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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 66 69 6c 74 65 72 20 |\section|{filter |
|00000010| 2d 2d 2d 20 44 69 67 69 | 74 61 6c 20 46 69 6c 74 |--- Digi|tal Filt|
|00000020| 65 72 20 53 74 72 75 63 | 74 75 72 65 7d 0d 5c 6c |er Struc|ture}.\l|
|00000030| 61 62 65 6c 7b 66 6e 3a | 66 69 6c 74 65 72 7d 0d |abel{fn:|filter}.|
|00000040| 5c 69 6e 64 65 78 7b 66 | 69 6c 74 65 72 28 29 7d |\index{f|ilter()}|
|00000050| 0d 5c 69 6e 64 65 78 7b | 64 69 67 69 74 61 6c 20 |.\index{|digital |
|00000060| 66 69 6c 74 65 72 20 73 | 74 72 75 63 74 75 72 65 |filter s|tructure|
|00000070| 7d 0d 5c 69 6e 64 65 78 | 7b 66 69 6c 74 65 72 69 |}.\index|{filteri|
|00000080| 6e 67 21 64 69 67 69 74 | 61 6c 7d 0d 5c 62 65 67 |ng!digit|al}.\beg|
|00000090| 69 6e 7b 72 61 69 6c 7d | 0d 46 69 6c 74 65 72 20 |in{rail}|.Filter |
|000000a0| 3a 20 27 66 69 6c 74 65 | 72 27 20 27 28 27 20 4d |: 'filte|r' '(' M|
|000000b0| 61 74 72 69 78 20 27 2c | 27 20 4d 61 74 72 69 78 |atrix ',|' Matrix|
|000000c0| 20 27 2c 27 20 4d 61 74 | 72 69 78 20 28 20 27 2c | ',' Mat|rix ( ',|
|000000d0| 27 20 20 28 4d 61 74 72 | 69 78 29 3f 20 29 3f 20 |'  (Matr|ix)? )? |
|000000e0| 27 29 27 20 3b 0d 5c 65 | 6e 64 7b 72 61 69 6c 7d |')' ;.\e|nd{rail}|
|000000f0| 0d 0d 5c 76 65 72 62 2b | 66 69 6c 74 65 72 2b 20 |..\verb+|filter+ |
|00000100| 69 73 20 61 20 66 72 61 | 6d 65 77 6f 72 6b 20 74 |is a fra|mework t|
|00000110| 68 61 74 20 61 6c 6c 6f | 77 73 20 79 6f 75 20 74 |hat allo|ws you t|
|00000120| 6f 20 70 65 72 66 6f 72 | 6d 69 6e 67 20 66 69 6c |o perfor|ming fil|
|00000130| 74 65 72 69 6e 67 0d 75 | 73 69 6e 67 20 20 66 69 |tering.u|sing  fi|
|00000140| 6e 69 74 65 20 69 6d 70 | 75 6c 73 65 20 72 65 73 |nite imp|ulse res|
|00000150| 70 6f 6e 73 65 20 28 46 | 49 52 29 20 6f 72 20 69 |ponse (F|IR) or i|
|00000160| 6e 66 69 6e 69 74 65 20 | 69 6d 70 75 6c 73 65 0d |nfinite |impulse.|
|00000170| 72 65 73 70 6f 6e 73 65 | 20 28 49 49 52 29 20 74 |response| (IIR) t|
|00000180| 65 63 68 6e 69 71 75 65 | 73 2e 20 20 0d 0d 45 61 |echnique|s.  ..Ea|
|00000190| 63 68 20 6d 61 74 72 69 | 78 20 61 72 67 75 6d 65 |ch matri|x argume|
|000001a0| 6e 74 20 6d 75 73 74 20 | 62 65 20 61 20 72 65 61 |nt must |be a rea|
