Warped filters and their audio applications

Applied Sciences, 2018

Eurasip Journal on Advances in Signal Processing, 2001

We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping. These effects alter the frequency content of a signal via spectral mapping. They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters. In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform. However, most musical signals require a time-varying frequency modification in order to be properly processed. Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations. Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing. The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation. The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response. Thus, time-varying warping results in a space-varying, inhomogeneous, propagation structure. We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis. Slow time-varying characteristics lead to slowly varying parameter sequences. The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays.

Proceedings of the SMC Conferences, 2013

Source-filter modeling of musical tones requires a filter model for the spectral envelope of the signal. Since the perceptual frequency resolution is best at low frequencies, frequency warping has been previously shown to improve spectral envelope estimation of audio signals. In this paper, considering low-order modeling for harmonic tones, we investigate the perceptual performance of three warped models which extend the filter models: Linear Prediction Coding (LPC), True-Envelope based Linear Prediction (TE-LPC), and Discrete All-Pole method (DAP). The respective warped methods allow a continuous control of the warping factor, and here we are interested in the perceptual quality of the envelope estimation according to the warping factor for all methods. Results of our listening tests show that the frequency warping which best approximates the Bark scale, does not always give the best results.

While the use of the Fast Fourier Transform (FFT) for signal processing in music applications has been widespread, applications in real-time systems for dynamic spectral transformation have been quite limited. The limitations have been largely due to the amount of computation required for the operations. With faster machines, and with suitable implementation for frequency-domain processing, real-time dynamic control of high-quality spectral processing can be accomplished with great efficiency and a simple approach. This paper will describe some recent work in dynamic real-time control of frequency-domain-based signal processing. Since the implementation of the FFT/IFFT is central to the approach and methods discussed below, the authors will provide a brief description of this implementation, as well as of the development environment used in our work. As seen in Figure 1, the index values provide a synchronization phasor, making it possible to identify bins within a frame, and recognize frame boundaries. The index values can be used to access bin-specific data for various operations, such as attenuation or spatialization, and to read lookup tables for windowing.

Audio equalization is a vast and active research area. The extent of research means that one often cannot identify the preferred technique for a particular problem. This review paper bridges those gaps, systemically providing a deep understanding of the problems and approaches in audio equalization, their relative merits and applications. Digital signal processing techniques for modifying the spectral balance in audio signals and applications of these techniques are reviewed, ranging from classic equalizers to emerging designs based on new advances in signal processing and machine learning. Emphasis is placed on putting the range of approaches within a common mathematical and conceptual framework. The application areas discussed herein are diverse, and include well-defined, solvable problems of filter design subject to constraints, as well as newly emerging challenges that touch on problems in semantics, perception and human computer interaction. Case studies are given in order to illustrate key concepts and how they are applied in practice. We also recommend preferred signal processing approaches for important audio equalization problems. Finally, we discuss current challenges and the uncharted frontiers in this field. The source code for methods discussed in this paper is made available at https://code.soundsoftware.ac.uk/projects/allaboutaudioeq.

… of the 10th International Conference on …, 2007

Frequency warping is a modifier that acts on sound signals by remapping the frequency axis. Thus, the spectral content of the original sound is displaced to other frequencies. At the same time, the phase relationship among the signal components is altered, nonlinearly with respect to frequency. While this effect is interesting and has several applications, including in the synthesis by physical models, its use has been so far limited by the lack of an accurate and flexible real-time algorithm. In this paper we present methods for frequency warping that are based on local approximations of the warping operators and allow for real-time implementation. Filter bank structures are derived that allow for efficient realization of the approximate technique. An analysis of the error is also presented, which shows that both numerical and perceptual errors are within acceptable limits. Furthermore, the approximate implementation allows for a larger variety of warping maps than that achieved by the classical (non-causal) first-order allpass cascade implementation.

2000

This paper describes the design and implementation of an FIR based 20-band stereo audio equalizer that offers good spectral selectivity and phase response. The underlying theory of fast filtering in the frequency domain is addressed, the architecture of the DSP system using a single TI TMS320C31 processor is presented, the functionality of the interface, either software-based or hardware-based is described, and a few test results are presented and discussed.

Advances in Electrical and Computer Engineering, 2012

ABSTRACT This paper presents an iterative method for designing FIR filters that implement arbitrary magnitude characteristics, defined by the user through a set of frequencymagnitude points (frequency samples). The proposed method is based on the non-uniform frequency sampling algorithm. For each iteration a new set of frequency samples is generated, by processing the set used in the previous run; this implies changing the samples location around the previous frequency values and adjusting their magnitude through interpolation. If necessary, additional samples can be introduced, as well. After each iteration the magnitude characteristic of the resulting filter is determined by using the non-uniform DFT and compared with the required one; if the errors are larger than the acceptable levels (set by the user) a new iteration is run; the length of the resulting filter and the values of its coefficients are also taken into consideration when deciding a re-run. To demonstrate the efficiency of the proposed method a tool for designing FIR filters that match human audiograms was implemented in LabVIEW. It was shown that the resulting filters have smaller coefficients than the standard one, and can also have lower order, while the errors remain relatively small.

Proc. DAFX98, 1998

Frequency warping is a unitary transformation [4] that can be interesting from the point of view of sound manipulation and synthesis. Novel applications, some of them recently published by the authors, make use of dispersive delay lines, ie, delay lines whose elements are ...