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A linear encoder is a sensor, transducer or readhead paired with a scale that encodes position. The sensor reads the scale in order to convert the encoded position into an analog or digital signal , which can then be decoded into position by a digital readout (DRO) or motion controller.
A linear code of length n transmits blocks containing n symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct codewords differ in at least three bits.
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in 1985. At the time, it provided significantly better quality than existing low bit-rate algorithms, such as residual-excited linear prediction (RELP) and linear predictive coding (LPC) vocoders (e.g., FS-1015).
Linear block codes are summarized by their symbol alphabets (e.g., binary or ternary) and parameters (n,m,d min) [5] where n is the length of the codeword, in symbols, m is the number of source symbols that will be used for encoding at once, d min is the minimum hamming distance for the code. There are many types of linear block codes, such as
The example encoder in Img. 2. is an 8-state encoder because the 3 registers will create 8 possible encoder states (2 3). A corresponding decoder trellis will typically use 8 states as well. Recursive systematic convolutional (RSC) codes have become more popular due to their use in Turbo Codes.
In particular, the most common speech coding scheme is the LPC-based code-excited linear prediction (CELP) coding, which is used for example in the GSM standard. In CELP, the modeling is divided in two stages, a linear predictive stage that models the spectral envelope and a code-book-based model of the residual of the linear predictive model.
The message to be systematically encoded is {1,6,3}. Using Lagrange interpolation, F(a i) = 3 x 2 + 2 x + 1, and applying F(a i) for a 4 = 3 to a 7 = 6, results in the code word {1,6,3,6,1,2,2}. Assume errors occur at c 2 and c 5 resulting in the received code word {1,5,3,6,3,2,2}. Start off with e = 2 and solve the linear equations:
Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model. [1] [2] LPC is the most widely used method in speech coding and speech synthesis.