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Sampling: Multiplication by Square Wave

  • Thread starter cepheid
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We are considering a system in which the input signal x(t) is multiplied by a periodic square wave s(t) in order to produce an output w(t). The input signal is band limited with [itex] |X(j\omega)| = 0 \ \ \textrm{for} \ \ |\omega| \geq \omega_M [/itex], where [itex] \omega_M [/itex] is the bandwidth. We are supposed to find (given a certain width of the periodic square wave, e.g. T/3), the maximum value of T (in terms of [itex] \omega_M [/itex]) for which there is no aliasing among the replicas of [itex] X(j\omega) [/itex] in [itex] W(j\omega) [/itex].

I do not know how to approach this problem. This is not simple impulse train sampling. It is not zero order hold sampling. In fact...what the hell is this? Multiplication by a square wave?!?!? Sorry, I don't know where to start.
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Multiplication by a square wave is a form of modulation. Start off multiplying by a sine wave instead, and work out the images with sum and difference math. Then consider what a square wave's spectra looks like....

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