Examples
+X = [0 0 0 1 2 3 ]; +Y = [1 2 3 ]; +[Xa,Ya] = alignsignals(X,Y,[],1) |  |  |
This function aligns the two input signals.
[Xa Ya] = ALIGNSIGNALS(X,Y) +[Xa Ya] = ALIGNSIGNALS(X,Y,MAXLAG) +[Xa Ya] = ALIGNSIGNALS(X,Y,MAXLAG,1) +[Xa Ya D] = ALIGNSIGNALS(...)
[Xa Ya] = ALIGNSIGNALS(X,Y) aligns the two vectors X and Y by estimating +the delay D between the two. If Y is delayed with respect to X, D is +positive , and X is delayed by D samples. If Y is advanced with respect +to X, D is negative, and Y is delayed by -D samples.
+[Xa Ya] = ALIGNSIGNALS(X,Y,MAXLAG) considers MAXLAG be the maximum correlation +window size which is used to calculate the estimated delay D between X and Y. +MAXLAG is an integer-valued scalar. By default, MAXLAG is equal to MAX(LX,LY)-1. +If MAXLAG is empty ([]),then default value is considered. If MAXLAG +is negative, it is replaced by its absolute value.
+[Xa Ya] = ALIGNSIGNALS(X,Y,MAXLAG,1) keeps the lengths of Xa +and Ya the same as those of X and Y, respectively. +Here, 1 implies truncation of the intermediate vectors. +Input argument 4 is 0 implies truncation_off (no truncation). +D is positive implies D zeros are pre-pended to X, and the last D samples of X are truncated. +D is negative implies -D zeros are pre-pended to Y, and the last -D samples +of Y are truncated. That means, when D>=Length(X), all samples of X are lost. +Similarly, when -D>=Length(Y), all samples of Y are lost. +Avoid assigning a specific value to MAXLAG when using the truncate=1 option, set MAXLAG to [].
+[Xa Ya D] = ALIGNSIGNALS(...) returns the estimated delay D.
+X = [0 0 0 1 2 3 ]; +Y = [1 2 3 ]; +[Xa,Ya] = alignsignals(X,Y,[],1) | | |
This function decodes the given code using arithmetic coding
SEQ = ARITHDECO(CODE, COUNT, LEN)
SEQ = ARITHDECO(CODE, COUNT, LEN) decodes the given received seq (CODE) to message using arithmetic coding. +COUNT is vector which gives information about the source statistics (i.e. frequency of each symbol in the source alphabet) +CODE is the binary arithmetic code
+Source Alphabet is assumed to be {1,2,....N} where N is a positive integer +Therefore, sequence should be finite and positive +Length of the COUNT should match the length of the source alphabet
+| - << FOSSEE_Communication_Systems_Toolbox + << arithdeco | @@ -20,7 +20,8 @@ | - + finddelay >> + |
This function encodes the given sequence using aritmetic coding
CODE = ARITHENCO(SEQ, COUNT)
CODE = ARITHENCO(SEQ, COUNT) encodes the given sequence (SEQ) using arithmetic coding. +COUNT is vector whihc gives information about the source statistics (i.e. frequency of each symbol in the source alphabet) +CODE is the binary arithmetic code +Source Alphabet is assumed to be {1,2,....N} where N is a positive integer +Therefore, sequence should be finite and positive +Length of the COUNT should match the length of the source alphabet
+counts = [40 1 9]; +len = 4; +seq = [1 3 2 1] +code = arithenco(seq,counts); +disp(code) | | |
Sayood, K., Introduction to Data Compression, Morgan Kaufmann, 2000, Chapter 4, Section 4.4.3.
This function returns the estimated delay between two input signals using crosscorrelation.
D = FINDDELAY(X,Y), returns estimated Delay D between X +and Y. D is positive implies Y is delayed with respect to X and vice versa. +If X, Y are matrices, then D is a row vector corresponding to delay between columns of X and Y
+D = FINDDELAY(...,MAXLAG), uses MAXLAG as the maximum correlation +window size used to find the estimated delay(s) between X and Y:
+> If MAXLAG is an integer-valued scalar, and X and Y are row or column +vectors or matrices, the vector D of estimated delays is found by +cross-correlating (the columns of) X and Y over a range of lags +-MAXLAG:MAXLAG. +> If MAXLAG is an integer-valued row or column vector, and one input is vector +and another be matirx (let X is a row or column vector , +and Y is a matrix) then the vector D of estimated delays is found by +cross-correlating X and column J of Y over a range of lags +-MAXLAG(J):MAXLAG(J), for J=1:Number of columns of Y. +> If MAXLAG is an integer-valued row or column vector, and X and Y are +both matrices. then vector D of estimated delays is found by +cross-correlating corresponding columns of X and Y over a range of lags +-MAXLAG(J):MAXLAG(J).
