»x=1 %scalar (% signs are comments and aren't evaluated)x = 1»y=[1 2 3 4 5 6] % sequence vector (row)y = 1 2 3 4 5 6»z=[1;2;3;4;5;6] % list vector (column)z = 1 2 3 4 5 6»a=[1 2 3;4 5 6;7 8 9] % matrix a = 1 2 3 4 5 6 7 8 9»b=[y;y;y] %matrix (list of sequences)b = 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6»c=[z z z] %matrix (sequences of lists)c = 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6»y' %conjugate transposeans = 1 2 3 4 5 6»y=[j*1, j*2, j*3, j*4, j*5, j*6]y = Columns 1 through 2 0 + 1.00000000000000i 0 + 2.00000000000000i Columns 3 through 4 0 + 3.00000000000000i 0 + 4.00000000000000i Columns 5 through 6 0 + 5.00000000000000i 0 + 6.00000000000000i»y' %conjugate transpose (watch out, it switches sign of the complex part!) (converts col to row, row to col)ans = 0 - 1.00000000000000i 0 - 2.00000000000000i 0 - 3.00000000000000i 0 - 4.00000000000000i 0 - 5.00000000000000i 0 - 6.00000000000000i»y(:) %makes column (this is another way -- this always makes it a column)ans = 0 + 1.00000000000000i 0 + 2.00000000000000i 0 + 3.00000000000000i 0 + 4.00000000000000i 0 + 5.00000000000000i 0 + 6.00000000000000i»d=0:1/10:1 %sequence (beg: step: end)d = Columns 1 through 4 0 0.10000000000000 0.20000000000000 0.30000000000000 Columns 5 through 8 0.40000000000000 0.50000000000000 0.60000000000000 0.70000000000000 Columns 9 through 11 0.80000000000000 0.90000000000000 1.00000000000000»e=sin(2*pi*d) %operation on sequence (operation on each element of sequence)e = Columns 1 through 4 0 0.58778525229247 0.95105651629515 0.95105651629515 Columns 5 through 8 0.58778525229247 0 -0.58778525229247 -0.95105651629515 Columns 9 through 11 -0.95105651629515 -0.58778525229247 0»f=[0:1/8:1;0:1/16:.5;0:1/32:.25] %list of sequencesf = Columns 1 through 4 0 0.12500000000000 0.25000000000000 0.37500000000000 0 0.06250000000000 0.12500000000000 0.18750000000000 0 0.03125000000000 0.06250000000000 0.09375000000000 Columns 5 through 8 0.50000000000000 0.62500000000000 0.75000000000000 0.87500000000000 0.25000000000000 0.31250000000000 0.37500000000000 0.437500000000000.12500000000000 0.15625000000000 0.18750000000000 0.21875000000000 Column 9 1.00000000000000 0.50000000000000 0.25000000000000»g=sin(2*pi*f) %operation on list of sequences (ex.could have a list of sines sequences with different frequencies)g = Columns 1 through 4 0 0.70710678118655 1.00000000000000 0.70710678118655 0 0.38268343236509 0.70710678118655 0.92387953251129 0 0.19509032201613 0.38268343236509 0.55557023301960 Columns 5 through 8 0 -0.70710678118655 -1.00000000000000 -0.70710678118655 1.00000000000000 0.92387953251129 0.70710678118655 0.38268343236509 0.70710678118655 0.83146961230255 0.92387953251129 0.98078528040323 Column 9 0 0 1.00000000000000»whos %variable list and sizes ( helpful when doing vector multiplication) Name Size Bytes Class a 3x3 72 double array ans 1x10 4192 struct array b 3x6 144 double array c 6x3 144 double array d 1x11 88 double array e 1x11 88 double array f 3x9 216 double array g 3x9 216 double array x 1x1 8 double array y 1x6 48 double array z 6x1 48 double arrayGrand total is 276 elements using 5264 bytesleaving 307693008 bytes of memory free.»»y-1 %additionans = 0 1 2 3 4 5»zz = 1 2 3 4 5 6»z*(y-1) %outer product 6x1 x 1x6 = 6x6 (makes a list of sequences, each sequence y multiplied by corresponding element of list in z)ans = 0 1 2 3 4 5 0 2 4 6 8 10 0 3 6 9 12 15 0 4 8 12 16 20 0 5 10 15 20 25 0 6 12 18 24 30»(y-1)*z %inner product 1x6 x 6x1 = 1x1 (multiplies each corresponding element of y and z, then adds the resulting elements together)ans = 70»0*1+1*2+2*3+3*4+4*5+5*6 inner product ans = 70»[1 2 3]*g %vector x matrix (sequence of inner products) ans = Columns 1 through 4 0 2.05774461196511 3.56226385946836 4.22157654526793 Columns 5 through 8 4.12132034355964 3.63506112074366 3.18585215990695 3.00061592475332 Column 9 3.00000000000000»%g was the list of sine sequences; »% but you can also think of it as a sequence of lists »%with each list being the values for the three sinewaves at different times in the sequence.»%you are doing an inner product between [1 2 3] and each column (list) of the sine sequence.»%at each time in the sequence, you are scaling each sine wave by a different amount then adding them together.»%g = [sine1(t0) sine1(t1) sine1(t2)... sine2(t0) sine2(t1) sine2(t2).. sine3(t0) sine3(t1) sine3(t2)...]»%[1 2 3]*g=[1*sin1(t0)+2*sin2(t0)+3*sine(t0), 1*sin1(t1)+2*sine2(t1)+3*sine3(t1), ...=====Function:input: f (row),X(row),fs(scalar),dur(scalar)output: xx(row)function xx=sumcos(f,X,fs,dur)...xx =?save as sumcos.m======»z1=5*exp(j*0.5*pi);»z2=5*exp(j*-0.25*pi);»zp=sumcos([1, 1/3],[z1,z2],10,1)zp = Columns 1 through 4 3.53553390593274 1.25442657826475 -0.08738044898976 0.18315912149992 Columns 5 through 8 2.05422141231050 4.82962913144534 7.39395888240421 8.64101238876062 Columns 9 through 11 7.90188453672496 5.20887876016010 1.29409522551261»plot(zp)1 2 3 4 5 6 7 8 9 10