Some Useful Operations of Matlab

4 Some useful operations on complex numbers:

4 Complex scalar >> x = 3+4j

4 Real part of x >> real(x) ->3

4 Imaginary part of x >> imag(x) ->4

4 Magnitude of x >> abs(x) ->5

4 Angle of x >> angle(x) ->0.9273

4 Complex conjugate of x >> conj(x) ->3 - 4i

>> x=[a:step:b]

4 Generate a vector that takes on the values a to b in increments of step

>> x=linspace(a,b,n)

4 generates a row vector x of n points linearly spaced between a and b

>> x=logspace(a,b,20)

4 generates a logarithmically spaced vector x of n points between 10^a and 10^b.

4 Matrix building functions:

>> A=zeros(m,n)

4 returns an m-by-n matrix of zeros

>> A=ones(m,n)

4 returns an m-by-n matrix of 1s

>> A=eye(m,n)

4 returns an m-by-n matrix with 1's on the diagonal and 0's elsewhere

>> A=rand(m,n)

4 returns an m-by-n matrix of random numbers whose elements are uniformly distributed in the interval (0,1)

>> A=randn(m,n)

4 returns an m-by-n matrix of random numbers whose elements are normally distributed with mean 0 and variance 1

>> A=randint(m,n,range)

4 generates an m-by-n integer matrix. The entries are uniformly distributed and independently chosen from the range:

4 [0, range-1] if range is a positive integer

4 [range+1, 0] if range is a negative integer

4 Elements of a matrix are accessed by specifying the row and column

>> A=[1 2 3; 4 5 6; 7 8 9];

>> x=A(1,3)

4 Returns the element in the first row and third column

>> y=A(2,:)

4 Returns the entire second row [4 5 6]

4 “:” means “take all the entries in the column”

>> B=A(1:2,1:3)

4 Returns a submatrix of A consisting of rows 1 and 2 and all three columns [1 2 3; 4 5 6]

4 The basic arithmetic operations on matrices are:

4 + addition

4 - subtraction

4 * multiplication

4 / division

4 ^ power

4 ’ conjugate transpose

4 MATLAB provides element-by-element operations by prepending a ‘.’ before the operator

4 .* multiplication

4 ./ division

4 .^ power

4 .’ transpose (unconjugated)

4 MATLAB defines the following relational operations:

4 < less than

4 <= less than or equal to

4 > greater than

4 >= greater than or equal to

4 == equal to

4 ~= not equal to

4 MATLAB defines the following logical operations:

4 & and

4 | or

4 ~ not

4 The following functions operate element-wise when applied to a matrix:

sin cos tan

asin acos atan

sinh cosh tanh

exp log(natural log) log10

abs sqrt sign

4 If statements

if expression

statements

else

statements

end

4 Example

If n<0

a=a-1;

else

a=a+1;

end

4 For

4 Repeats a group of statements a fixed, predetermined number of times.

a=0;

for n = 1:10

a=a+1;

end

To simplify your matlab file structure, you can use functions. An example of how to use matlab functions is the following:

Main Matlab Program

SegEqRx = SegEqNew + 1*SegRx(DimC*TTaps+1:LRx-DimC*TTaps);

clear SegEqNew; clear SegEqOld;

[SAMPLE_CENTRAL, BIT_DETECTED] = =syncronizer(SegEqRx,PNSEQ_VECTOR,NS_BIT,NBIT_PNSEQ);

…

Function declaration:

function [ SAMPLE_CENTRAL, BIT_DETECTED]

=syncro(SIGNAL,PNSEQ_VECTOR,NS_BIT,NBIT_PNSEQ);

Main of the function

>> plot(x,y)

4 produces a graph of y versus x, where x and y are two vectors

x=linspace(0,2*pi,100);

plot(x,sin(x));

4 It is possible to specify color, line styles, and markers when you plot your data using the plot command

plot(x,y,'color_style_marker')

4 color_style_marker is a string containing from one to four characters constructed from a color, a line style, and a marker type:

4 Color strings: 'c', 'm', 'y', 'r', 'g', 'b', 'w', and 'k'. These correspond to cyan, magenta, yellow, red, green, blue, white, and black

4 Linestyle strings are '-' for solid, '--' for dashed, ':' for dotted, '-.' for dash-dot, and 'none' for no line

4 The marker types are '+', 'o', '*' and 'x'

4 xlabel('string')

4 labels the x-axis of the current axes

4 ylabel('string')

4 labels the y-axis of the current axes

4 Title(‘string’)

4 add a title to a graph at the MATLAB command prompt or from an M-file

4 MATLAB directs graphics output to a figure window

4 Graphics functions automatically create new figure windows if none currently exist

>>figure

4 creates a new window and makes it the current figure

>>figure(h)

4 make an existing figure current by passing its handle (the number indicated in the window title bar), as an argument to figure

>>clf

4 Clear current figure window

4 Setting hold to on, MATLAB doesn’t remove the existing graph and adds the new data to the current graph

x=linspace(0,2*pi,100);

plot(x,sin(x));

hold on;

plot(x,cos(x));

xlabel('x');

ylabel('Sine of x');

With more graphics functionalities:

x=linspace(0,2*pi,100);

plot(x,sin(x),’-ob’);

hold on; grid on;

plot(x,cos(x),’->r’);

xlabel('x');

ylabel('Sine of x');

legend('sin(x)','cos(x)',3)

4 Plot

4 Graph 2-D data with linear scales for both axes

4 Loglog

4 Graph with logarithmic scales for both axes

4 Semilogx

4 Graph with a logarithmic scale for the x-axis and a linear scale for the y-axis

4 Semilogy

4 Graph with a logarithmic scale for the y-axis and a linear scale for the x-axis

4 bar(x,Y)

4 draws a bar for each element in Y at locations specified in x, where x is a monotonically increasing vector defining the x-axis intervals for the vertical bars

>> bar((1:1:10),(1:1:10))

4 Stem

4 displays data as lines (stems) terminated with a marker symbol at each data value

x=linspace(0,2*pi,10);

stem(x,sin(x));

4 Stairs

4 Stairstep plots are useful for drawing time-history plots of digitally sampled data systems

x=linspace(0,2*pi,20);

stairs(x,sin(x));