Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronic Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

Find period of this signal

Status
Not open for further replies.

JupiW

Newbie level 1
Joined
Aug 25, 2009
Messages
1
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,291
x(t) = Sin(2t) + Sin(3t)

Thnx :)
 

prestonee

Full Member level 3
Joined
Jan 9, 2013
Messages
177
Helped
45
Reputation
94
Reaction score
45
Trophy points
1,308
Location
United States
Activity points
2,713
6t, it is 1st common number between them...just as sin(9t)+sin(3t) would have a period of 9t because its a common multiple of both.
this should be in homework section though, would request a move
 

Mityan

Full Member level 5
Joined
Jul 11, 2012
Messages
281
Helped
48
Reputation
96
Reaction score
47
Trophy points
1,308
Activity points
2,835
Sin(a) + Sin(b) = 2*( sin((a+b)/2)*cos((a-b)/2) ). So this = 2*sin(2.5t)*cos(0.5t)

I think the period will be 2.5t. Am I right?

This is one of basic trigonomery equations. They are available in google and should be searched prior to asking there.
 

permute

Advanced Member level 3
Joined
Jul 16, 2010
Messages
923
Helped
294
Reputation
588
Reaction score
267
Trophy points
1,343
Activity points
8,543
If the example were sin(2t)+sin(0.5t), then you would have a period of 4pi (seconds). likewise sin(2t) + sin(6t) would be periodic with pi (seconds). sin(6t) + sin(10t) would have a period of pi (seconds) as well. Using these examples, it should be easy to find the answer to what appears to be a homework question.

For sin(w*t), w would be an angular frequency (rad/second), not a period.
 

Mityan

Full Member level 5
Joined
Jul 11, 2012
Messages
281
Helped
48
Reputation
96
Reaction score
47
Trophy points
1,308
Activity points
2,835
If the example were sin(2t)+sin(0.5t), then you would have a period of 4pi (seconds). likewise sin(2t) + sin(6t) would be periodic with pi (seconds). sin(6t) + sin(10t) would have a period of pi (seconds) as well. Using these examples, it should be easy to find the answer to what appears to be a homework question.

For sin(w*t), w would be an angular frequency (rad/second), not a period.
Indeed. In my example 2*pi*f = 2.5, so period T = 2*pi/2.5
 

albbg

Advanced Member level 4
Joined
Nov 7, 2009
Messages
1,234
Helped
425
Reputation
850
Reaction score
378
Trophy points
1,363
Location
Italy
Activity points
9,351
The period of the sum of periodic signal is given by the least common multiple (lcm) among the periods of each signal.

In your example: x(t) = Sin(2t) + Sin(3t)

sin (and cos) function complete a period every 2Π rad, then (supposing to start from 0 rad):

2•t1=2Π --> t1=Π
3•t2=2Π --> t2=2•Π/3

to find lcm you have to ignore the denominator if it is an integer and take the factor having maximum exponent at the two numerators. In this case we have the factors Π (numerator of t1), 2 and Π (numerator of t2) so I'll take Π only once and 2.
lcm=2•Π ==> the period of x(t) will be 2•Π

As another example, let's consider x(t) = sin(1.3t)+sin(3t)

1.3•t1=2Π --> t1=2Π/1.3 --> I have to transform the denominator into integer --> t1=20Π/13
3•t2=2Π --> t2=2Π/3

The lcm (an then the period) will be now 20Π

factors were 2²,5,Π and 2,Π so I'll take 2²,5,Π
 
  • Like
Reactions: Mityan

    Mityan

    points: 2
    Helpful Answer Positive Rating

Mityan

Full Member level 5
Joined
Jul 11, 2012
Messages
281
Helped
48
Reputation
96
Reaction score
47
Trophy points
1,308
Activity points
2,835
The period of the sum of periodic signal is given by the least common multiple (lcm) among the periods of each signal.

In your example: x(t) = Sin(2t) + Sin(3t)

sin (and cos) function complete a period every 2Π rad, then (supposing to start from 0 rad):

2•t1=2Π --> t1=Π
3•t2=2Π --> t2=2•Π/3

to find lcm you have to ignore the denominator if it is an integer and take the factor having maximum exponent at the two numerators. In this case we have the factors Π (numerator of t1), 2 and Π (numerator of t2) so I'll take Π only once and 2.
lcm=2•Π ==> the period of x(t) will be 2•Π

As another example, let's consider x(t) = sin(1.3t)+sin(3t)

1.3•t1=2Π --> t1=2Π/1.3 --> I have to transform the denominator into integer --> t1=20Π/13
3•t2=2Π --> t2=2Π/3

The lcm (an then the period) will be now 20Π

factors were 2²,5,Π and 2,Π so I'll take 2²,5,Π
You are right.

Lets make a small simulink model:


The frequencies of sources are 3/2/pi and 2/2/pi, cause 3 = 2*pi*f1, 2 = 2*pi*f2
The result diagram will be the following:


As we can see from picture, the period of sum is 2*pi = 6.xxx
 

ahmad1954

Full Member level 4
Joined
Jun 30, 2012
Messages
192
Helped
26
Reputation
52
Reaction score
26
Trophy points
1,308
Activity points
2,102
I draw this function in matlab and found that period is 2*pi. you can see the result in below:
1.png
 

Status
Not open for further replies.
Toggle Sidebar

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top