|000001b0| 6c 20 72 6f 77 20 6f 72 | 20 63 6f 6c 75 6d 6e 20 |l row or| column |
|000001c0| 76 65 63 74 6f 72 20 28 | 6f 72 20 61 20 73 63 61 |vector (|or a sca|
|000001d0| 6c 61 72 2c 0d 77 68 69 | 63 68 20 77 69 6c 6c 20 |lar,.whi|ch will |
|000001e0| 62 65 20 63 6f 6e 76 65 | 72 74 65 64 20 74 6f 20 |be conve|rted to |
|000001f0| 61 20 6f 6e 65 20 65 6c | 65 6d 65 6e 74 20 76 65 |a one el|ement ve|
|00000200| 63 74 6f 72 29 2e 20 20 | 54 68 65 20 66 69 72 73 |ctor).  |The firs|
|00000210| 74 0d 61 72 67 75 6d 65 | 6e 74 20 63 6f 6e 74 61 |t.argume|nt conta|
|00000220| 69 6e 73 20 74 68 65 20 | 7a 65 72 6f 73 20 6f 66 |ins the |zeros of|
|00000230| 20 74 68 65 20 74 72 61 | 6e 73 66 65 72 20 66 75 | the tra|nsfer fu|
|00000240| 6e 63 74 69 6f 6e 20 2d | 2d 2d 20 63 61 6c 6c 20 |nction -|-- call |
|00000250| 69 74 20 5c 5e 7b 62 7d | 2c 0d 63 6f 6e 74 61 69 |it \^{b}|,.contai|
|00000260| 6e 69 6e 67 20 24 6e 62 | 24 20 74 65 72 6d 73 20 |ning $nb|$ terms |
|00000270| 66 72 6f 6d 20 5c 28 20 | 5b 62 5f 7b 31 7d 2c 62 |from \( |[b_{1},b|
|00000280| 5f 7b 32 7d 2c 5c 6c 64 | 6f 74 73 2c 62 5f 7b 6e |_{2},\ld|ots,b_{n|
|00000290| 62 7d 5d 20 5c 29 2e 20 | 20 54 68 65 20 6e 65 78 |b}] \). | The nex|
|000002a0| 74 0d 61 72 67 75 6d 65 | 6e 74 20 63 6f 6e 74 61 |t.argume|nt conta|
|000002b0| 69 6e 73 20 74 68 65 20 | 70 6f 6c 65 73 20 6f 66 |ins the |poles of|
|000002c0| 20 74 68 65 20 74 72 61 | 6e 73 66 65 72 20 66 75 | the tra|nsfer fu|
|000002d0| 6e 63 74 69 6f 6e 20 2d | 2d 2d 20 63 61 6c 6c 20 |nction -|-- call |
|000002e0| 69 74 20 5c 5e 7b 61 7d | 2c 0d 63 6f 6e 74 61 69 |it \^{a}|,.contai|
|000002f0| 6e 69 6e 67 20 24 6e 61 | 24 20 74 65 72 6d 73 20 |ning $na|$ terms |
|00000300| 66 72 6f 6d 20 5c 28 20 | 5b 61 5f 7b 31 7d 2c 61 |from \( |[a_{1},a|
|00000310| 5f 7b 32 7d 2c 5c 6c 64 | 6f 74 73 2c 61 5f 7b 6e |_{2},\ld|ots,a_{n|
|00000320| 61 7d 5d 20 5c 29 2e 20 | 5c 66 6f 6f 74 6e 6f 74 |a}] \). |\footnot|
|00000330| 65 7b 53 6f 6d 65 0d 74 | 65 78 74 20 62 6f 6f 6b |e{Some.t|ext book|
|00000340| 73 28 20 65 2e 67 2e 20 | 52 61 62 69 6e 65 72 20 |s( e.g. |Rabiner |
|00000350| 61 6e 64 20 47 6f 6c 64 | 2c 20 54 68 65 6f 72 79 |and Gold|, Theory|
|00000360| 20 61 6e 64 20 41 70 70 | 6c 69 63 61 74 69 6f 6e | and App|lication|
