# multiplication of a periodic signal by rectangular pulse

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

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

• 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. Commented Feb 23, 2016 at 22:42
• I think it will be from -T/2 to T/2 since the rec pulse is scaled Commented Feb 23, 2016 at 22:44
• it is rectangular pulse Commented Feb 23, 2016 at 22:44
• what about the survived area? what does it look like? Commented Feb 23, 2016 at 22:49
• This is a homework question, and you didn't even try before you came and got help Commented Feb 23, 2016 at 23:29

• 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. Commented Feb 23, 2016 at 23:05