The reduced speech intelligibility caused by feed feedback oscillation is a major problem for hearing aid users. The demand for improved signal quality has led researchers to look for feedback reduction techniques. In this Thesis, we studied several feedback reduction schemes with emphasis in adaptive feedback cancellation algorithms. The main goal was to develop a system for feedback cancellation that is able to adapt to non-stationary environments while having reasonable computational complexity. This requirement is imposed by the need to implement the feedback cancellation scheme in low power DSP systems. In Chapter 1, we briefly introduced hearing aid systems. We examined the parts that are made of and the types of hearing aids that are available in the market. Then, we described the mechanism that causes feedback oscillation in hearing aids and the adverse effects it has on signal quality. Chapter 2 contains some theoretical results on the field of adaptive linear system identification algorithms and simulation results that support this theory. The chapter begins by giving a derivation of the popular LMS algorithm. A theoretical analysis of LMS using the independence assumption is also provided. Then we are concerned with the least squares filter. We described the RLS algorithm and a linear complexity version of it, the FAEST algorithm. Subsequently, we discussed the FNTF algorithm that trades computational complexity for performance in solving the system identification problem. Next, we developed a new algorithm, the FLMS, by making simplifications to FNTF. We also proved that the proposed algorithm outperforms LMS at least when the input signal is an AR process. Finally, we provided simulation results which prove the superiority of FLMS over LMS. Chapter 3 is devoted in using some algorithms described in Chapter 2 for feedback cancellation in hearing aids. The chapter begins with a hearing aid model that includes an acoustic feedback mechanism. On this system, a linear filter is added that estimates the acoustic feedback so that it can be removed from he signal captured by the microphone. The feedback estimation is performed with LMS and FLMS. Using simulation results, we saw that FLMS can be successfully used in feedback systems and continues to outperform LMS. We also saw that, contrary to the open loop case, when feedback is present, the stochastic approximation theory does not satisfactorily predict the mean learning curves of LMS. / Ένα από τα σημαντικότερα προβλήματα που πρέπει να αντιμετωπιστούν κατά το σχεδιασμό ενός ακουστικού βαρηκοΐας είναι αυτό της ακουστικής ανάδρασης. Με τον όρο ακουστική ανάδραση αναφερόμαστε στο φαινόμενο κατά το οποίο ένα μέρος της εξόδου του ακουστικού επιστρέφει στην είσοδο και ενισχύεται εκ νέου. Γνωστό και ως μικροφωνισμός, το φαινόμενο αυτό γίνεται αντιληπτό από τους ασθενείς ως ένα συνεχές σφύριγμα και είναι ιδιαίτερα ενοχλητικό. Για την αντιμετώπιση του φαινομένου έχουν προταθεί διάφορες τεχνικές. Για παράδειγμα, ο περιορισμός του κέρδους ενίσχυσης στις συχνότητες όπου εμφανίζεται ο μικροφωνισμός είναι μια λύση που συναντάται συχνά σε αναλογικά ακουστικά βαρηκοΐας. Η μέθοδος αυτή, όμως, απαιτεί τον προσδιορισμό των επικίνδυνων συχνοτήτων κατά τη διαδικασία προσαρμογής του ακουστικού στον εκάστοτε ασθενή. Ακόμα και αν ο προσδιορισμός γίνει με μεγάλη ακρίβεια, οι συχνότητες στις οποίες εμφανίζεται ο μικροφωνισμός αλλάζουν κατά τη διάρκεια χρήσης του ακουστικού, περιορίζοντας έτσι την αποτελεσματικότητα της μεθόδου. Με την καθιέρωση της ψηφιακής τεχνολογίας στα ακουστικά βαρηκοΐας, εμφανίζονται νέες δυνατότητες για την αντιμετώπιση του μικροφωνισμού. Είμαστε σε θέση, πλέον, να μοντελοποιήσουμε το σύστημα της ακουστικής ανάδρασης και να χρησιμοποιήσουμε το μοντέλο αυτό για εξαλείψουμε το μικροφωνισμό. Για την μοντελοποίηση αυτή χρησιμοποιείται κατά κόρον ο αλγόριθμος LMS. Η χαμηλή υπολογιστική πολυπλοκότητα που τον χαρακτηρίζει τον κάνει ιδανικό για ακουστικά βαρηκοΐας. Στην εργασία αυτή παρουσιάζουμε έναν νέο αλγόριθμο, επίσης χαμηλής πολυπλοκότητας, για το πρόβλημα της αναγνώρισης γραμμικών συστημάτων. Αποδεικνύουμε με μαθηματικό τρόπο ότι είναι πιο αποτελεσματικός από τον LMS για συγκεκριμένα μοντέλα σημάτων εισόδου, ενώ με εξομοιώσεις ότι υπερτερεί του LMS και για πολύ πιο γενικές εισόδους. Επιπρόσθετα, δείχνουμε ότι ο νέος αλγόριθμος μπορεί να χρησιμοποιηθεί για την ακύρωση της ανάδρασης σε ακουστικά βαρηκοΐας, όπου παραμένει πιο αποτελεσματικός από τον LMS.

