Spektral çıkarma tabanlı kalman filtresi ile ses sinyallerinin iyileştirilmesi

Öz

Kalman filtresinin, özellikle GPS ve Navigasyon uygulamalarında sunduğu üstün tahmin yeteneği, son yıllarda ses sinyallerinin işlenmesinde de kullanılmaya çalışılmıştır. Kalman filtresi en etkili ses iyileştirme yöntemlerinden biridir ancak, Kalman filtresi ile ses sinyallerini iyileştirebilmek için bir takım parametrelerin bilinmesi gerekmektedir. Temiz sinyale ait AR (Autoregressive) katsayıları ve gürültüye ait kovaryans matrisi, Kalman filtresinin başarısını çok büyük ölçüde etkileyen ve bilinmesi gereken parametrelerdir. Pratikte mevcut olan sadece gürültülü sinyal olduğu için bu parametrelerin tahmin edilmesi oldukça zordur ve hala bu konu üzerinde çalışmalar devam etmektedir. Bu çalışmada, farklı tipteki gürültülerle bozulmuş sinyallere, Spektral çıkarma, Wiener filtresi ve Kalman filtresi ayrı ayrı uygulanmıştır.Kalman filtresi için gerekli olan katsayılar temiz sinyal kullanılarak hesaplanmıştır. Daha sonra Spektral çıkarma ile birleştirilmiş Kalman filtresi uygulanmıştır. Kalman filtresi için gerekli olan parametreler Spektral çıkarma yöntemi ile iyileştirilmiş sinyal kullanılarak belirlenmiştir. Uygulama sonuçları, objektif bir ölçüm olan SNR değerleri baz alınarak karşılaştırılmıştır. Elde edilen sonuçlar; birleştirilmiş Kalman filtresinin Wiener filtresine ve Spektral çıkarmaya oranla daha iyi bir SNR artışı sağladığını göstermiştir. Ayrıca birleştirilmiş Kalman filtresinin Spektral çıkarmadan kaynaklanan müzikal gürültüyü bastırdığı da gözlemlenmiştir.

Anahtar Kelimeler

• Ses iyileştirme, Kalman filtresi, Spektral çıkarma

Speech enhancement with spectral subtraction based kalman filter

Abstract

Speech enhancement techniques aim to improve the quality or intelligibility of speech signals contaminated with background noise and can be implemented both in time and frequency domains. Spectral subtraction, one of the most feasible methods in practice, is an effective technique to enhance the noisy speech signals. However, a residual noise called musical noise occurs with the estimated speech signal and this is the major inconvenience of Spectral subtraction. Wiener filter is an alternative approach for speech enhancement in the manner of Spectral subtraction filter. The drawback of the Wiener filter is the fixed frequency response at all frequencies and the requirement to estimate the power spectral density of the clean signal and the noise prior to filtering. Kalman filtering is also one of the most effective methods in speech enhancement. In recent years, due to its magnificent accurate estimation characteristics especially in the research field of navigation and GPS, researchers tried to manipulate its advantages for useful purposes in signal processing. However, to improve the speech signals with the Kalman filter, some parameters such as the autoregressive (AR) coefficients of the clean signal and the noise covariance matrix must be known. Determining the AR coefficients of clean speech signal plays a crucial role for the success of the Kalman filter while the only noisy observations are available. In such condition it is very difficult to estimate these parameters and today researches on this issue are ongoing. In this study, the parameters necessary to implement the Kalman filter is determined using Spectral subtraction. First of all, Spectral subtraction, Wiener filter and Kalman filter is analyzed respectively. Then all three methods mentioned above are carried out for speech signals corrupted with different types of noise. Finally, Kalman filter combined with Spectral Subtraction proposed in this study is applied to those signals and all results are compared based on output SNR values as an objective measurement for the enhancement performance. The results achieved in this study has shown that, if the AR cofficients of the original signal and noise variance is known Kalman filter is sufficient alone for the enhancement of noisy speech signals. In addition, musical noise which occurs with the methods based on the noise spectrum estimation, does not occur with the Kalman filtering. However, the assumption that these parameters are known is not workable in practice. Therefore, the AR coefficients are calculated by using the signal enhanced with Spectral subtraction and also noise variance is calculated by subtracting the enhanced signal from the noisy signal. In the last stage, Kalman filter was applied to the noisy signal using the parameters determined with Spectral subtraction. Considering the obtained results, combined Kalman filter provided a better SNR improvement compared to the Wiener filter and Spectral subtraction. Also combined Kalman filter suppressed the musical noise that occurred owing to Spectral subtraction. When the SNR values are taken into account, it is seen that the Kalman filter alone provided a better SNR improvement than combined Kalman filter.This is because of using the original signal while calculating the AR parameters for the Kalman filter alone.

Keywords

• Speech enhancement, Kalman fitler, Spectral subtraction