|00000370| 20 6f 66 20 44 69 67 69 | 74 61 6c 0d 53 69 67 6e | of Digi|tal.Sign|
|00000380| 61 6c 20 50 72 6f 63 65 | 73 73 69 6e 67 29 20 75 |al Proce|ssing) u|
|00000390| 73 65 20 74 68 65 73 65 | 20 73 61 6d 65 20 76 61 |se these| same va|
|000003a0| 72 69 61 62 6c 65 73 20 | 69 6e 20 74 68 65 20 6f |riables |in the o|
|000003b0| 70 70 6f 73 69 74 65 20 | 73 65 6e 73 65 7d 2e 0d |pposite |sense}..|
|000003c0| 0d 4e 6f 74 65 20 74 68 | 61 74 20 74 68 65 20 5c |.Note th|at the \|
|000003d0| 28 20 61 5f 7b 31 7d 20 | 5c 29 20 74 65 72 6d 20 |( a_{1} |\) term |
|000003e0| 6d 75 73 74 20 6e 6f 74 | 20 62 65 20 7a 65 72 6f |must not| be zero|
|000003f0| 2c 20 61 73 20 61 6c 6c | 20 74 68 65 20 6f 74 68 |, as all| the oth|
|00000400| 65 72 20 74 65 72 6d 73 | 0d 61 72 65 20 64 69 76 |er terms|.are div|
|00000410| 69 64 65 64 20 62 79 20 | 74 68 69 73 20 74 65 72 |ided by |this ter|
|00000420| 6d 20 69 6e 20 61 20 70 | 72 65 70 72 6f 63 65 73 |m in a p|reproces|
|00000430| 73 69 6e 67 20 73 74 61 | 67 65 2e 20 20 49 66 20 |sing sta|ge.  If |
|00000440| 79 6f 75 20 61 72 65 0d | 61 74 74 65 6d 70 74 69 |you are.|attempti|
|00000450| 6e 67 20 74 6f 20 6d 61 | 6b 65 20 61 20 46 49 52 |ng to ma|ke a FIR|
|00000460| 20 66 69 6c 74 65 72 20 | 28 7a 65 72 6f 73 20 6f | filter |(zeros o|
|00000470| 6e 6c 79 29 2c 20 74 68 | 69 73 20 74 65 72 6d 20 |nly), th|is term |
|00000480| 69 73 20 6e 6f 72 6d 61 | 6c 6c 79 0d 73 65 74 20 |is norma|lly.set |
|00000490| 74 6f 20 24 31 24 2e 0d | 0d 54 68 65 20 6e 65 78 |to $1$..|.The nex|
|000004a0| 74 20 61 72 67 75 6d 65 | 6e 74 20 69 73 20 74 68 |t argume|nt is th|
|000004b0| 65 20 69 6e 70 75 74 20 | 73 74 72 65 61 6d 20 74 |e input |stream t|
|000004c0| 6f 20 74 68 65 20 66 69 | 6c 74 65 72 2c 20 75 73 |o the fi|lter, us|
|000004d0| 75 61 6c 6c 79 20 64 65 | 6e 6f 74 65 64 0d 61 73 |ually de|noted.as|
|000004e0| 20 5c 5e 7b 78 7d 2c 20 | 63 6f 6e 74 61 69 6e 69 | \^{x}, |containi|
|000004f0| 6e 67 20 24 6e 78 24 20 | 74 65 72 6d 73 2c 20 66 |ng $nx$ |terms, f|
|00000500| 72 6f 6d 5c 28 20 5b 78 | 5f 7b 31 7d 2c 78 5f 7b |rom\( [x|_{1},x_{|
|00000510| 32 7d 2c 5c 6c 64 6f 74 | 73 2c 78 5f 7b 6e 78 7d |2},\ldot|s,x_{nx}|
|00000520| 5d 20 5c 29 2e 20 0d 0d | 54 68 65 20 6c 61 73 74 |] \). ..|The last|
|00000530| 20 61 72 67 20 69 73 20 | 61 6e 20 6f 70 74 69 6f | arg is |an optio|
