Digital Signal Processing

2608 Submissions

[2] ai.viXra.org:2608.0064 [pdf] submitted on 2026-08-18 19:26:57

A Feasibility Study of Analog Audio Transmission over Near-Ultrasonic Frequency Bands Using Consumer Audio Equipment

Authors: Dinuo Chen
Comments: 16 Pages.

Near-ultrasonic frequency bands provide an underutilized portion of the acoustic spectrum with relatively low perceptual salience[1, 2] while remaining potentially usable with conventional audio hardware. This paper investigates the feasibility of transmitting analog audio over near-ultrasonic frequency bands using consumer-grade loudspeakers, microphones, and sound cards. A singlesideband (SSB) modulation scheme is employed to shift baseband audio into the near-ultrasonicrange, where it is transmitted through an acoustic channel and subsequently demodulated at the receiver. The system is evaluated under various transmission conditions using commonly available audio equipment. Signal quality is assessed through spectral analysis and objective similarity metrics between the original and recovered audio signals. Experimental results demonstrate that consumer audio devices are capable of supporting near-ultrasonic analog audio transmission within the limits imposed by their frequency response. Although attenuation and distortion increase toward the upper end of the transmission band, the original audio can still be recovered with acceptable quality under suitable conditions. These findings suggest that near-ultrasonic acoustic channels couldprovide a low-cost communication medium for specialized applications without requiring dedicated ultrasonic transducers.
Category: Digital Signal Processing

[1] ai.viXra.org:2608.0029 [pdf] submitted on 2026-08-10 02:01:56

Irreducible Channel Mixing and Exponential Calibration Laws for Matrix-Polynomial and Linear-Phase MIMO FIR Filters

Authors: Lluis Eriksson
Comments: 18 pages; Exact-arithmetic, numerical, and Lean/mathlib reproducibility artifacts are linked in the paper.

Scalar Chebyshev filtering treats every vector in a block Krylov iterate with the same polynomial, while simultaneously diagonalizable matrix coefficients amount to independent scalar filters after a fixed channel rotation. We study the larger class of Hermitian matrix-polynomial filters under tangential pass constraints. Already at fixed channel dimension d=3, we construct rationally generated signatures with quantitative full-spark margin for which an irreducible symmetric filter has stopband leakage O(exp(-cN)). In contrast, every exactly calibrated symmetric coefficient family with any common nontrivial invariant channel subspace has leakage at least one; this comparator strictly contains the pairwise-commuting class and permits a fully noncommutative 2 by 2 block. A quantitative theorem covers approximately reducible filters by charging their sampled off-block coupling together with calibration error. The signature margin and the admissible combined error are both exp(-O(N)), not exp(-N^3). This exponential scale is unavoidable: for arbitrary pass nodes and signatures in the same separated bands, an explicit scalar binomial-tail polynomial has both pass error and stopband leakage at most exp(-2N/81). Thus constant-error separation is impossible, while the irreducible construction achieves the correct exponential scale class. An affine cosine substitution gives the same robust law for fixed-latency reciprocal linear-phase MIMO FIR filters. We also give an exact rational five-tap certificate with stopband norm at most 25/32 and prove that its advantage survives reducible calibration errors delta < 7/1920. A second exact-arithmetic certificate is calibrated from a public triaxial pump-vibration data set: it gives leakage below 0.96 versus one for every exactly calibrated reducible symmetric class, while its maximum directional error on six held-out records is 0.00385. In a frequency-domain-decomposition test on the frozen held-out cospectra, filtering rotates the leading modal direction by at most 0.222 degrees and changes its leading spectral ordinate by at most 2.4 × 10^-5 relatively. Numerical programs test the mechanism and expose an ordinary graph-denoising setting in which scalar Chebyshev filtering is instead preferable. Tangential matrix interpolation, MIMO filtering, scalar two-band approximation and convex FIR design are not claimed as new; the contribution is the fixed-order reducible/irreducible separation together with its two-sided calibration scale.
Category: Digital Signal Processing