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If the input to a demodulator is a signal having the spectrum shown below, how would I figure out what local oscillator frequency is required to shift the signal to baseband?

image

Is there a formula for this? I'm getting no where on google.

Thanks.

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  • \$\begingroup\$ Mix with the fundamental to get to baseband. (This can sometimes not work as well as expected... any slight differences in frequency (of the fundamentals) becomes a slow modulation.) \$\endgroup\$ – George Herold Apr 27 '15 at 19:59
  • \$\begingroup\$ Could you explain a little better? I'm trying to do this out on paper as study revision \$\endgroup\$ – roukzz Apr 27 '15 at 20:07
  • \$\begingroup\$ Remember that multiplication in the time domain corresponds to convolution in the frequency domain. Also remember that a sinusoid in the time domain corresponds to an impulse in the frequency domain (at the sinusoid's frequency, and another at the negative of the sinusoid's frequency). The question then becomes: When convoluted with the signal spectrum shown, which is centered around 100MHz, what impulse will produce a signal spectrum that's centered around 0Hz after convolution? \$\endgroup\$ – Zulu Apr 28 '15 at 0:30
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The simplest signal that has the spectrum shown is a 100 MHz carrier that is amplitude modulated with 100 kHz bandwidth information. If Fc = carrier frequency, a modulating frequency Fm causes sidebands at (Fc + Fm) and (Fc - Fm). To demodulate the signal, mix it with a local oscillator at Fc. You can write a formula for the output of the demodulator by representing each frequency as a trig function of time i.e. sine(2 pi F) or cosine(2 pi F). The important output is sine(2 pi Fm) which shows the modulating signal is recovered, which is what is meant by baseband. There are also higher frequency products but these will be filtered away in a receiver. See http://en.wikipedia.org/wiki/Sideband or see http://en.wikipedia.org/wiki/Amplitude_modulation for a full math analysis that also considers phase.

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