Signal transfer function

Abstract: Necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived. These conditions state that a signal must be locally monotone to pass through a median filter unchanged. It is proven that the form of successive median filtering of a signal (i.e., the filtered output is itself again filtered) eventually reduces the original signal to an invariant signal called a root signal. For a signal of length L samples, a maximum of \frac{1}{2}(L - 2) repeated filterings produces a root signal.

Abstract: A signal enhancement algorithm is developed that seeks to recover a signal from noise-contaminated distorted measurements made on that signal. This object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing. The measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties. Conditions for the algorithm's convergence are established in which the primary requirement is that a composite property mapping be closed. This is a relatively unrestricted condition in comparison to that required of most existing signal-enhancement algorithms. >

Abstract: In this paper, a signal-filtering method based on empirical mode decomposition is proposed. The filtering method is a fully data-driven approach. A noisy signal is adaptively decomposed into intrinsic oscillatory components called intrinsic mode functions (IMFs) by means of an algorithm referred to as a sifting process. The basic principle of the method is to make use of partial reconstructions of the signal, with the relevant IMFs corresponding to the most important structures of the signal (low-frequency components). A criterion is proposed to determine the IMF, after which, the energy distribution of the important structures of the signal overcomes that of the noise and that of the high-frequency components of the signal. The method is illustrated on simulated and real data, and the results are compared to well-known filtering methods. The study is limited to signals that were corrupted by additive white Gaussian noise and is conducted on the basis of extended numerical experiments.

Abstract: A method and an apparatus measure blood oxygenation in a subject. A first signal source applies a first input signal during a first time interval. A second signal source applies a second input signal during a second time interval. A detector detects a first parametric signal responsive to the first input signal passing through a portion of the subject having blood therein. The detector also detects a second parametric signal responsive to the second input signal passing through the portion of the subject. The detector generates a detector output signal responsive to the first and second parametric signals. A signal processor receives the detector output signal and demodulates the detector output signal by applying a first demodulation signal to a signal responsive to the detector output signal to generate a first output signal responsive to the first parametric signal. The signal processor applies a second demodulation signal to the signal responsive to the detector output signal to generate a second output signal responsive to the second parametric signal. The first demodulation signal and the second demodulation signal both include at least a first component having a first frequency and a first amplitude and a second component having a second frequency and a second amplitude. The second frequency is a harmonic of the first frequency. The second amplitude is related to the first amplitude to minimize crosstalk from the first parametric signal to the second output signal and to minimize crosstalk from the second parametric signal to the first output signal.