This paper presents an algorithm for detecting and estimating pitch in acoustic audio signals using the Generalized Spectrum (GS). A performance evaluation of a GS-based and two classical (autocorrelation-and cepstrum-based) pitch determination algorithms was conducted on a set of wavetable-synthesized musical signals. The experiment separately evaluates the tasks of pitch detection and estimation. Pitch estimation performance is presented in terms of gross pitch errors (indicating algorithm stability) and meansquared fine pitch error. Pitch detection performance is evaluated by a Receiver Operating Characteristic analysis of the detection statistics. Results demonstrate that the GS-based estimator generally performs worse than the autocorrelation and cepstrum-based methods. However, the GSbased method performed consistently better for the detection problem, especially at low signal-to-noise values.GS-based PDA and compares its performance to the autocorrelation (AC) and cepstrum (CEP) approach. GENERALIZED SPECTRUM THEORY Consider a continuous time signal x(t), whose continuous Fourier transform is denoted by Xy). The GS ofx(t) is defined as [7]:the expected value operator, and superscript * denotes the complex conjugate transpose. Sampling x(t) at multiples of time interval T, results in the discrete sequence x(nTS), hereafter designated as x(n), where n = 0, 1, . . . , The discrete Fourier transform (DFT) coefficient of x(n), denoted as X(m), will be expressed in an M element column vector x, where each element is a DFT value corresponding to m = 0, LIM, 2f;lM ... , (M-N -1.
Source-Separation Non-Negative Matrix Factorization (SSNMF) is a mathematical algorithm recently developed to extract scalp-recorded frequency-following responses (FFRs) from noise. Despite its initial success, the effects of silent intervals on algorithm performance remain undetermined. Our purpose in this study was to determine the effects of silent intervals on the extraction of FFRs, which are electrophysiological responses that are commonly used to evaluate auditory processing and neuroplasticity in the human brain. We used an English vowel /i/ with a rising frequency contour to evoke FFRs in 23 normal-hearing adults. The stimulus had a duration of 150 ms, while the silent interval between the onset of one stimulus and the offset of the next one was also 150 ms. We computed FFR Enhancement and Noise Residue to estimate algorithm performance, while silent intervals were either included (i.e., the WithSI condition) or excluded (i.e., the WithoutSI condition) in our analysis. The FFR Enhancements and Noise Residues obtained in the WithoutSI condition were significantly better ( p < .05) than those obtained in the WithSI condition. On average, the exclusion of silent intervals produced a 11.78% increment in FFR Enhancement and a 20.69% decrement in Noise Residue. These results not only quantify the effects of silent intervals on the extraction of human FFRs, but also provide recommendations for designing and improving the SSNMF algorithm in future research.
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