|00000540| 6e 61 6c 20 76 65 63 74 | 6f 72 20 6f 66 20 74 68 |nal vect|or of th|
|00000550| 65 20 69 6e 69 74 69 61 | 6c 20 76 61 6c 75 65 73 |e initia|l values|
|00000560| 20 69 6e 20 65 61 63 68 | 20 64 65 6c 61 79 20 62 | in each| delay b|
|00000570| 69 6e 2e 0d 49 74 20 6d | 75 73 74 20 68 61 76 65 |in..It m|ust have|
|00000580| 20 6e 75 6d 62 65 72 20 | 6f 66 20 74 65 72 6d 73 | number |of terms|
|00000590| 20 65 71 75 61 6c 20 74 | 6f 20 74 68 65 20 6d 61 | equal t|o the ma|
|000005a0| 78 69 6d 75 6d 20 6f 66 | 0d 74 68 65 20 6c 65 6e |ximum of|.the len|
|000005b0| 67 74 68 20 6f 66 20 41 | 20 6f 72 20 42 2e 0d 0d |gth of A| or B...|
|000005c0| 54 68 65 20 66 69 6c 74 | 65 72 20 6f 75 74 70 75 |The filt|er outpu|
|000005d0| 74 73 20 61 72 65 20 69 | 6e 20 61 20 6c 69 73 74 |ts are i|n a list|
|000005e0| 20 77 69 74 68 20 65 6c | 65 6d 65 6e 74 73 20 6e | with el|ements n|
|000005f0| 61 6d 65 64 20 5c 76 65 | 72 62 2b 79 2b 2c 0d 77 |amed \ve|rb+y+,.w|
|00000600| 68 69 63 68 20 69 73 20 | 74 68 65 20 6f 75 74 70 |hich is |the outp|
|00000610| 75 74 20 6f 66 20 74 68 | 65 20 66 69 6c 74 65 72 |ut of th|e filter|
|00000620| 20 2d 20 69 74 20 68 61 | 73 20 74 68 65 20 73 61 | - it ha|s the sa|
|00000630| 6d 65 20 6e 75 6d 62 65 | 72 20 6f 66 20 74 65 72 |me numbe|r of ter|
|00000640| 6d 73 20 61 73 0d 74 68 | 65 20 69 6e 70 75 74 3b |ms as.th|e input;|
|00000650| 20 61 6e 64 20 5c 76 65 | 72 62 2b 7a 66 2b 2c 20 | and \ve|rb+zf+, |
|00000660| 77 68 69 63 68 20 69 73 | 20 61 20 76 65 63 74 6f |which is| a vecto|
|00000670| 72 20 6f 66 20 74 68 65 | 20 66 69 6e 61 6c 20 76 |r of the| final v|
|00000680| 61 6c 75 65 73 20 69 6e | 0d 65 61 63 68 20 62 69 |alues in|.each bi|
|00000690| 6e 2e 0d 0d 54 68 65 20 | 72 65 73 75 6c 74 20 69 |n...The |result i|
|000006a0| 73 20 63 61 6c 63 75 6c | 61 74 65 64 20 62 79 0d |s calcul|ated by.|
|000006b0| 0d 5c 5b 20 79 5f 7b 6e | 7d 20 3d 20 62 5f 7b 31 |.\[ y_{n|} = b_{1|
|000006c0| 7d 78 5f 7b 6e 7d 20 2b | 20 62 5f 7b 32 7d 78 5f |}x_{n} +| b_{2}x_|
|000006d0| 7b 6e 2d 31 7d 20 2b 20 | 5c 6c 64 6f 74 73 20 2b |{n-1} + |\ldots +|
|000006e0| 20 62 5f 7b 6e 62 2b 31 | 7d 78 5f 7b 6e 2d 6e 62 | b_{nb+1|}x_{n-nb|
|000006f0| 7d 20 2d 20 61 5f 7b 32 | 7d 79 5f 7b 6e 2d 31 7d |} - a_{2|}y_{n-1}|
