighbor classifier using the Kullback-Leibler divergence between Gaussian mixture models of songs' melfrequency cepstral coefficients is commonly used to match songs by timbre. In this paper, we analyze this distance measure analytically and experimentally by the use of synthesized MIDI files, and we find that it is highly sensitive to different instrument realizations. Despite the lack of theoretical foundation, it handles the multipitch case quite well when all pitches originate from the same instrument, but it has some weaknesses when different instruments play simultaneously. As a proof of concept, we demonstrate that a source separation frontend can improve performance. Furthermore, we have evaluated the robustness to changes in key, sample rate, and bitrate.

Recently, we proposed using Capon's minimum variance principle to find the fundamental frequency of a periodic waveform. The resulting estimator is formed such that it maximizes the output power of a bank of filters. We present an alternative optimal single filter design and then proceed to quantify the similarities and differences between the estimators using asymptotic analysis and Monte Carlo simulations. Our analysis shows that the single filter can be expressed in terms of the optimal filterbank and that the methods are asymptotically equivalent but generally different for finite length signals.

We present a distance measure between audio files designed to identify cover songs, which are new renditions of previously recorded songs. For each song we compute the chromagram, remove phase information and apply exponentially distributed bands in order to obtain a feature matrix that compactly describes a song and is insensitive to changes in instrumentation, tempo and time shifts. As distance between two songs, we use the Frobenius norm of the difference between their feature matrices normalized to unit norm. When computing the distance, we take possible transpositions into account. In a test collection of 80 songs with two versions of each, 38% of the covers were identified. The system was also evaluated on an independent, international evaluation where it despite having much lower complexity performed on par with the winner of last year.