We further adopt the very reasonable assumption that the original source signals, denoted as s 1 ( t ), s 2 ( t ), and s 3 ( t ), are independent and (similarly as before) the values at different time instants correspond to the values of three latent variables, denoted together as a random vector s.įigure 19.10. To this end and in order to bring the task in the formulation we have previously adopted, we consider the values of the three signals at different time instants as different observations of the corresponding random variables, x 1, x 2, and x 3, which are put together to form the random vector x. The goal is to use ICA and recover the original speech and music from the recorded mixed signals. In the simplest of the models, the three recorded signals can be considered as linear combinations of the individual source signals. We denote the inputs to the three microphones as x 1 ( t ), x 2 ( t ), and x 3 ( t ), respectively. Then, three microphones (as many as the sources) are placed in different places in the room and the mixed speech signals are recorded. Let us say that there are people (a female and a male) and there is also monophonic music, making three sources of sound in total. In a party, there are various people speaking in our case, we are going to consider music as well. Sergios Theodoridis, in Machine Learning (Second Edition), 2020 The Cocktail Party ProblemĪ classical application that demonstrates the power of the ICA is the so-called cocktail party problem. Note that in addition to updating a quarter of the adaptive coefficients, the set-membership partial-update NLMS algorithm updates only 8% of the time on average in this case. The set-membership partial-update NLMS algorithm stands out as the fasting converging data-dependent partial-update NLMS algorithm. On the other hand, the data-dependent partial-update NLMS algorithms appear to perform very well (see Figure 5.3(b)), almost having the same convergence performance as the full-update NLMS algorithm. As can be seen from Figure 5.3(a) the periodic-partial-update and sequential-partial-update NLMS algorithms exhibit slow convergence compared with the full-update NLMS algorithm. Figure 5.3 shows the time evolution of misalignment for the full-update and partial-update NLMS algorithms. The error magnitude bound for the set-membership partial-update NLMS algorithm is γ = 0.012. The step-size parameter for all adaptive filters is μ = 0.22 except for the selective-partial-update NLMS algorithm which uses μ = 0.16. The periodic-partial-update NLMS algorithm updates the entire coefficient vector every S = 4 iterations, which amounts to updating 64 coefficients per iteration on average.
The partial-update NLMS filters update M = 64 coefficients at each iteration out of N = 256. The adaptive filters have N = 256 coefficients. To prevent saturation resulting from high peak amplitudes, the detector circuit must be capable of sustaining a crest factor, the ratio of peak to rms signal, of at least 5.
Current standards specify a time constant of 35 msec, in an attempt to simulate the response of the human ear, plus the capability of storing the peak or rms value of the applied signal. Impulsive signals present something of a problem. The fast response follows time-varying sound pressures more closely at the expense of accuracy the slow response offers a higher confidence level for the rms sound pressure measurement. For stationary or quasi-stationary signals, a “fast” or “slow” time constant, based on the response to a 200- or 500-msec signal, respectively, is used. The weighting networks are linear (unweighted), A, B, C, and sometimes D ( Section II.A.3).
Two switch selections available to the user are weighting and time constant. In a diffuse field, the random response curve must be relied on: The smaller the microphone, the more accurate are the results.
In a free field, corrections are based on curves such as those in Fig. The directional response of the microphone affects the accuracy of the measurement. There are a variety of additional features such as calibration, overload indication, and external connectors for filters and output signal. The detector is a square-law detector followed by an averaging (mean or rms) network. The microphone signal is preamplified (attenuated), weighted, again amplified (attenuated), detected, and displayed on an analog meter.
Zuckerwar, in Encyclopedia of Physical Science and Technology (Third Edition), 2003 II.C Sound Level MetersĪ sound level meter is a compact portable instrument, usually battery-operated, for measuring SPL at a selected location.