|00000700| 20 2d 20 5c 6c 64 6f 74 | 73 20 2d 20 61 5f 7b 6e | - \ldot|s - a_{n|
|00000710| 61 2b 31 7d 79 5f 7b 6e | 2d 6e 61 7d 20 5c 5d 0d |a+1}y_{n|-na} \].|
|00000720| 0d 0d 5c 70 61 72 61 67 | 72 61 70 68 7b 45 78 61 |..\parag|raph{Exa|
|00000730| 6d 70 6c 65 7d 0d 5c 69 | 6e 64 65 78 7b 65 78 61 |mple}.\i|ndex{exa|
|00000740| 6d 70 6c 65 20 6f 66 20 | 66 69 6c 74 65 72 28 29 |mple of |filter()|
|00000750| 7d 0d 5c 69 6e 64 65 78 | 7b 66 69 6c 74 65 72 28 |}.\index|{filter(|
|00000760| 29 21 65 78 61 6d 70 6c | 65 7d 0d 5c 62 65 67 69 |)!exampl|e}.\begi|
|00000770| 6e 7b 76 65 72 62 61 74 | 69 6d 7d 0d 3e 20 2f 2f |n{verbat|im}.> //|
|00000780| 20 57 65 20 77 61 6e 74 | 20 61 20 62 61 6e 64 70 | We want| a bandp|
|00000790| 61 73 73 20 66 69 6c 74 | 65 72 2c 20 75 6e 69 74 |ass filt|er, unit|
|000007a0| 79 20 67 61 69 6e 20 66 | 72 6f 6d 20 30 2e 32 20 |y gain f|rom 0.2 |
|000007b0| 74 6f 20 30 2e 34 0d 3e | 20 2f 2f 20 52 65 66 65 |to 0.4.>| // Refe|
|000007c0| 72 20 57 69 6c 6c 69 61 | 6d 73 20 61 6e 64 20 54 |r Willia|ms and T|
|000007d0| 61 79 6c 6f 72 2c 20 27 | 45 6c 65 63 74 72 6f 6e |aylor, '|Electron|
|000007e0| 69 63 20 46 69 6c 74 65 | 72 20 44 65 73 69 67 6e |ic Filte|r Design|
|000007f0| 20 48 61 6e 64 62 6f 6f | 6b 27 2c 0d 3e 20 2f 2f | Handboo|k',.> //|
|00000800| 20 45 78 61 6d 70 6c 65 | 20 31 33 2e 31 2c 20 70 | Example| 13.1, p|
|00000810| 61 67 65 20 31 33 2d 38 | 2e 20 20 33 31 73 74 20 |age 13-8|.  31st |
|00000820| 6f 72 64 65 72 20 46 49 | 52 2e 20 20 55 73 65 20 |order FI|R.  Use |
|00000830| 74 68 65 69 72 20 63 6f | 2d 65 66 66 69 63 69 65 |their co|-efficie|
|00000840| 6e 74 73 0d 3e 20 62 20 | 3d 20 5b 20 30 2e 30 33 |nts.> b |= [ 0.03|
|00000850| 38 32 30 2c 30 2e 30 31 | 35 35 31 2c 30 2e 30 38 |820,0.01|551,0.08|
|00000860| 33 37 36 2c 2d 30 2e 31 | 32 35 32 35 2c 2d 30 2e |376,-0.1|2525,-0.|
|00000870| 30 35 31 33 34 2c 30 2e | 30 31 34 38 31 2c 2d 30 |05134,0.|01481,-0|
|00000880| 2e 30 31 34 36 31 2c 20 | 2e 2e 2e 0d 30 2e 30 33 |.01461, |....0.03|
|00000890| 36 31 36 2c 2d 30 2e 30 | 38 36 34 35 2c 2d 30 2e |616,-0.0|8645,-0.|
|000008a0| 30 33 35 39 32 2c 30 2e | 30 30 39 30 36 2c 30 2e |03592,0.|00906,0.|
|000008b0| 30 31 34 36 32 2c 30 2e | 31 34 39 36 33 2c 2d 30 |01462,0.|14963,-0|
