Embed Size (px)
Citation preview
2
3
1. Unit sample sequence
Write a Matlab function to generate
x(n)=delta(n-no), n1<=n<=n2
4
Note
5
function [x,n]=impseq(no,n1,n2)
n=[n1:n2];
x=[(n-no) == 0];
end
Write a Matlab function to generate
x(n)=delta(n-no), n1<=n<=n2
[x,n]=impseq(5,2,6)
Results:
n =2 3 4 5 6
x = 0 0 0 1 02 3 4 5 6
0
0.2
0.4
0.6
0.8
1
6
2. Unit step sequence
Write a Matlab function to generate
x(n)=step(n-no), n1<=n<=n2
7
8
function [x,n]=stepseq(no,n1,n2)
n=[n1:n2];
x=[(n-no) >= 0];
end
Write a Matlab function to generate
x(n)=step(n-no), n1<=n<=n2
[x,n]=stepseq(3,2,6)
Results:
n =2 3 4 5 6
x = 0 1 1 1 12 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
9
3. Real-valued exponential sequence
10
n=[-10:10];
x1=(0.7).^n;
subplot(221),stem(n,x1),title('0<a<1')
x2=(1.4).^n;
subplot(222),stem(n,x2),title('a>1')
x3=(-0.7).^n;
subplot(223),stem(n,x3),title('-1<a<0')
x4=(-1.4).^n;
subplot(224),stem(n,x4),title('-1>a')
11
-10 -5 0 5 100
10
20
30
400<a<1
-10 -5 0 5 100
10
20
30a>1
-10 -5 0 5 10-40
-20
0
20
40
-1<a<0
-10 -5 0 5 10-40
-20
0
20
40
-1>a
12
4. Complex-valued exponential sequence
cos sinje j
cos sin 1je j
Euler's equation:
13
-5 0 5-5
0
5
Quadra
ture
In-Phase
Scatter plot
>> scatterplot(3+j*5)
14
1n nj n je e
n=-10:10;
y=exp((j*pi)*n);
stem(n,y)
scatterplot(y)
-10 -5 0 5 10-1
-0.5
0
0.5
1
-1 0 1-1
0
1
Quadra
ture
In-Phase
Scatter plot
stem(n,y)scatterplot(y)
15
16
What is the mathematical definition of a complex sinusoid?
The complex sinusoid can be thought of as a two-dimensional sinusoid. One dimension
contains a cosine wave, and the perpendicular dimension contains a sinewave. Here is
a picture of a complex sinusoid with the third dimension being time:
17-1 0 1
-1
-0.5
0
0.5
1
Quadra
ture
In-Phase
Scatter plot
n=-10:10;
y=exp((j*pi/3)*n);
scatterplot(y)
/3n
j n je e
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
18
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
theta=linspace(0,2*pi,100);
y=exp(j*theta);
scatterplot(y)
>> help linspace
LINSPACE Linearly spaced vector.
LINSPACE(X1, X2)
generates a row vector of 100 linearly
equally spaced points between X1 and X2.
LINSPACE(X1, X2, N)
generates N points between X1 and X2.
19
>> L=linspace(0,10,5)
L =0 2.5000 5.0000 7.5000 10.0000
>> L=linspace(3,9,6)
L= 3.0000 4.2000 5.4000 6.6000 7.8000 9.0000
10 02.5
Number of elements 1 5 1
end value start valueStep
9 31.2
6 1Step
Start end points
>> L=linspace(0,10,5)
L =0 2.5000 5.0000 7.5000 10.0000
>> L=0:2.5:10
L =0 2.5000 5.0000 7.5000 10.0000
21
22
histogram
0 1 2 3 4 5 6 7 8 9 1011121314150
0.5
1
1.5
2
2.5
3
>> A=[15 15 6 8 6 6 1];
>> hist(A)
3
>> help randn
RANDN Normally distributed random numbers.
