Digital Signal and Image Processing using MATLAB

1 downloads 0 Views 6MB Size Report
tal relation between linear filtering with rational transfer functions and linear ...... The exponents T and H refer to the transposition and the transposition- conjugation ..... Using the properties of the continuous-time Fourier transform, show that ..... The answers to these questions are provided by the sampling theorem 2.1.
Digital Signal and Image Processing using MATLAB®

This page intentionally left blank

Digital Signal and Image Processing using MATLAB®

Gérard Blanchet Maurice Charbit

Part of this book adapted from “Signaux et images sous Matlab : méthodes, applications et exercices corrigés” published in France by Hermès Science Publications in 2001 First published in Great Britain and the United States in 2006 by ISTE Ltd Translated by Antoine Hervier Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 6 Fitzroy Square London W1T 5DX UK

ISTE USA 4308 Patrice Road Newport Beach, CA 92663 USA

www.iste.co.uk © HERMES Science Europe Ltd, 2001 © ISTE Ltd, 2006 The rights of Gérard Blanchet and Maurice Charbit to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Blanchet, Gérard. [Signaux et images sous Matlab. English] Digital signal and image processing using Matlab / Gérard Blanchet, Maurice Charbit. p. cm. Translation of: Signaux et images sous Matlab. Includes index. ISBN-13: 978-1-905209-13-2 ISBN-10: 1-905209-13-4 1. Signal processing--Digital techniques--Data processing. 2. MATLAB. I.Charbit, Maurice. II. Title. TK5102.9.B545 2006 621.382'2--dc22 2006012690 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 10: 1-905209-13-4 ISBN 13: 978-1-905209-13-2 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.

 Ê                               Ê                                Ê                    

This page intentionally left blank

  



     



                                                                    "                 $%                     & %              '  %             " 

   )         *                  +             !   &                # $ +               ,  -  %         -  %                .%+   % -  

           "  -  +   -       % /  %                    !  - ' -                  

 

                 

                 

                 

                 

                 

                 

                 

                 

   

"+%   0 -  1    +  %  -                ' -               0%  %    -    + " %               0                   

   ! #   (        !   (

     

    

    

    

    

    

    

    

    

    

    

   ! , (

, 2 -  0 -    -  

-  -  Ê "+%   2     0 -    0%  + % - +                                 2 - 3 3  -           

-  -                0%  %                   2  3  1      4215  2   1      4215      1 1                    

       

       

       

       

       

       

       

   ! ! !# !# # ##

"+%   0%  $   0%                 $     %& &%     

-   + 21       16                78

 '  ' - +     0+   1                 0 - %                      %%  &%   &          %              16             

         

         

         

         

         

         

         

, , , , , ,# (    ,

         

"+%     1    2*   % %                       + 3                               2*   % %                    ' &%                              *  -                    2 8  6     1 *              0                       19   9 *                       "                  " - +  %                   0     + :                  "   ' -   %  /)             !   %+  *                        # 1    -  +                         # . -   +    3  *  +   3

 *                           # 19 *   -  - + '  '  +        # 9 *   -                      , $ % -     % -                 , $ % -                      

( ( (! (! (# (     # ,     # # ( 

" 

 ,

;  % -                       

"+%   1   %   1   %                       7&%  *                2   - +     19 *   19  < *  -                   11 *  -                      1    <                           2    &%              1    <                    

       

       

       

   ! ! !# # # ##

"+%  !     -  

!                         ! -  % =    %

         ! %  - -              !  +     -  %    ! .         -       ! + %             !  - - -               ! 16      -           !   *  -                     ! $ + % -             ! ;  % -                ! $ % -                ! "                 !   *  -               ! &   +            !! -   )              !#  %+  -  *  -    -  !! : 7. 

 %

              !!   -  +               !! > - +  %

      !! > - +  %

     !# > < -                     !# 0%  - ' < -        !# 0%  - ' < -       

                       

                       

                       

,# ,# ,#   ! !  ( (# # # # ( ! #   ! ! # (   

 

!" 

                       

                       

                       

                       

#

"+%  # 9     # # 9   %+   -  % 

-             # #    %

                     ,

( 2 -  0 -    -  

-  -  Ê #

# #

"  %                    # ;   %      4 5      # 9 .

