Double side band modulation is one of the simplest ways of modulating a signal. It has the advantages of being mathematically simple and easy to understand, but it can be difficult to implement because the phase of the modulating carrier must match that of the demodulating carrier. Basically, DSB modulation modulates a signal by multiplying it by a carrier signal (of much higher frequency than the message signal), and then demodulates it by multiplying by a signal identical to the modulating signal, except for a scaling factor. A filter is then applied to retrieve the message signal.

Using double sideband modulation, the message signal, m(t), is simply multiplied by a carrier signal, usually a cosine. Thus,

xc(t) = Acm(t) cost(ωct)

where xc(t) is the modulated signal, ω is the angular frequency, Ac is a scaling constant, and the subscript c denotes a property of the carrier signal.

Once modulated, a signal may then be transmitted through some medium, such as the atmosphere. Once it reaches a receiver, the signal must be demodulated, decoded to regain the original message signal. This is where the difficulty arises for double side band modulation.

To demodulate the signal, it must be multiplied by a demodulating carrier. This is easily expressed as

d(t) = 2Ac[m(t) cos(ωct)] cos(ωct)

The factor of two on the front is needed because the cos2 identity produces a fact of 1/2. Without it, you would recover a message signal with 1/2 the amplitude of the input message signal. If we apply the cos2 identity and multiply out, we have:

d(t) = Acm(t) + Acm(t) cos(2ωc;t)

By applying a lowpass filter around the message signal, the high frequency cos components can be eliminated.

The problem with double sideband modulation is that both the phase of the modulating carrier and the demodulating carrier must match exactly for it to work. Even a small phase offset could cause serious distortion of the received message signal.

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