R = RANDN(N) returns an N-by-N matrix containingpseudo-random values drawn from a normal distributionwith mean zero and standard deviation one
>> randn(1,4)
ans =1.9574 0.5045 1.8645 -0.3398
23
randn Gaussian distribution
6. Random sequence (rand ,randn)
24
-3 -2 -1 0 1 2 3 40
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180 200-4
-2
0
2
4
>> randn(1,200)
x=randn(1,200)
figure(1), plot(x)
figure(2), hist(x)
25
>> rand(1,5)
ans = 0.8147 0.9058 0.1270 0.9134
26
▪ OPERATIONS ON SEQUENCES
1. Signal addition:
Build a Matlab function that takes two sequences with its indices
and return the sum of them with the index of the result
sequence.
Before build this function follow the helpful notes next slides
27
For example find: x1+x2
28
%% means find x that is not equal to zero
29
30
>> A=[1 2 3;4 5 6;7 8 9]
A = 1 2 3
4 5 6
7 8 9
>> min(A)
ans =1 2 3
>> min(min(A))
ans = 1
31
>> a=[0 0 0 0 0 0 0 0 0 0 ];
>> b=[10 20 30 40 50];
>> y([6 7 8 9 10])=b
y =0 0 0 0 0 10 20 30 40 50
32
n1=[0,1,2,3,4];
n2=[-2,-1,0,1,2];
n=min( min(n1),min(n2)):max( max(n1),max(n2));
n = -2 -1 0 1 2 3 4>> A=n>=min(n1) % n>=0 {0,0,1,1,1,1,1}
>> B=n<=max(n1) % n<=4 {1,1,1,1,1,1,1}
>> A&B
>> z=find(A&B==1) % index
A = 0 0 1 1 1 1 1
B = 1 1 1 1 1 1 1
A&B = 0 0 1 1 1 1 1
z = 3 4 5 6 7
33
34
35
========================================================
% Function adds two discrete time sequences
y(n)=x1(n)+x2(n)
function [y,n]=sigadd(x1,n1,x2,n2)
n=min(min(n1),min(n2)):max(max(n1),max(n2));
y1=zeros(1,length(n));
y2=y1;
y1(find((n>=min(n1))&(n<=max(n1))==1))=x1;
y2(find((n>=min(n2))&(n<=max(n2))==1))=x2;
y=y1+y2;
end
========================================================
36
using sidadd function x1=[0,2,4,6,8];
n1=[0,1,2,3,4];
x2=[1,3,5,7,9];
n2=[-2,-1,0,1,2];
[y,n]=sigadd(x1,n1,x2,n2)
y = 1 3 5 9 13 6 8
n =-2 -1 0 1 2 3 4
37
2. Signal multiplication :
38
3. Signal scaling:
In this operation each sample is multiplied by a scalar α.
39
4. Signal shifting:
x=[1,1,1,1];
n=[1,2,3,4];
n2=n+6;
n3=n-6;
stem(n,x),hold on
stem(n2,x),hold on
stem(n3,x)
For example:
40
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 120
0.5
1
1.5
2
41
=============================================
% Function does signal shifting y(n)=x(n-no)
function [y,n]=sigshift(x,n,no)
n=n+no;
y=x;
end
=============================================
% x=[1,1,1,1];
% n=[1,2,3,4];
%[y1,n2]=sigshift(x,n,6)
%[y2,n3]=sigshift(x,n,-6)
42
5. Signal Folding:
each sample of x(n) is flipped around n=0
43
x=[1,2,3];
n=[2,3,4];
y=fliplr(x);
n2=-fliplr(n);
% [y,n2]=sigfold(x,n)
stem(n,x),hold on,stem(n2,y)
For example:
44
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 60
1
2
3
4
45
==========================================
% Function does signal folding y(n)=x(-n)
function [y,n]=sigfold(x,n)
y=fliplr(x);
n=-fliplr(n);
end
==========================================
46
6. Sample summation :
47
7. Sample product:
48
LOGO
49
