Frequency-warped autoregressive modeling and filtering

This thesis consists of an introduction and nine articles. The articles are related to the application of frequency-warping techniques to audio signal processing, and in particular, predictive coding of wideband audio signals. The introduction reviews the literature and summarizes the results of the articles. Frequency-warping, or simply warping techniques are based on a modification of a conventional signal processing system so that the inherent frequency representation in the system is changed. It is demonstrated that this may be done for basically all traditional signal processing algorithms. In audio applications it is beneficial to modify the system so that the new frequency representation is close to that of human hearing. One of the articles is a tutorial paper on the use of warping techniques in audio applications. Majority of the articles studies warped linear prediction, WLP, and its use in wideband audio coding. It is proposed that warped linear prediction would be particularly attractive method for low-delay wideband audio coding. Warping techniques are also applied to various modifications of classical linear predictive coding techniques. This was made possible partly by the introduction of a class of new implementation techniques for recursive filters in one of the articles. The proposed implementation algorithm for recursive filters having delay-free loops is a generic technique. This inspired to write an article which introduces a generalized warped linear predictive coding scheme. One example of the generalized approach is a linear predictive algorithm using almost logarithmic frequency representation.reviewe

Digital audio filter design using frequency transformations

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 80-81).by Chalee Asavathiratham.M.Eng

Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network

Because of their effectiveness in broad practical applications, LSTM networks have received a wealth of coverage in scientific journals, technical blogs, and implementation guides. However, in most articles, the inference formulas for the LSTM network and its parent, RNN, are stated axiomatically, while the training formulas are omitted altogether. In addition, the technique of "unrolling" an RNN is routinely presented without justification throughout the literature. The goal of this paper is to explain the essential RNN and LSTM fundamentals in a single document. Drawing from concepts in signal processing, we formally derive the canonical RNN formulation from differential equations. We then propose and prove a precise statement, which yields the RNN unrolling technique. We also review the difficulties with training the standard RNN and address them by transforming the RNN into the "Vanilla LSTM" network through a series of logical arguments. We provide all equations pertaining to the LSTM system together with detailed descriptions of its constituent entities. Albeit unconventional, our choice of notation and the method for presenting the LSTM system emphasizes ease of understanding. As part of the analysis, we identify new opportunities to enrich the LSTM system and incorporate these extensions into the Vanilla LSTM network, producing the most general LSTM variant to date. The target reader has already been exposed to RNNs and LSTM networks through numerous available resources and is open to an alternative pedagogical approach. A Machine Learning practitioner seeking guidance for implementing our new augmented LSTM model in software for experimentation and research will find the insights and derivations in this tutorial valuable as well.Comment: 43 pages, 10 figures, 78 reference

Graafinen ekvalisointi taajuusvarpattujen digitaalisten suotimien avulla

The aim of this thesis is to design a graphic equalizer with frequency warped digital filters. The proposed design consists of a warped FIR filter for the low frequency bands and a standard FIR filter for the high frequency bands. This de- sign is used to implement both an octave and a one-third octave equalizer in Matlab. Low frequency equalization with FIR filters requires high filter orders. The frequency resolution of the lowest band of the graphic equalizer requires filter orders that are impractical for real life applications. With frequency warping filter orders can be lowered, so that a practical graphic equalizer can be designed. With this design common gain build-up problems, which are present in most of the IIR designs, can be avoided. The proposed equalizer design is found to be accurate and comparable to the previous equalizer designs. Filter orders required are small enough to this design to be used in real life applications. The gain build-up problem is avoided in this design, as several equalizer bands are filtered with a single filter. The computational costs of the design are higher than the costs of the other compared designs. However, the difference can be smaller if the accuracy restrictions are lowered.Tämän työn tavoitteena on suunnitella graafinen ekvalisaattori taajuusvarpattujen digitaalisten suotimien avulla. Ehdotettu ekvalisaattorimalli koostuu taajuusvarpatusta ja tavallisesta FIR suotimesta. Varpattua suodinta käytetään alimpien taajuuskaistojen suodattamiseen ja tavallista FIR suodinta ylimpien kaistojen suodattamiseen. Tätä mallia käytetään sekä oktaavi- että terssikaista-ekvalisaattorien totetutamiseen Matlabilla. Matalien taajuuksien ekvalisointi edellyttää korkeaa astelukua FIR suotimilta. Alimpien taajuuskaistojen taajuusresoluutio edellyttää astelukuja, jotka ovat epäkäytännöllisiä tosielämän sovelluksissa. Taajuusvarppauksella suotimien astelukuja voidaan pienentää, jolloin graafinen ekvalisaattori voidaan toteuttaa käytännössä. Tällä mallilla voidaan välttää IIR ekvalisaattorien yleinen ongelma, jossa ekvalisaattorien kaistojen vahvistus vaikuttaa viereisiin kaistoihin. Ehdotettu ekvalisaattorimalli todetaan olevan tarkka ja vertailukelpoinen aikaisempien toteutuksien kanssa. Suotimien asteluvut ovat tarpeeksi pieniä, jotta tätä mallia voidaan käyttää tosielämän toteutuksissa. Kaistojen välinen vaikutus vältetään tällä mallilla, sillä useampi kaista suodatetaan yhdellä suotimella. Laskennallinen kuorma on tällä toteutuksella suurempi kuin muilla vertailluilla toteutuksilla. Eroa voidaan pienentää, jos ekvalisaattorin tarkkuusvaatimuksia lasketaan

