addition in Galois fields ademod ademodce A-law companders amod amodce amplitude modulation (AM) sample code for basic example using demodulation offsets using filters using Hilbert filter using Hilbert filter in baseband simulation using single and double sidebands amplitude shift keying (ASK) sample code for mapping to plot waveforms using passband simulation analog signals, representing analog-to-digital conversion apkconst arbitrary signal constellations arithmetic in Galois fields sample code using extension fields using prime fields awgn baseband modulated signal simulation BCH coding discussion of generatorpolynomial for sample code for tracking errors using various coding methods summary of tools for bchdeco bchenco bchpoly bi2de binary codes matrix format for messages and codewords in Reed-Solomon codes sample code numbers, order of digits and vector format for messages and codewords sample code binary-to-decimal conversion bipolar random numbers bit error rates biterr bits random block coding functions techniques See also specific coding techniques Bose-Chaudhuri-Hocquenghem (BCH) coding discussion of generator polynomial for sample code for tracking errors using various coding methods summary of tools for burst errors carrier frequency (Fc) relative to sampling rate carrier signal initial phase for analog modulation for digital modulation circle signal constellations default values for plotting code generator matrices converting to parity-check matrices sample code finding representing code generator polynomials finding representing codebooks optimizing for DPCM sample code sample code for DPCM representing codewords definition representing coding block functions techniques convolutional examples features of the toolbox sample code using polynomial description using trellis description source features of the toolbox compand companders sample code complex envelope compression of data compressors sample code conjugate elements of Galois fields constellations, signal arbitrary circle default values for plotting hexagonal, sample code plots interpreting square plotting triangular, sample code constraint length of convolutional code convenc converting analog to digital binary to decimal decimal to binary exponential to polynomial format for Galois field elements sample code generator matrices to parity-check matrices sample code polynomial representations polynomial to exponential format for Galois field elements sample code sampling rates vectors to matrices convolutional coding examples features of the toolbox sample code using polynomial description sample code using trellis description correction vector correlation techniques in demodulation cosets, cyclotomic Costas phase-locked loop for analog modulation for digital modulation cyclgen cyclic coding discussion of generator polynomial for sample code sample code using various coding methods summary of tools for cyclotomic cosets cyclpoly data compression ddemod ddemodce de2bi decimal format for messages and codewords in Reed-Solomon coding sample code decision timing and eye diagrams sample code for eye diagrams for scatter plots decode decoding tables representing default Galois field parameters, in error-control coding primitive polynomials delta modulation sample code See also differential pulse code modulation demodmap demodulation definition of digital functions for features of the toolbox noncoherent See also modulation diagrams eye sample code scatter sample code differential pulse code modulation (DPCM) parameters, optimizing sample code parameters, representing sample code digital modulation functions for signals, representing displaying polynomials distortion from DPCM, reducing from quantization, reducing division in Galois fields dmod dmodce DPCM parameters, optimizing sample code parameters, representing sample code dpcmdeco dpcmenco dpcmopt encode error analysis, features of the toolbox integers patterns predictive rates bit versus symbol sample code error-control coding base 2 only features of the toolbox methods supported in toolbox terminology and notation with default Galois field parameters error-correction capability of BCH codes of Hamming codes of Reed-Solomon codes error-rate analysis expanders sample code exponential format for Galois field elements in Reed-Solomon coding eye diagrams sample code eyediagram features of the toolbox error-analysis error-control coding modulation/demodulation source coding feedback connection polynomials fields, finite See also Galois fields filtering data over Galois fields filters designing and applying raised cosine designing Hilbert transform designing raised cosine using after analog demodulation choosing cutoff frequency resulting time lag using after digital demodulation using raised cosine using square-root raised cosine finite fields See also Galois fields font when using gfpretty format of Galois field elements simplifying and converting to exponential format sample code simplifying and converting to polynomial format sample code formatting polynomials formatting, of signals frequency modulation (FM) sample code frequency shift keying (FSK) sample code Galois fields in error-control coding avoiding explicit reference to representing elements of Gaussian elimination in gflineq in gfrank Gaussian noise, generating gen2par generator matrices converting to parity-check matrices sample code finding representing generator polynomials finding for convolutional code representing gfadd gfconv gfcosets gfdeconv gfdiv gffilter gflineq gfminpol gfmul gfplus gfpretty gfprimck gfprimdf gfprimfd gfrank gfrepcov gfroots gfsub gftrunc gftuple gfweight hammgen Hamming coding for single-error-correction sample code using