Organizations: Department of Electrical and Computer Engineering, University of Colorado Colorado Springs, Colorado Springs, Colorado, USA
Abstract
Signal synthesis is used in every aspect of the electronics world, where sinusoidal waveforms are used to perform functions such as clocking, signal transmission, feedback controls, and other applications. Digital synthesis is the method of approximating sinusoidal waveforms using digital logic, where the waveform is approximated to an accurate degree at a specific frequency which can be either implemented digitally or converted into the analog domain for use elsewhere. This project details the creation of a digital synthesizer commonly used for professional audio applications through the implementation of hardware in an FPGA.
Self-supervised learning advances audio representation for multimedia analysis. However, prevailing data-centric approaches rely on massive real-world corpora, increasing training costs, curation burdens, and privacy barriers. To address this, we present AudioPG, a procedural synthesis framework eliminating real audio recordings during pre-training. AudioPG trains a Transformer-based masked autoencoder on waveforms generated on-the-fly from basic acoustic primitives and composition rules. The encoder transfers effectively to real audio benchmarks, achieving 90.60% accuracy on ESC-50, 0.546 mAP on FSD50K, 88.17% on UrbanSound8K, and 97.03% on Speech Commands V2. Notably, pre-training completes in under 20 minutes on a single GPU. Latent space analysis reveals physical factors, including fundamental frequency and relative intensity, emerge in orthogonal subspaces, making representations linearly decodable. These results establish procedural synthesis as an efficient, interpretable pre-training signal when large-scale corpora are unavailable. Our code is available at: https://github.com/Freyliu0516/audioPG.
Quadratic difference tones (QDTs) are a species of auditory distortion product in which a "phantom" pure tone, absent from the acoustic signal, is clearly audible to listeners. Exploiting this phenomenon, one can synthesize harmonically rich tones for musical purposes, a technique called Quadratic Difference Tone Spectrum (QDTS) synthesis. Previous works have introduced numerical methods to synthesize QDTS based on the distortion function, which links a target QDTS and an overtone-structured carrier signal. While accurate, these methods were stochastic and discontinuous, making them difficult to control for musical purposes and effectively limiting them to stationary signals. This paper proposes a neural network-based approach that learns an approximate inverse of the distortion mapping in an autoencoder-like configuration, producing a continuous approximation that addresses prior limitations. Experimental results show that, although slightly less numerically precise, the method is sufficient for perceptual and musical applications. We also implement a real-time version in Max and evaluate its performance. Various sound examples demonstrate its expressive and musical potential. The source code, audio examples, tutorials, and software accompanying this work are available at https://cordutie.github.io/projects/qdts.html
Esteban Gutiérrez, Behzad Haki, Christopher Haworth +2
Efficient hardware implementation of nonlinear activation functions is a crucial task in deploying artificial neural networks on resource-constrained and edge devices such as Field-Programmable Gate Arrays (FPGAs). The sigmoid activation function is widely used for probabilistic output, binary classification, and gating mechanisms in recurrent neural networks, despite its reliance on exponential computations. This paper presents a hardware-efficient FPGA implementation of the sigmoid activation function using a mixed-radix CORDIC-based architecture. The proposed approach leverages the mathematical relationship between the sigmoid and hyperbolic tangent functions. The input range is normalized to 1, enabling the corresponding tanh computation to operate within a reduced range of 0.5, which significantly improves convergence behavior. To achieve high accuracy with minimal hardware overhead, a modified mixed-radix hyperbolic rotation CORDIC (MR-HRC) algorithm combining radix-2 and radix-4 iterations is introduced. The initial radix-2 stage ensures stable convergence, while the subsequent radix-4 stage accelerates convergence without requiring scale-factor compensation. In the final stage, a radix-2 linear vectoring CORDIC (R2-LVC) is used to compute the hyperbolic tangent by dividing hyperbolic sine and cosine values derived from the MR-HRC algorithm. The entire architecture is fully pipelined and implemented on an FPGA. The design is realized on an Xilinx Virtex-7 FPGA using a 16-bit fixed-point representation. Experimental results demonstrate a significant reduction in hardware utilization, requiring only 835 logic slices with zero DSP usage. Additionally, the design achieves a mean absolute error of 4.23 10^-4, outperforming several recent sigmoid implementations.