Notation for a periodic square wave?
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What is the notation to write a periodic square wave with say, period Ts and 25% duty cycle? I think it should be something like an infinite sum of a unit step minus another unit step, but I'm not quite sure.
functions notation
asked Nov 18 '15 at 16:05
AustinAustin
343112
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add a comment |
$begingroup$
What is the notation to write a periodic square wave with say, period Ts and 25% duty cycle? I think it should be something like an infinite sum of a unit step minus another unit step, but I'm not quite sure.
functions notation
asked Nov 18 '15 at 16:05
AustinAustin
343112
$endgroup$
$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59
add a comment |
$begingroup$
What is the notation to write a periodic square wave with say, period Ts and 25% duty cycle? I think it should be something like an infinite sum of a unit step minus another unit step, but I'm not quite sure.
functions notation
asked Nov 18 '15 at 16:05
AustinAustin
343112
$endgroup$
What is the notation to write a periodic square wave with say, period Ts and 25% duty cycle? I think it should be something like an infinite sum of a unit step minus another unit step, but I'm not quite sure.
functions notation
functions notation
asked Nov 18 '15 at 16:05
AustinAustin
343112
asked Nov 18 '15 at 16:05
AustinAustin
343112
asked Nov 18 '15 at 16:05
AustinAustin
343112
asked Nov 18 '15 at 16:05
AustinAustin
343112
asked Nov 18 '15 at 16:05
AustinAustin
343112
343112
$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59
add a comment |
$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59
$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59
$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59
add a comment |
1 Answer
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As used in Signal Analysis you can use the periodic extension of a basic pulse to represent a periodic square wave. A periodic extension is nothing more than in infinite sum of basic pulses $X_p(t)$. For a period $T_0$ the extension is:
$$X(t) = sum_{r=-infty}^infty X_p(t - rT_0)$$
The only thing we have to sort out is how to represent the basic pulse. We will palce the rising edge at the origin for simplicity. As your intuition told you, the expression for such pulse would be:
$$X_p(t) = U(t) - U(t - a); t in [-a, a]$$
The example is for a pulse of period $T_0 = a - (-a) = 2a$ whose rising edge is at the origin with a 50% duty cycle. It shouldn't be hard to get the expression for a 25% duty cycle. Substitute in the first equation and you have got the expression of the periodic square wave!
If you have any doubts or you spot a mistake please do let me know.
answered Jan 4 at 16:17
P. ColladoP. Collado
262
$endgroup$
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
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active
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votes
$begingroup$
As used in Signal Analysis you can use the periodic extension of a basic pulse to represent a periodic square wave. A periodic extension is nothing more than in infinite sum of basic pulses $X_p(t)$. For a period $T_0$ the extension is:
$$X(t) = sum_{r=-infty}^infty X_p(t - rT_0)$$
The only thing we have to sort out is how to represent the basic pulse. We will palce the rising edge at the origin for simplicity. As your intuition told you, the expression for such pulse would be:
$$X_p(t) = U(t) - U(t - a); t in [-a, a]$$
The example is for a pulse of period $T_0 = a - (-a) = 2a$ whose rising edge is at the origin with a 50% duty cycle. It shouldn't be hard to get the expression for a 25% duty cycle. Substitute in the first equation and you have got the expression of the periodic square wave!
If you have any doubts or you spot a mistake please do let me know.
answered Jan 4 at 16:17
P. ColladoP. Collado
262
$endgroup$
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
add a comment |
$begingroup$
As used in Signal Analysis you can use the periodic extension of a basic pulse to represent a periodic square wave. A periodic extension is nothing more than in infinite sum of basic pulses $X_p(t)$. For a period $T_0$ the extension is:
$$X(t) = sum_{r=-infty}^infty X_p(t - rT_0)$$
The only thing we have to sort out is how to represent the basic pulse. We will palce the rising edge at the origin for simplicity. As your intuition told you, the expression for such pulse would be:
$$X_p(t) = U(t) - U(t - a); t in [-a, a]$$
The example is for a pulse of period $T_0 = a - (-a) = 2a$ whose rising edge is at the origin with a 50% duty cycle. It shouldn't be hard to get the expression for a 25% duty cycle. Substitute in the first equation and you have got the expression of the periodic square wave!
If you have any doubts or you spot a mistake please do let me know.
answered Jan 4 at 16:17
P. ColladoP. Collado
262
$endgroup$
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
add a comment |
$begingroup$
As used in Signal Analysis you can use the periodic extension of a basic pulse to represent a periodic square wave. A periodic extension is nothing more than in infinite sum of basic pulses $X_p(t)$. For a period $T_0$ the extension is:
$$X(t) = sum_{r=-infty}^infty X_p(t - rT_0)$$
The only thing we have to sort out is how to represent the basic pulse. We will palce the rising edge at the origin for simplicity. As your intuition told you, the expression for such pulse would be:
$$X_p(t) = U(t) - U(t - a); t in [-a, a]$$
The example is for a pulse of period $T_0 = a - (-a) = 2a$ whose rising edge is at the origin with a 50% duty cycle. It shouldn't be hard to get the expression for a 25% duty cycle. Substitute in the first equation and you have got the expression of the periodic square wave!
If you have any doubts or you spot a mistake please do let me know.
answered Jan 4 at 16:17
P. ColladoP. Collado
262
$endgroup$
As used in Signal Analysis you can use the periodic extension of a basic pulse to represent a periodic square wave. A periodic extension is nothing more than in infinite sum of basic pulses $X_p(t)$. For a period $T_0$ the extension is:
$$X(t) = sum_{r=-infty}^infty X_p(t - rT_0)$$
The only thing we have to sort out is how to represent the basic pulse. We will palce the rising edge at the origin for simplicity. As your intuition told you, the expression for such pulse would be:
$$X_p(t) = U(t) - U(t - a); t in [-a, a]$$
The example is for a pulse of period $T_0 = a - (-a) = 2a$ whose rising edge is at the origin with a 50% duty cycle. It shouldn't be hard to get the expression for a 25% duty cycle. Substitute in the first equation and you have got the expression of the periodic square wave!
If you have any doubts or you spot a mistake please do let me know.
answered Jan 4 at 16:17
P. ColladoP. Collado
262
answered Jan 4 at 16:17
P. ColladoP. Collado
262
answered Jan 4 at 16:17
P. ColladoP. Collado
262
answered Jan 4 at 16:17
P. ColladoP. Collado
262
262
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
add a comment |
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
$begingroup$
Welcome to Math.SE! Thanks for choosing an old unanswered Question to tackle. Unfortunately the content of the Question itself is somewhat open to interpretation, and the OP has not be on the site in the past couple of months to respond to requests for clarification. So you may find your efforts are more appreciated if you pick some recent problems to answer.
$endgroup$
– hardmath
Jan 4 at 16:29
add a comment |
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$begingroup$
See en.wikipedia.org/wiki/Pulse_wave.
$endgroup$
– HDE 226868
Nov 21 '15 at 16:59