Calculating a periodic signal (way of solving this)?
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
|
show 1 more comment
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
1
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:
$$x(t)=sum_{n=-infty}^infty Pileft({t-4nover2}right) + sum_{n=-infty}^infty Π{(t-4n)} $$
So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?
What concernes me is how i tackle the sums.
fourier-analysis fourier-transform signal-processing periodic-functions
fourier-analysis fourier-transform signal-processing periodic-functions
edited Dec 26 '18 at 22:34
saulspatz
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
edited Dec 26 '18 at 22:34
saulspatz
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
edited Dec 26 '18 at 22:34
saulspatz
14k21329
edited Dec 26 '18 at 22:34
saulspatz
14k21329
edited Dec 26 '18 at 22:34
saulspatz
14k21329
14k21329
asked Dec 26 '18 at 14:09
Agaeus
626
asked Dec 26 '18 at 14:09
Agaeus
626
asked Dec 26 '18 at 14:09
Agaeus
626
626
What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
1
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
1
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31
What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
1
1
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31
|
show 1 more comment
1 Answer
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HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjo
12.3k1329
add a comment |
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HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjo
12.3k1329
add a comment |
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjo
12.3k1329
add a comment |
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjo
12.3k1329
HINT: Let be $f(t)=Pi(t/2)+Pi(t)$. So we have
$$
x(t)=sum_{n=-infty}^infty f(t-4n)
$$
Can you see that $x(t)$ is periodic with period $T=4$?
answered Jan 3 at 21:57
alexjo
12.3k1329
answered Jan 3 at 21:57
alexjo
12.3k1329
answered Jan 3 at 21:57
alexjo
12.3k1329
answered Jan 3 at 21:57
alexjo
12.3k1329
12.3k1329
add a comment |
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What is $Pi?$ Do you mean the number $pi?$
– saulspatz
Dec 26 '18 at 16:47
no by Π i mean the rectangular function en.wikipedia.org/wiki/Rectangular_function
– Agaeus
Dec 26 '18 at 18:20
Okay, what about $Πfrac{(t-4n)}{(2)}?$ Is that supposed to be $$Pileft({t-4nover2}right)?$$
– saulspatz
Dec 26 '18 at 20:46
well yeah that's it saulspatz.
– Agaeus
Dec 26 '18 at 21:55
1
The infinite sums are not truly infinite. For any particular $t$, only a finite number (a very low finite number) of the terms are non-zero. So to find the value for $t$, just sum up those few terms. And as a hint, consider what happens if you replace the index $n$ with a new index $m = n+1$.
– Paul Sinclair
Dec 27 '18 at 1:31