+By default, MAXLAG is equal to MAX(LX,LY)-1 for vectors,
+This function produces cyclotomic cosets for a Galois field GF(P)
GFCS = GFCOSETS(M) produces cyclotomic cosets mod(2^M - 1). Each row of the +output GFCS contains one cyclotomic coset.
+GFCS = GFCOSETS(M, P) produces cyclotomic cosets mod(P^M - 1), where +P is a prime number.
+Because the length of the cosets varies in the complete set, %nan is used to +fill out the extra space in order to make all variables have the same +length in the output matrix GFCS.
+ +c = gfcosets(2,3) +disp(c) | | |
This function finds a solution for linear equation Ax = b over a prime Galois field.
[X, SFLAG] = GFLINEQ(A, B) returns a particular solution (X) of AX=B in GF(2). +If the equation has no solution, then X is empty and SFLAG = 0 else SFLAG = 1.
+[X, SFLAG]= GFLINEQ(A, B, P) returns a particular solution of the linear +equation A X = B in GF(P) and SFLAG=1. +If the equation has no solution, then X is empty and SFLAG = 0.
+ +This function represents a binary polynomial in standard ascending order format.
Q = GFREPCOV(P) converts vector (P) to standard ascending +order format vector (Q), which is a vector that lists the coefficients in +order of ascending exponents, if P represents a binary polynomial +as a vector of exponents with non-zero coefficients.
+This function is used to truncate the higher order zeroes in the given polynomial equation
A is considered to be matrix that gives the coefficients of polynomial GF(p) in ascending order powers +A = [1 2 3] denotes 1 + 2 x + 3 x^2 +AT=GFTRUNC(A) returns a matrix which gives the polynomial GF(p) truncating the input matrix +that is if A(i)=0, where i > d + 1, where d is the degree of the polynomial, that zero is removed
+A= [ 0 0 1 4 0 0] +c = gftrunc([0 0 1 2 3 0 0 0 4 5 0 1 0 0]) | | |
This function returns the amplitude imbalance and phase imbalance
[AMP_IMB_DB, PH_IMB_DEG] = IQCOEF2IMBAL(COMP_COEF) returns +the amplitude imbalance and phase imbalance +that a given compensator coefficient will correct. +Comp_Coef is a scalar or a vector of complex numbers. +AMP_IMB_DB and PH_IMB_DEG are the amplitude imbalance in dB +and the phase imbalance in degrees.
+This function returns the I/Q imbalance compensator coefficient for given amplitude and phase imbalance.
COMP_COEF = IQIMBAL2COEF(AMP_IMB_DB, PH_IMB_DEG) returns the I/Q imbalance +compensator coefficient for given amplitude and phase imbalance. +Comp_Coef is a scalar or a vector of complex numbers. +AMP_IMB_DB and PH_IMB_DEG are the amplitude imbalance in dB +and the phase imbalance in degrees and should be of same size.
+This function determines if a convolutional code is catastrophic or not
RESULT = ISCATASTROPHIC(TRELLIS) returns 1 if the specified +trellis corresponds to a catastrophic convolutional code, else 0.
eg_1.numInputSymbols = 4; +eg_1.numOutputSymbols = 4; +eg_1.numStates = 3; +eg_1.nextStates = [0 1 2 1;0 1 2 1; 0 1 2 1]; +eg_1.outputs = [0 0 1 1;1 1 2 1; 1 0 1 1]; +res_t_eg_1=istrellis(eg_1) +res_c_eg_1=iscatastrophic(eg_1) +if (res_c_eg_1) then +disp('Example 1 is catastrophic') +else +disp('Example 1 is not catastrophic') +end +eg_2.numInputSymbols = 2; +eg_2.numOutputSymbols = 4; +eg_2.numStates = 2; +eg_2.nextStates = [0 0; 1 1 ] +eg_2.outputs = [0 0; 1 1]; +res_t_eg_2=istrellis(eg_2) +res_c_eg_2=iscatastrophic(eg_2) +if (res_c_eg_2) then +disp('Example 2 is catastrophic') +else +disp('Example 2 is not catastrophic') +end | | |
This function checks if the given input is of trellis structure
[ISOK, STATUS] = ISTRELLIS(S) returns [T,''] if the given input is valid trellis structure. Otherwise ISOK is F and STATUS +indicates the reason for invalidity
+Fields in trellis structure are +numInputSymbols, (number of input symbols) +numOutputSymbols, (number of output symbols) +numStates, (number of states) +nextStates, (next state matrix) +outputs, (output matrix)
+Properties of the fields are as follows +numInputSymbols and numOutputSymbols should be a power of 2 (as data is represented in bits). +The 'nextStates' and 'outputs' fields are matrices of size 'numStates' x 'numInputSymbols' . +Each element in the 'nextStates' matrix and 'output' matrix is an integer value between zero and (numStates-1). +The (r,c) element of the 'nextStates' matrix and 'output' matrix,denotes the next state and output respectively when +the starting state is (r-1) and the input bits have decimal representation (c-1).
+To convert to decimal value, use the first input bit as the most significant bit (MSB).