|000008c0| 2e 32 35 37 38 36 2c 2d | 30 2e 31 32 38 32 35 2c |.25786,-|0.12825,|
|000008d0| 20 2e 2e 2e 0d 30 2e 34 | 31 32 35 36 2c 2d 30 2e | ....0.4|1256,-0.|
|000008e0| 31 32 38 32 35 2c 2d 30 | 2e 32 35 37 38 36 2c 30 |12825,-0|.25786,0|
|000008f0| 2e 31 34 39 36 33 2c 30 | 2e 30 31 34 36 32 2c 30 |.14963,0|.01462,0|
|00000900| 2e 30 30 39 30 36 2c 2d | 30 2e 30 33 35 39 32 2c |.00906,-|0.03592,|
|00000910| 2d 30 2e 30 38 36 34 35 | 2c 20 2e 2e 2e 0d 30 2e |-0.08645|, ....0.|
|00000920| 30 33 36 31 36 2c 2d 30 | 2e 30 31 34 36 31 2c 30 |03616,-0|.01461,0|
|00000930| 2e 30 31 34 38 31 2c 2d | 30 2e 30 35 31 33 34 2c |.01481,-|0.05134,|
|00000940| 2d 30 2e 31 32 35 32 35 | 2c 30 2e 30 38 33 37 36 |-0.12525|,0.08376|
|00000950| 2c 30 2e 30 31 35 35 31 | 2c 30 2e 30 33 38 32 30 |,0.01551|,0.03820|
|00000960| 5d 0d 20 62 20 3d 0d 20 | 6d 61 74 72 69 78 20 63 |]. b =. |matrix c|
|00000970| 6f 6c 75 6d 6e 73 20 31 | 20 74 68 72 75 20 36 0d |olumns 1| thru 6.|
|00000980| 20 20 20 30 2e 30 33 38 | 32 20 20 20 20 20 30 2e |   0.038|2     0.|
|00000990| 30 31 35 35 20 20 20 20 | 20 30 2e 30 38 33 38 20 |0155    | 0.0838 |
|000009a0| 20 20 20 20 2d 30 2e 31 | 32 35 20 20 20 20 2d 30 |    -0.1|25    -0|
|000009b0| 2e 30 35 31 33 20 20 20 | 20 20 30 2e 30 31 34 38 |.0513   |  0.0148|
|000009c0| 20 20 0d 0d 20 6d 61 74 | 72 69 78 20 63 6f 6c 75 |  .. mat|rix colu|
|000009d0| 6d 6e 73 20 37 20 74 68 | 72 75 20 31 32 0d 20 20 |mns 7 th|ru 12.  |
|000009e0| 2d 30 2e 30 31 34 36 20 | 20 20 20 20 30 2e 30 33 |-0.0146 |    0.03|
|000009f0| 36 32 20 20 20 20 2d 30 | 2e 30 38 36 34 20 20 20 |62    -0|.0864   |
|00000a00| 20 2d 30 2e 30 33 35 39 | 20 20 20 20 30 2e 30 30 | -0.0359|    0.00|
|00000a10| 39 30 36 20 20 20 20 20 | 30 2e 30 31 34 36 20 20 |906     |0.0146  |
|00000a20| 0d 0d 20 6d 61 74 72 69 | 78 20 63 6f 6c 75 6d 6e |.. matri|x column|
|00000a30| 73 20 31 33 20 74 68 72 | 75 20 31 38 0d 20 20 20 |s 13 thr|u 18.   |
|00000a40| 20 20 30 2e 31 35 20 20 | 20 20 20 2d 30 2e 32 35 |  0.15  |   -0.25|
|00000a50| 38 20 20 20 20 20 2d 30 | 2e 31 32 38 20 20 20 20 |8     -0|.128    |
|00000a60| 20 20 30 2e 34 31 33 20 | 20 20 20 20 2d 30 2e 31 |  0.413 |    -0.1|
|00000a70| 32 38 20 20 20 20 20 2d | 30 2e 32 35 38 20 20 0d |28     -|0.258  .|
