digital signal processing with examples in m atlab ® chap 1 introduction ming-hong shih, aug 25,...

Digital Signal Processingwith Examples in MATLAB®

Chap 1 Introduction

Ming-Hong Shih, Aug 25, 2003

Ming-Hong Shih Digital Signal Processing with Example in MATLAB

2

Introduction to MATLAB

Why is MATLAB in use by a large fraction of

the DSP community?

(1)The user do most DSP operations

with very simple lines of code.

(2)MATLAB’s graphics support.

(3)Don’t to be an expert in MATLAB.


3

Variables, Vectors, Matrices, and Arrays

1. Variable: 一個單獨的元素 ( 整數、實數、複數 ) 。

2. 向量 (Vector): 一維的矩陣，可分為 Column Vectors 及 Row Vectors 。

3. 矩陣 (Matrices): 二維的陣列，一維向量為其特例。

4. 陣列 (Arrays): Using array as an inclusive term to designate a vector or a matrix.


4

Variables, Vectors, Matrices, and Arrays

──→ Variable

──→ Vector

──→ Matrix


5

Indexing a matrix

A=[1 2; 3 4]; A(1,1)=1; % the index starts from 1 A(1,2)=2; A(2,1)=3; A(2,2)=4;


6

Array Operation - Sum(+) and Difference(-)

The sum or difference of two array is obtained simply by adding or subtracting the individual element.

122

211

143

021


7

Array Operation - Sum(+) and Difference(-) (cont.)

Dimensions must be the same

unless one variable is a scalar.

矩陣與純量可以直接進行加減，MATLAB 會直接將加減應用到每一個元素。


8

Array Operation - Product(*)

純量對矩陣的乘或除，可比照一般寫法。

矩陣與純量可以直接進行乘法，MATLAB 會直接將乘法應用到每一個元素。


9

Array Operation - Product(*) (cont.)

進行矩陣相乘，必需確認第一個矩陣的直行數目 (Column Dimension) 必需等於第二個矩陣的橫列數目 (Row Dimension)，否則其乘法無從定義， MATLAB 會產生錯誤訊息。

72

32

11

21

10

*243

021


10

Array Operation - Exponentiation(^)

矩陣的次方運算，可由「 ^ 」來達成，但矩陣必需是方矩陣，其次方運算才有意義。

2227

1831

43

25

43

25

43

252


11

Array Operation - Product(.*) and Exponentiation(.^)

83

610

21

32

43

25

若在「 * 」及「 ^ 」之前加上一個句點， MATLAB 將會執行矩陣內「元素對元素」(Element-by-element) 的運算

163

825

21

32^

43

25


12

Array Operation - Transpose( ′ and . ′)

654

321a

63

52

41

ca

若處理的是實數，那麼 ‘ 和 .‘ 後的結果是一樣的。

63

52

41

da


13

Array Operation - Transpose( ′ and . ′) (cont.)

jjb 4321

j

jeb

43

21若處理的是複數，那麼 ′和 .′ 後的結果是不一樣的。所以，若不希望conjugation 出現，就要用 .′ 。

j

jfb

43

21


14

Example – M-file

% ex1.mA=[1 2 3 4 2; 3 4 2 1 2; 4 2 1 2 3; 1 2 3 4 2];map=[0 0 0; 85/255 85/255 85/255; 170/255 170/255 170/255; 1 1 1]; image(A); colormap(map); colorbar;


15

Example – M-file(cont.)


16

Matlab functions

Matlab has lot of toolboxes, which contain many functions

help function-name On-line help for a function

lookfor keyword Search for functions that are related to this key

word


17

Loop

Example:

for i=1:1:10

a(i) = i;

end;


18

Laboratory exercise #1 Read and show an image:

> I=double(imread(‘swim.bmp’));

> imshow(I, []);

Perform the following operation to matrix I:

1 2 3 4

2 2 3 4

3 4 3 2

1 3 2 4

1 2 3 4

2 2.55

3

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digital signal processing with examples in m atlab ® chap 1 introduction ming-hong shih, aug 25,...

Documents

matlab functions matlab

matlab element

loop example

element slide

keyword slide

introduction minghong

end slide

array operation product