# Amplitude modulation of unit step signal

What will be the amplitude modulated signal, if the input is an unit step signal? You can take any carrier signal (though I would recommend sine wave) and take any carrier frequency because that is not of interest here as I want to know the shape of the net modulated signal.

• The frequency domain will be quite busy a t=0... please don't put that on an antenna without some pulse shaping or band limiting! Aug 11 '14 at 20:59

Before the start of the unit step, the waveform will be a constant amplitude sine wave at the carrier frequency. After the unit step, if we assume the amplitude of the step is sufficient for 100% modulation, the waveform will be a constant amplitude sine wave at twice the amplitude that existed before the start of the unit step. A unit step amounts to a DC level so that it affects the amplitude of the carrier but not its shape.

Wolfram alpha visual depiction of what was described.  • Note that the frequency spectrum would show a large change in frequency at the moment the step function jumps due to the non-differentiable point at 0. Aug 11 '14 at 21:19
• This answer assumes normal broadcast type AM and not DSBSC or 4 quadrant multiplication type AM. Aug 11 '14 at 21:23
• @Andy The question did not specify the type of AM so I assumed the most commonly used. Aug 11 '14 at 23:09
• actually the point where i got confused was this, at the origin unit step has value half (1/2 , as we are taking the case of continuous time signal case) so waveform should start from 1/2 despite of zero and yet i am not cleared about this that why it would start from zero. Aug 13 '14 at 8:03

Before the step, the modulation signal is 0, so the output is 0. After the step, the modulation signal is 1, so the output will be a full amplitude carrier. This is the same as turning the carrier on from having been off.

Such modulation is called OOK (On/off keying), and is a common way to send morse code. The carrier is on for the dits and dahs, and off during the spaces in between them.