                 # " %& .

              # .  - +   %       # 7  - + %             #! .

                    .  -   ' +  %  %           ;   6 )                     

        

        

! ! # ,  ! ! ! #(

"+%  , 9    

 ,                           , > 3     % 

             , 2*   % %   >00 % 

 , 0%  %     >00 % 

  , 0% -  >00 % 

           , 7  - +                    , 1   -     >00    % 

     , = 9   9                ,    4 ! !  5 % 

   ,   9 4 ! 5  

    , +  -  +             , 9 4 5 % 

            

           

           

           

           

           

# # # # #, , , ! ( ( (  

"+%   "   0%  7    3%      + 02          7    +         7    + %  -                             9                     7  - + %    9 % 

  + 2  +         

      

      

      

      

      

# # # (   # ,

"+%  ( 2   0%  7  ( 7  - + %    + 6     ( +     -  %& &%   ( 9 +   &            ( " %& +   &         (   -   +            ( ? -+    +                (    -      6  ( +   +               ( + ;0" -  +           (     % 

-     

         

         

         

         

         

     # , , ! !! #

         

         

" 

 "+%   +  06  +   + % @ +                    +  6  +                   1  - + %              +                      +  6               + 90 -  + 4   6 5    - + %   %    +     %   + >00 % 

         A3>00 +  % 

        -    93 % 

       9B  Æ 

  

 *      >   *  -                       1  %   %           .  -  +                >   6 )                + 0 4  65 -  +         +   % -  +           +  ) 0 -  +         7+   -                  ! %%  C + D -  +           ! + D *                 ! +                    

                      

                      

                      

                      

                      

, ,     ( ( (# (# (,   #  ( # ( (   ! ! 

"+%   0   %   0      3        0   %% &        7&             2    316  4215       0%+ % 

-                   %+ -              " %

-  %+ -        2>                            - +     -     0$                   +                  ! E )  +% -            # 7    +  /   = /$-

 + 6    C     '    ' +          +       % -                  H

   0

   & + +  J    

-    H

 

   & '+    J   H

      

   & '+    J  

 1       : 9 %; 

 6      -    

C  

   % =     + +    H '+  + % ! 4%  %+5   @-     &= + %3

! 4% 3%  %+5  %  ' +   @- -

           2     %C   ?@   

 ?    & "

 :  

 & "

 ?  



     

" # '        3  +  

#= #= "  %* C # 

;  ';= 5= 0= #=  = = 0= #= =  

    

 #         %C (  7  (:  !



( 6."$ 6      !



2 7 , 9#" # , 3@337 &36 !



B    4(  5   & A    +      % -=  +    + %  % -= +    ?C C D7 ( 6 # 7

9 /< /<  /< /
 +   + 4(  5   & #   +    #  # % = # %   +     + 3

 & # 

- 5    

+  -       +     - +  Ê  -- 0   %   ' + +  Ê % = '+  + +  %   =  %  &      - +     +    = +   '    &% *   +    +  + &%   5= +  - +  = +    -            + +    ' + -    - +  + 1      ((= + 2    0=   0   +     '

 +  Ê  --= '+  +  '

 +   --=     & %

 $ 6   

7     

  %C

 Ê  % + &  + 0    = '+ +        +     +3  ? '=  +  = (( & =  Ê   C = 0 

@@@ 4#:# (0#

 - + +    %    +

     



 2 -  0 -    -  

-  -  Ê  +      Ê =    +    '

  F G % - 4  %-%+ !5 ' '

   ' %%  F4#:#G

" ) (       ' +  = + 5       + &%    + 3   +   &  + %      ' + +   & &%   + 

 FG  +    +   5 3  3 > 3    + '   - ' +   &    1  &%=  *   C 

J O

 O

O  O

Q Q

     ' + +   5 3 +      ( +              &  %  ( 

" + 8       + #     +  -    +  -       & + =     + +   %    

      &=   %    '+  

  -    +      + 

  %   

 %  /     5   %C        

:  ?   :  :     +  +       - % - +  * +     % -

 +    '  ' 0+  % -       ' +    %  - +  * +   +=  

+    +   '  (0# Q  + ' %

 - +     - *=   +         + *=  +     

+ 

 + *      4   - ' +  R  5   % - 4     5   %  '+ +     &    '  +   + % -   -       + %

  '   '  +    %  +      Ê  +  ) +    %  '

     --

+  "=    1    +  % -  - + %  7S + -+  +   +   '   -  +  *   % %   

 +  %

 > '      - +      + + % +  

 @  + %    > '  