An Introduction to Digital Signal Processing

An Introduction to Digital Signal Processing aims at undergraduate students who have basic knowledge in C programming, Circuit Theory, Systems and Simulations, and Spectral Analysis. The book is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware in which the candidate is introduced to the basic concepts first before embarking to the practical part which comes in the later chapters. Initially Digital Signal Processing evolved as a postgraduate course which slowly filtered into the undergraduate curriculum as a simplified version of the latter. The goal was to study DSP concepts and to provide a foundation for further research where new and more efficient concepts and algorithms can be developed. Though this was very useful it did not arm the student with all the necessary tools that many industries using DSP technology would require to develop applications. This book is an attempt to bridge the gap. It is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware. The objective is to win the student to use a variety of development tools to develop applications. Contents• Introduction to Digital Signal processing.• The transform domain analysis: the Discrete-Time Fourier Transform• The transform domain analysis: the Discrete Fourier Transform• The transform domain analysis: the z-transform• Review of Analogue Filter• Digital filter design.• Digital Signal Processing Implementation Issues• Digital Signal Processing Hardware and Software• Examples of DSK Filter Implementatio

Model-based analysis of noisy musical recordings with application to audio restoration

This thesis proposes digital signal processing algorithms for noise reduction and enhancement of audio signals. Approximately half of the work concerns signal modeling techniques for suppression of localized disturbances in audio signals, such as impulsive noise and low-frequency pulses. In this regard, novel algorithms and modifications to previous propositions are introduced with the aim of achieving a better balance between computational complexity and qualitative performance, in comparison with other schemes presented in the literature. The main contributions related to this set of articles are: an efficient algorithm for suppression of low-frequency pulses in audio signals; a scheme for impulsive noise detection that uses frequency-warped linear prediction; and two methods for reconstruction of audio signals within long gaps of missing samples. The remaining part of the work discusses applications of sound source modeling (SSM) techniques to audio restoration. It comprises application examples, such as a method for bandwidth extension of guitar tones, and discusses the challenge of model calibration based on noisy recorded sources. Regarding this matter, a frequency-selective spectral analysis technique called frequency-zooming ARMA (FZ-ARMA) modeling is proposed as an effective way to estimate the frequency and decay time of resonance modes associated with the partials of a given tone, despite the presence of corrupting noise in the observable signal.reviewe

