# 1.2 Trigonometric relationships

## The basic mixing process

#### 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.
#### 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. |
#### 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.