<p>A common problem of hearing aids is whistling caused by feedback from the loudspeaker back to the microphone. A method of reducing the negative effects, caused by the feedback, is called feedback cancellation. A variant of feedback cancellation uses a probe signal, which is applied to the speaker of the hearing aid and is used to continuously estimate the feedback. Oticon A/S has suggested a master's thesis with the purpose of designing and evaluating an algorithm generating a probe signal for feedback cancellation systems. The challenge was to find an inaudible probe signal with as much energy as possible. </p><p>Two approaches have been investigated for generating a probe signal. In the first approach the psychoacoustic principle of masking was used to estimate how much noise that could be added to a signal without being heard. Psychoacoustic models, including masking, are used in MPEG (Moving Pictures Expert Group) audio coding and one of these models has been examined in the thesis. In the second approach a standard LPC (Linear Prediction Coding) algorithm was used. In both the MPEG and the LPC approach, warped signal processing has been utilized improving the methods. </p><p>A listening test was performed, evaluating the methods generating the probe signal. The purpose of the test was to determine whether the noise, generated using the MPEG and LPC approach, was inaudible. A hearing aid system with feedback cancellation, using the probe signal, was also simulated. The listening test showed that the noise (probe signal) had to be lowered, much more than expected, to be inaudible. As a consequence, shown in the simulations, the feedback cancellation system, using the probe signal, had trouble identifying the feedback of the hearing aid.</p>

A common problem of hearing aids is whistling caused by feedback from the loudspeaker back to the microphone. A method of reducing the negative effects, caused by the feedback, is called feedback cancellation. A variant of feedback cancellation uses a probe signal, which is applied to the speaker of the hearing aid and is used to continuously estimate the feedback. Oticon A/S has suggested a master's thesis with the purpose of designing and evaluating an algorithm generating a probe signal for feedback cancellation systems. The challenge was to find an inaudible probe signal with as much energy as possible. Two approaches have been investigated for generating a probe signal. In the first approach the psychoacoustic principle of masking was used to estimate how much noise that could be added to a signal without being heard. Psychoacoustic models, including masking, are used in MPEG (Moving Pictures Expert Group) audio coding and one of these models has been examined in the thesis. In the second approach a standard LPC (Linear Prediction Coding) algorithm was used. In both the MPEG and the LPC approach, warped signal processing has been utilized improving the methods. A listening test was performed, evaluating the methods generating the probe signal. The purpose of the test was to determine whether the noise, generated using the MPEG and LPC approach, was inaudible. A hearing aid system with feedback cancellation, using the probe signal, was also simulated. The listening test showed that the noise (probe signal) had to be lowered, much more than expected, to be inaudible. As a consequence, shown in the simulations, the feedback cancellation system, using the probe signal, had trouble identifying the feedback of the hearing aid.