various coding methods using various formats summary of tools for Hamming weight hank2sys hard-decision decoding Hilbert filters designing for amplitude modulation sample code for baseband amplitude modulation sample code hilbiir initial phases of carrier signal for analog modulation for digital modulation in-phase/quadrature coordinates inverses, multiplicative in Galois fields irreducible polynomials sample code istrellis length of polynomial representations minimizing linear block coding sample code linear equations over Galois fields and filtering linear predictors optimizing sample code representing list of elements of Galois fields generating sample code in error-control coding, avoiding explicit reference to Lloyd algorithm, for optimizing quantization parameters lloyds mapped signals representing for PSK and QASK mapping functions for without modulating marcumq matrices over Galois fields rank messages definition representing for coding functions for modulation functions minimal polynomials of Galois field elements sample code minimum distance minimum shift keying (MSK) modmap modulated signals, representing modulation definition of delta sample code See also differential pulse code modulation differential pulse code. See differential pulse code modulation digital functions for features of the toolbox methods supported in toolbox of several signals sample code terminology without mapping mu-law companders sample code multiple roots of polynomials over Galois fields multiplication in Galois fields multiplicative inverses in Galois fields nonbinary codes Reed-Solomon noncausality of filters noncoherent demodulation Nyquist sampling theorem oct2dec optimizing DPCM parameters sample code quantization parameters sample code order of digits in binary numbers order, predictive parity-check matrices finding representing partitions optimizing for DPCM sample code sample code for DPCM representing passband simulation phase modulation (PM) sample code phase shift keying (PSK) sample code for basic example for demapping for mapping for plotting signal constellation phase-locked loop, Costas for analog modulation for digital modulation points, decision and eye diagrams sample code for eye diagrams for scatter plots poly2trellis polynomial description of an encoder sample code description of encoder format for Galois field elements polynomials displaying formatted generator, finding polynomials over Galois fields adding dividing irreducible minimal sample code multiplying primitive default definition finding representation choices for roots of sample code subtracting truncating predictive error order predictive quantization features of the toolbox parameters, optimizing sample code parameters, representing sample code predictors linear optimizing sample code representing primitive element, definition polynomials consistent use of default definition finding in error-control coding, avoiding explicit reference to sample code punctured convolutional code QAM representing signals for sample code QASK sample code using eye diagram using scatter plot and square constellation qaskdeco qaskenco quadrature amplitude modulation (QAM) representing signals for sample code quadrature amplitude shift keying (QASK) sample code using eye diagram using scatter plot and square constellation quantiz quantization coding DPCM parameters, optimizing sample code features of the toolbox parameters, optimizing sample code parameters, representing predictive sample code sample code vector raised cosine filters designing and applying designing but not applying filtering with square-root randerr randint random bipolar symbols bits in error patterns integers signals features of the toolbox symbols randsrc rank of matrices over Galois fields rcosfir rcosflt rcosiir rcosine redundancy, reducing Reed-Solomon coding discussion of generator polynomial for summary of tools for references convolutional coding error-control coding Galois fields modulation/demodulation representation of polynomials, shortening representing analog signals codebooks codewords decoding tables digital signals Galois field elements in a list in exponential format in polynomial format generator matrices generator polynomials mapped signals for PSK and QASK messages for coding functions for modulation functions modulated signals parity-check matrices partitions predictors quantization parameters signal constellations roots of polynomials over Galois fields sample code rsdeco rsdecode rsdecof rsenco rsencode rsencof rspoly sampling rate change during mapping individual of signals, relative relative to carrier frequency significance of scalar quantization coding features of the toolbox parameters, representing sample code scatter plots sample code using modulation scatterplot signal constellations arbitrary circle default values for plotting hexagonal, sample code plots interpreting square plotting triangular, sample code signal formatting features of the toolbox Signal Processing Toolbox for filter design simplifying exponential format of Galois field elements sample code polynomial format of Galois field elements sample code soft-decision decoding sample code source coding features of the toolbox square signal constellations plotting subtraction in Galois fields symbol error rates symerr syndrome syndtable terminology modulation/demodulation timing, decision and eye diagrams sample code for eye diagrams for scatter plots training data for optimizing DPCM quantization parameters for optimizing quantization parameters trellis description of encoder structure sample code truncating polynomials over Galois fields vec2mat vector quantization vitdec weight, Hamming wgn white Gaussian noise, generating