+Valid trellis structure +trellis.numInputSymbols = 4; +trellis.numOutputSymbols = 4; +trellis.numStates = 3; +trellis.nextStates = [0 1 2 1;0 1 2 1; 0 1 2 1]; +trellis.outputs = [0 0 1 1;1 1 2 1; 1 0 1 1]; +[isok,status] = istrellis(trellis) + +Inavlid trellis structure +trellis.numInputSymbols = 3; +trellis.numOutputSymbols = 3; +trellis.numStates = 3; +trellis.nextStates = [0 1 2 ;0 1 2 ; 0 1 2 ]; +trellis.outputs = [0 0 1 ;1 1 2 ; 1 0 1 ]; +[isok,status] = istrellis(trellis) | | |
This function generates root Zadoff-Chu sequence of complex symbols as per LTE specifications.
SEQ = LTEZADOFFCHUSEQ(R, N) generates the Rth root Zadoff-Chu sequence (SEQ) +of length N.
+3rd Generation Partnership Project, Technical Specification Group Radio
+Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA),
+Physical channels and modulation, Release 10, 3GPP TS 36.211, v10.0.0,
+2010-12.
Call functions available in communications (and any other) package of Octave. The actual function call is "octave_fun" and is available as a part of "FOSSEE-Scilab-Octave-Toolbox"
[y1, y2, ...] = octave_fun("octave_function",input1,input2,...) +[y1, y2, ...] = octave_fun("octave_function",input1,input2,...,optional_input1,optional_input2,...) +[y1, y2, ...] = octave_fun("octave_function","octave_package",input1,input2,...) +[y1, y2, ...] = octave_fun("octave_function","octave_package",input1,input2,...,optional_input1,optional_input2,...)
ouput as returned by octave. It can be a vector or matrix of doubles
name of the function in octave that has to be called. It has to be a string in double quotes
input as expected by the octave function. It can be a vector or matrix of doubles
an optional argument that the given octave function can accept. It has to be a string in double quotes
name of the package in octave that has to be loaded as required by the octave function. It has to be a string in double quotes
This function accepts an octave function name with the relevant inputs and returns the output as generated. It requires Octave to be installed along with necessary packages.
+ +// Reshape a given array using octave and its "communications" package. +// See help in octave for more information about "reshape" function. +// Note that this example requires the "communications" package to be installed in octave and the "FOSSEE-Scilab-Octave-Toolbox" loaded in scilab. +x = [1, 2, 3, 4]; +dim1 = 2; +dim2 = 2; +output = octave_fun("reshape", "communications", x, dim1, dim2) | | |
// Compute the Q function using octave and its "communications" package. +// See help in octave for more information about "qfunc" function. +// Note that this example requires the "communications" package to be installed in octave and the "FOSSEE-Scilab-Octave-Toolbox" loaded in scilab. +M = [1, 2; 3, 4]; +output = octave_fun("qfunc", "communications", M) | | |
This function performs Single Side Band Amplitude Demodulation
Z = SSBDEMOD(Y,Fc,Fs) +demodulates the single sideband amplitude modulated signal Y +with the carrier frequency Fc (Hz). +Sample frequency Fs (Hz). zero initial phase (ini_phase). +The modulated signal can be an upper or lower sideband signal. +A lowpass butterworth filter is used in the demodulation.
+Z = SSBDEMOD(Y,Fc,Fs,INI_PHASE) +adds an extra argument the initial phase (rad) of the modulated signal.
+Z = SSBDEMOD(Y,Fc,Fs,INI_PHASE,NUM,DEN) +adds extra arguments about the filter specifications +i.e., the numerator and denominator of the lowpass filter.
+Fs must satisfy Fs >2*(Fc + BW), where BW is the bandwidth of the +modulating signal.
+ +Fs =200; +t = [0:2*Fs+1]'/Fs; +ini_phase = 5; +Fc = 20; +fm1= 2; +fm2= 3 +x =sin(2*fm1*%pi*t)+sin(2*fm2*%pi*t); +y = ssbmod(x,Fc,Fs,ini_phase); +o = ssbdemod(y,Fc,Fs,ini_phase); +z = fft(y); +zz =abs(z(1:length(z)/2+1 )); +axis = (0:Fs/length(zz):Fs -(Fs/length(zz)))/2; + +figure +subplot(3,1,1); plot(x); +title(' Message signal'); +subplot(3,1,2); plot(y); +title('Amplitude modulated signal'); +subplot(3,1,3); plot(axis,zz); +title('Spectrum of amplitude modulated signal'); +z1 =fft(o); +zz1 =abs(z1(1:length(z1)/2+1 )); +axis = (0:Fs/length(zz1):Fs -(Fs/length(zz1)))/2; +figure +subplot(3,1,1); plot(y); +title(' Modulated signal'); +subplot(3,1,2); plot(o); +title('Demodulated signal'); +subplot(3,1,3); plot(axis,zz1); +title('Spectrum of Demodulated signal'); | | |