In most designs of data modem, the frequency content of a
baseband data stream, (which we have just found using the Fourier
series expansion), does not match the frequency transmission property of the
transmission channel.
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For example, a radio channel will have a bandpass
response only passing frequency components grouped together and many times higher than
those making up the input data stream.
In order to translate the spectrum of the input signal to fit within the passband of a
channel, a process of modulation is employed as described in Chapter 5. This process often involves mixing the
input data signal with a high frequency sine or cosine term, called the carrier.
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In order to understand how this mixing process achieves
the desired goal, we need to revise the basic trigonometric relationships between sine and
cosine terms.
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