By Ken Steiglitz
This article is directed on the marketplace of DSP clients led to by way of the advance of strong and cheap software program instruments to investigate indications. those instruments enable refined manipulation of indications yet don't offer an figuring out of the idea or the root for the ideas. This paintings develops an method of the advance of the maths of DSP and makes use of examples from parts of the spectrum standard to newcomers, including questions and instructed experiments
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Additional resources for A digital signal processing primer with applications to digital audio and computer music
Cichocki A, Unbehauen R, Rummert E (1994) Robust learning algorithm for blind separation of signals. Electronic Letters 30(17): 1386—1387 ! Cichocki A, Unbehauen R (1996) Robust neural networks with on-line learning for blind identification and blind separation of sources. IEEE Transactions on Circuits and Systems 43(11): 894—906 ! K arhunen J, Joutsensalo J (1994) Representation and separation of signals using nonlinear PCA type learning. Neural Networks 7(1): 113 —127 ! Karhunen J, Oja E, Wang L et al (1997) A class of neural networks for independent component analysis.
Using Eqs. 9), the relation between moment sequence and cumulant sequence can be obtained. 10)!! 11) where m W 1) is the autocorrelation sequence. 12) where m W 1 W 2) is the third-order moment sequence. 13) If the |X[k]~ process is zero mean m1x>0, then the second-order cumulant and third-order cumulant are equal to the second-order moment and third-order moment respectively. However, to obtain fourth-order cumulant, the fourthorder moment and second-order moment are needed. 1) is the n-order moment function of the equivalent Gaussian process with the same mean and autocorrelation sequence.
Cardoso and Laheld researched the stability of the equivariant adaptive separation via independence, and presented stability analysis results for the case of any number of source signals and gave a qualitative explanation for the selection of the network activation function. Amari and Chen et al. did special research on the stability of the blind source separation algorithm, the object of the research being to use the nature gradient to optimize the contract function of the maximum likelihood algorithm.