-2
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enter image description here

Here is the shape of rectangular pulse and sin(pi*t) in time domain enter image description here

enter image description here

I am trying to sketch this signal, but I kind of don't fully understand the concept. since the two signal are multiplied in time domain, therefore the only area that survives is from -T/2 to T/2 ( bandwidth of rec) ?. Also it cannot be periodic, correct? and I am assuming it is energy type ( not power type) since the area of the signal is finite. can anyone help me to sketch the x(t)? Thank you

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  • \$\begingroup\$ You are correct, it is sinc(pi t) from -T to T (assuming that's how the PI function is defined in your class) and 0 everywhere else. Should be easy to sketch. \$\endgroup\$
    – The Photon
    Feb 23, 2016 at 22:42
  • \$\begingroup\$ I think it will be from -T/2 to T/2 since the rec pulse is scaled \$\endgroup\$
    – user65652
    Feb 23, 2016 at 22:44
  • \$\begingroup\$ it is rectangular pulse \$\endgroup\$
    – user65652
    Feb 23, 2016 at 22:44
  • \$\begingroup\$ what about the survived area? what does it look like? \$\endgroup\$
    – user65652
    Feb 23, 2016 at 22:49
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    \$\begingroup\$ This is a homework question, and you didn't even try before you came and got help \$\endgroup\$
    – Voltage Spike
    Feb 23, 2016 at 23:29

1 Answer 1

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The only area that survives is from -T/2 to T/2 (width, not bandwidth of the rectangle). Take the sinusoid , chop off everything below -T/2 and above T/2. Done.

Update: Imagine a sine wave generator connected to a scope through a switch. Normally the switch connects the scope's input to ground (multiplication by zero), . At t=-T/2 it instanteneously connects it to the sine wave generator (multiplication by one). At t=T/2, back to ground. It's not an absolutely perfect analogy, mathematically, but I hope it helps.

Update 2: of course, the function is still defined and equals zero outside [-T/2, T/2].

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  • \$\begingroup\$ can you sketch for me? what does it look like ? \$\endgroup\$
    – user65652
    Feb 23, 2016 at 22:46
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    \$\begingroup\$ Yes, \$x(t) = \sin(\pi{}t)\Pi(t/T)\$ means you multiply the value of the sine by the value of the rectangular pulse at each point in time. \$\endgroup\$
    – The Photon
    Feb 23, 2016 at 23:05
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    \$\begingroup\$ No, you are describing the DC component of a signal. \$\endgroup\$ Feb 23, 2016 at 23:21
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    \$\begingroup\$ No, gain is not the same as offset. The function is defined from minus to plus infinity but equals zero outside the pulse (see the answer updated a few minutes ago). Try to get a solid understanding of basic concepts before getting into advanced topics. You would get the right answer by doing convolution in the frequency domain, as you were planning, but for this problem it's sort of like going from the kitchen to the living room by crawling out the window, walking on your hands around the house and getting back in through the living room window. \$\endgroup\$ Feb 23, 2016 at 23:36
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    \$\begingroup\$ Yes, integrate the sine function from -T/2 to T/2. \$\endgroup\$ Feb 23, 2016 at 23:59

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