|00000a80| 0d 20 6d 61 74 72 69 78 | 20 63 6f 6c 75 6d 6e 73 |. matrix| columns|
|00000a90| 20 31 39 20 74 68 72 75 | 20 32 34 0d 20 20 20 20 | 19 thru| 24.    |
|00000aa0| 20 30 2e 31 35 20 20 20 | 20 20 30 2e 30 31 34 36 | 0.15   |  0.0146|
|00000ab0| 20 20 20 20 30 2e 30 30 | 39 30 36 20 20 20 20 2d |    0.00|906    -|
|00000ac0| 30 2e 30 33 35 39 20 20 | 20 20 2d 30 2e 30 38 36 |0.0359  |  -0.086|
|00000ad0| 34 20 20 20 20 20 30 2e | 30 33 36 32 20 20 0d 0d |4     0.|0362  ..|
|00000ae0| 20 6d 61 74 72 69 78 20 | 63 6f 6c 75 6d 6e 73 20 | matrix |columns |
|00000af0| 32 35 20 74 68 72 75 20 | 33 30 0d 20 20 2d 30 2e |25 thru |30.  -0.|
|00000b00| 30 31 34 36 20 20 20 20 | 20 30 2e 30 31 34 38 20 |0146    | 0.0148 |
|00000b10| 20 20 20 2d 30 2e 30 35 | 31 33 20 20 20 20 20 2d |   -0.05|13     -|
|00000b20| 30 2e 31 32 35 20 20 20 | 20 20 30 2e 30 38 33 38 |0.125   |  0.0838|
|00000b30| 20 20 20 20 20 30 2e 30 | 31 35 35 20 20 0d 0d 20 |     0.0|155  .. |
|00000b40| 6d 61 74 72 69 78 20 63 | 6f 6c 75 6d 6e 73 20 33 |matrix c|olumns 3|
|00000b50| 31 20 74 68 72 75 20 33 | 31 0d 20 20 20 30 2e 30 |1 thru 3|1.   0.0|
|00000b60| 33 38 32 20 20 0d 3e 20 | 61 20 3d 20 31 3b 0d 3e |382  .> |a = 1;.>|
|00000b70| 20 78 20 3d 20 5b 31 3b | 20 7a 65 72 6f 73 28 39 | x = [1;| zeros(9|
|00000b80| 39 2c 31 29 5d 3b 0d 3e | 20 2f 2f 20 74 68 69 73 |9,1)];.>| // this|
|00000b90| 20 69 73 20 75 73 65 66 | 75 6c 20 66 6f 72 20 74 | is usef|ul for t|
|00000ba0| 68 65 20 70 6c 6f 74 0d | 3e 20 74 20 3d 20 30 3a |he plot.|> t = 0:|
|00000bb0| 31 3a 30 2e 30 31 3b 0d | 3e 20 6f 75 74 70 75 74 |1:0.01;.|> output|
|00000bc0| 20 3d 20 66 69 6c 74 65 | 72 28 62 2c 61 2c 78 29 | = filte|r(b,a,x)|
|00000bd0| 3b 0d 3e 20 70 6c 6f 74 | 28 5b 74 27 2c 6c 6f 67 |;.> plot|([t',log|
|00000be0| 28 66 66 74 28 78 29 29 | 5d 29 3b 0d 3e 20 70 6c |(fft(x))|]);.> pl|
|00000bf0| 6f 74 28 5b 74 27 2c 6c | 6f 67 28 66 66 74 28 6f |ot([t',l|og(fft(o|
|00000c00| 75 74 70 75 74 2e 79 29 | 29 5d 29 3b 0d 5c 65 6e |utput.y)|)]);.\en|
|00000c10| 64 7b 76 65 72 62 61 74 | 69 6d 7d 0d 0d 5c 6e 65 |d{verbat|im}..\ne|
|00000c20| 77 70 61 67 65 0d 0d 0d | 0d 0d 0d 0d             |wpage...|....    |
+--------+-------------------------+-------------------------+--------+--------+