An Introduction to Digital Signal Processing

An Introduction to Digital Signal Processing aims at undergraduate students who have basic knowledge in C programming, Circuit Theory, Systems and Simulations, and Spectral Analysis. The book is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware in which the candidate is introduced to the basic concepts first before embarking to the practical part which comes in the later chapters. Initially Digital Signal Processing evolved as a postgraduate course which slowly filtered into the undergraduate curriculum as a simplified version of the latter. The goal was to study DSP concepts and to provide a foundation for further research where new and more efficient concepts and algorithms can be developed. Though this was very useful it did not arm the student with all the necessary tools that many industries using DSP technology would require to develop applications. This book is an attempt to bridge the gap. It is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware. The objective is to win the student to use a variety of development tools to develop applications. Contents• Introduction to Digital Signal processing.• The transform domain analysis: the Discrete-Time Fourier Transform• The transform domain analysis: the Discrete Fourier Transform• The transform domain analysis: the z-transform• Review of Analogue Filter• Digital filter design.• Digital Signal Processing Implementation Issues• Digital Signal Processing Hardware and Software• Examples of DSK Filter Implementatio

Physically-based auralization : design, implementation, and evaluation

The aim of this research is to implement an auralization system that renders audible a 3D model of an acoustic environment. The design of such a system is an iterative process where successive evaluation of auralization quality is utilized to further refine the model and develop the rendering methods. The work can be divided into two parts corresponding to design and implementation of an auralization system and evaluation of the system employing objective and subjective criteria. The presented auralization method enables both static and dynamic rendering. In dynamic rendering positions and orientations of sound sources, surfaces, or a listener can change. These changes are allowed by modeling the direct sound and early reflections with the image-source method. In addition, the late reverberation is modeled with a time-invariant recursive digital filter structure. The core of the thesis deals with the processing of image sources for auralization. The sound signal emitted by each image source is processed with digital filters modeling such acoustic phenomena as sound source directivity, distance delay and attenuation, air and material absorption, and the characteristics of spatial hearing. The digital filter design and implementation of these filters are presented in detail. The traditional image-source method has also been extended to handle diffraction in addition to specular reflections. The evaluation of quality of the implemented auralization system was performed by comparing recorded and auralized soundtracks subjectively. The compared soundtracks were prepared by recording sound signals in a real room and by auralizing these signals with a 3D model of the room. The auralization quality was assessed with objective and subjective methods. The objective analysis was based on both traditional room acoustic criteria and on a simplified auditory model developed for this purpose. This new analysis method mimics the behavior of human cochlea. Therefore, with the developed method, impulse responses and sound signals can be visualized with similar time and frequency resolution as human hearing applies. The evaluation was completed subjectively by conducting listening tests. The utilized listening test methodology is explained and the final results are presented. The results show that the implemented auralization system provides plausible and natural sounding auralizations in rooms similar to the lecture room employed for evaluation.reviewe

Perkeptuaalinen spektrisovitus glottisherätevokoodatussa tilastollisessa parametrisessa puhesynteesissä käyttäen mel-suodinpankkia

This thesis presents a novel perceptual spectral matching technique for parametric statistical speech synthesis with glottal vocoding. The proposed method utilizes a perceptual matching criterion based on mel-scale filterbanks. The background section discusses the physiology and modelling of human speech production and perception, necessary for speech synthesis and perceptual spectral matching. Additionally, the working principles of statistical parametric speech synthesis and the baseline glottal source excited vocoder are described. The proposed method is evaluated by comparing it to the baseline method first by an objective measure based on the mel-cepstral distance, and second by a subjective listening test. The novel method was found to give comparable performance to the baseline spectral matching method of the glottal vocoder.Tämä työ esittää uuden perkeptuaalisen spektrisovitustekniikan glottisvokoodattua tilastollista parametristä puhesynteesiä varten. Ehdotettu menetelmä käyttää mel-suodinpankkeihin perustuvaa perkeptuaalista sovituskriteeriä. Työn taustaosuus käsittelee ihmisen puheentuoton ja havaitsemisen fysiologiaa ja mallintamista tilastollisen parametrisen puhesynteesin ja perkeptuaalisen spektrisovituksen näkökulmasta. Lisäksi kuvataan tilastollisen parametrisen puhesynteesin ja perusmuotoisen glottisherätevokooderin toimintaperiaatteet. Uutta menetelmää arvioidaan vertaamalla sitä alkuperäiseen metodiin ensin käyttämällä mel-kepstrikertoimia käyttävää objektiivista etäisyysmittaa ja toiseksi käyttäen subjektiivisia kuuntelukokeita. Uuden metodin havaittiin olevan laadullisesti samalla tasolla alkuperäisen spektrisovitusmenetelmän kanssa