 + +      $ +  < '

 + 1          '    +   ' - *   +    %     > '    +  %  6  &%

 4* = &3 %

5=    6    +      6  

 4%  5 &%4 %$  5  



4   " "     

 

 $   %    7$%8    "   4% 5

> ' - < + % - +    - +  + + 1  

    +4  % 5 ! 4$ 5   = + 1       45= *   =   '

 C  4$ 5

J J

 





! 4$ 5 



4%  5  ! 4$ 5   

 





 4$  $5

J ! 4$ 5

 







4%  5   

45

+ =  $ -  - = +  8     4$  $5  %=    % 

 - !   4$ 5 J  4$  4-  - 55=  4$ 5

2     0 -    0% -  1 X(F) Ts F rect 2B ( F )

n =+

1 ∑ X ( F−nF s) Ts n =− Transition band F

−F s

−B −F s /2

B F s /2

Fs

   M %        &  ' +  4$ 5 1 -     +       -   +  = - J -   - J -  7&%  % * +' = ' '  

   ' + 45  + Æ        '

    ' C $ 4!5 +   6  -  + #"  "  0  +   = + 1        %

     ! 4$ 5 J    4$ 5=   + C

4 -5 4#5 + 45 J 

$

 +    + + *  ! 4$ 5 J    4$ 5 +  %

 *   $ 

     -  + - = + '  +   *  ' + -    4  1 - 5= < -  

 -  >+ + %

   = ' '     + %   - =   % '  +45   + 45

 5 4  +     = =   - +

I   =  3

   ' + + %  )  + %   4$ 5 ' + + %  $  

  ' + =   $  - = +  8 3) %

 + %  3 %= < - %   %

 + %% - %+        1 -     + %    - %+      -  '+  6     + F '3%

G %= %    - +

F* %G +   4$  O$ 5

! 2 -  0 -    -  

-  -  Ê 7&%  %    4  &%      5= ' '  

 + %  -    + %=  + +     * * +   %  1 X(F) Ts F rect F s( F )

1 n =+ ∑ X ( F−nF s) Ts n =− F

−F s

F s /2

Fs

  M      1    - = + ' -   -  + + 6     + 6  $    F -+  '  '

+ ' +  %

     ' % -    + = 

   + 1       + -  45 J  4%  5+4  %  5 -   &%

C  4$ 5

J ! 4$ 5 

 





 4$  $5

+   +   + =     4$ 5    ' +

+ '   ' -   +   C

 4$ 5=

 + %  )  

 4$  $5

 +   1 - !5

 

! 4$ 5

J



+ '   - 41 - !5H

$  $   $

  ( +'  4 

, 2 -  0 -    -  

-  -  Ê Fs

Fs

X(F)

−Fs

F −Fmax

−Fmin

Fmin

Fmax

  M &      + 3  -   45    6     '+ +  + +   ' - 6   C $  $  $   4 O 5$  $  $ '+ + 6  +   C $ $  $  4,5 O  '+   - + +    '+  + - %  $ 4$  $ 5 1   J (= >      - +  6 3 6  $ =     (= ' - %

 % - 6   + 

 + $  "  45  +   ' -    3

C

4 W$ 5 +45 J   4 $5 

' + W$ J $  $   $ J 4$ O $ 5 

'                45   = &%

 6  +  +  

%    4      5   %   *  < '  ? '3 =   +45     '   "+%    %    +   )   '   *  -    %   +  +  '+ +    

2     0 -    0% - 

     *  &     +    3   - C 45

J  4 $5 ' + $ J ( ?)

4(5

%   6   $ J ,(( ?) + % 6    '

    ' C  4%5 J 4% $5 J  4  %5 ' +  J $ $      +    3   -   6  $ J $  $ C 45 J  4 $ 5 ' + $ J ( ?)

%  +  6  $ J ,(( ?) + % 6  C  4%5 J 4% $ 5 J  4  %5 ' +  J $ $ ; - $ J $ O $= ' -  J  O  9% - 4%5   C  4%5 J  4 4 O 5%5 J  4  %5 J  4%5 +   + ' + +    % 4  4   4 4 :4  7,   77  7,> 7, , $  334 377    +     4%5 J  4%5  +    45 J 4 $ 5 '    4%5 J   4%5

9     

> '  ' %  ' % &% 

+ '   '  F+G +

%    - %+   + *  % 

   - %+   6   ,