# Spectral analysis and modulation, part 4: Modulation

*This series is excerpted from "Digital Signal Processing
and Applications, 2nd Edition." Order this book today at www.newnespress.com
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*

*
Part 3 covers parametric estimation and wavelets. Part 5 introduces Phase Shift Keying (PSK) and its variants BPSK, QPSK, QAM, and GMSK. It will be published Thursday, March 20.*

**5.3 Modulation**

In many communication systems, especially in radio systems, the information ("digital" or "analog"), or the **baseband **signal to be transmitted is **modulated**, i.e. "encoded" onto a **carrier **signal. The carrier is chosen depending on the type of media available for the transmission, for instance, a limited band in the radio frequency spectrum, or an appropriate frequency for transmission over cables or fibers. If we assume that the carrier signal is a plain **cosine **signal there are three parameters of the carrier that can be modulated and used for information transfer. These parameters are the **amplitude ***a*(*t*), the **frequency ***f*(*t*) and the **phase ***Φ*(*t*). The modulated carrier is then

The corresponding modulation types are denoted **amplitude modulation (AM)**, **frequency modulation (FM) **and **phase modulation (PM)**. FM and PM are also referred to as **angular modulation **and are related in that the frequency is the phase changing speed; in other words, the derivative of the phase function is the frequency. Hence, frequency modulation can be achieved by first integrating the baseband signal and then feeding it into a phase modulator. This method is called Armstrong's indirect FM (Miller and Beasley, 2002).

In a **digital **radio communication system, it is common to modulate either by changing *f*(*t*) between a number of discrete frequencies, **frequency shift keying (FSK) **or by changing *Φ*(*t*) between a number of discrete phases, **phase shift keying (PSK)**. In some systems, the amplitude is also changed between discrete levels, **amplitude shift keying (ASK)**. So, if we are to design a modulation scheme which is able to transmit *M *different discrete symbols (for binary signals, *M *= 2), we hence have to define *M *unique combinations of amplitude, frequency and/or phase values of the carrier signal. The trick is to define these **signal points**, *a _{n}*(

*t*),

*f*(

_{n}*t*) or

*Φ*(

_{n}*t*), where

*n*∈ {0,

*...*,

*M*−1}, in a way that communication speed can be high, influence of interference low, spectral occupancy low, and modulation and demodulation equipment can be made fairly simple.

**5.3.1 Amplitude shift keying (ASK)**

The concept of ASK is rather straightforward. Using this modulation method, the amplitude of the carrier can be one out of *M *given baseband amplitude functions *a _{n}*(

*t*), corresponding to the

*M*information symbols used in the system.

The carrier frequency *f*(*t*) = *f*_{c} and the phase shift *Φ*(*t*) = *Φ *are constant. The amplitude functions *a _{n}*(

*t*) are defined over a finite period of time, i.e.

*t*

_{0}≤

*t < t*

_{0}+

*T*, where

*T*is the

**symbol time**. A simple example would be a system using binary symbols, i.e.

*M*= 2 and square pulses for amplitude functions according to the below (see Figure 5-5)

*symbol "0":*

*symbol "1":*

*Figure 5-5.*

*Baseband signal and modulated signal for ASK,*M =

*2*