[7.7 APPLICATION TO](#page-13-0) COMMUNICATIONS: AMPLITUDE MODULATION

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7.7 APPLICATION TO COMMUNICATIONS: AMPLITUDE MODULATION

Modulation causes a spectral shift in a signal and is used to gain certain advantages mentioned in our discussion of the frequency-shifting property. Broadly speaking, there are two classes of modulation: amplitude (linear) modulation and angle (nonlinear) modulation. In this section, we shall discuss some practical forms of amplitude modulation.

^† For lowpass signals, the essential bandwidth may also be defined as a frequency at which the value of the amplitude spectrum is a small fraction (about 1%) of its peak value. In Ex. 7.20, for instance, the peak value, which occurs at ω = 0, is 1/a.

7.7-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation

In amplitude modulation, the amplitude A of the carrier Acos(ωct + θc) is varied in some manner with the baseband (message)† signal m(t) (known as the modulating signal). The frequency ω*^c* and the phase θ*^c* are constant. We can assume θ*^c* = 0 without loss of generality. If the carrier amplitude A is made directly proportional to the modulating signal m(t), the modulated signal is m(t) cos ωct (Fig. 7.36). As was indicated earlier [Eq. (7.32)], this type of modulation simply shifts the spectrum of m(t) to the carrier frequency (Fig. 7.36c). Thus, if

Figure 7.36 DSB-SC modulation.

^† The term baseband is used to designate the band of frequencies of the signal delivered by the source or the input transducer.

then

$$m(t)\cos\omega_c t \Longleftrightarrow \frac{1}{2}[M(\omega + \omega_c) + M(\omega - \omega_c)] \tag{7.48}$$

Recall that M(ω − ωc) is M(ω)-shifted to the right by ω*^c* and M(ω + ωc) is M(ω)-shifted to the left by ωc. Thus, the process of modulation shifts the spectrum of the modulating signal to the left and the right by ωc. Note also that if the bandwidth of m(t) is B Hz, then, as indicated in Fig. 7.36c, the bandwidth of the modulated signal is 2B Hz. We also observe that the modulated signal spectrum centered at ω*^c* is composed of two parts: a portion that lies above ωc, known as the upper sideband (USB), and a portion that lies below ωc, known as the lower sideband (LSB). Similarly, the spectrum centered at −ω*^c* has upper and lower sidebands. This form of modulation is called double sideband (DSB) modulation for the obvious reason.

The relationship of B to ω*^c* is of interest. Figure 7.36c shows that ω*^c* ≥ 2πB to avoid the overlap of the spectra centered at ±ωc. If ω*^c* < 2πB, the spectra overlap and the information of m(t) are lost in the process of modulation, a loss that makes it impossible to get back m(t) from the modulated signal m(t) cos ωct. †

EXAMPLE 7.21 Double-Sideband Suppressed-Carrier Modulation

For a baseband signal m(t) = cos ωmt, find the DSB-SC signal and sketch its spectrum. Identify the upper and lower sidebands.

We shall work this problem in the frequency domain as well as the time domain to clarify the basic concepts of DSB-SC modulation. In the frequency-domain approach, we work with the signal spectra. The spectrum of the baseband signal m(t) = cos ωmt is given by

$$M(\omega) = \pi \left[ \delta(\omega - \omega_m) + \delta(\omega + \omega_m) \right]$$

The spectrum consists of two impulses located at ±ωm, as depicted in Fig. 7.37a.

The DSB-SC (modulated) spectrum, as indicated by Eq. (7.48), is the baseband spectrum in Fig. 7.37a shifted to the right and the left by ω*^c* (times 0.5), as depicted in Fig. 7.37b. This spectrum consists of impulses at ±(ω*^c* − ωm) and ±(ω*^c* + ωm). The spectrum beyond ω*^c* is the upper sideband (USB), and the one below ω*^c* is the lower sideband (LSB). Observe that the DSB-SC spectrum does not have as a component the carrier frequency ωc. This is why the term double-sideband, suppressed carrier (DSB-SC) is used for this type of modulation.

^† Practical factors may impose additional restrictions on ωc. For instance, in broadcast applications, a radiating antenna can radiate only a narrow band without distortion. This restriction implies that avoiding distortion caused by the radiating antenna calls for ωc/2πB 1. The broadcast band AM radio, for instance, with B = 5 kHz and the band of 550–1600 kHz for carrier frequency gives a ratio of ωc/2πB roughly in the range of 100–300.

Figure 7.37 An example of DSB-SC modulation.

In the time-domain approach, we work directly with signals in the time domain. For the baseband signal m(t) = cos ωmt, the DSB-SC signal ϕDSB-SC(t) is

$$\varphi_{\text{DSB-SC}}(t) = m(t) \cos \omega_c t$$

= $\cos \omega_m t \cos \omega_c t$
= $\frac{1}{2} [\cos (\omega_c + \omega_m)t + \cos (\omega_c - \omega_m)t]$ (7.49)

This result shows that when the baseband (message) signal is a single sinusoid of frequency ωm, the modulated signal consists of two sinusoids: the component of frequency ω*^c* + ω*^m* (the upper sideband), and the component of frequency ω*^c* − ω*^m* (the lower sideband). Figure 7.37b illustrates precisely the spectrum of ϕDSB-SC(t). Thus, each component of frequency ω*^m* in the modulating signal results in two components of frequencies ω*^c* + ω*^m* and ω*^c* − ω*^m* in the modulated signal. This being a DSB-SC (suppressed-carrier) modulation, there is no component of the carrier frequency ω*^c* on the right-hand side of Eq. (7.49).†

DEMODULATION OF DSB-SC SIGNALS

The DSB-SC modulation translates or shifts the frequency spectrum to the left and the right by ω*^c* (i.e., at +ω*^c* and −ωc), as seen from Eq. (7.48). To recover the original signal m(t) from

^† The term suppressed carrier does not necessarily mean absence of the spectrum at the carrier frequency. “Suppressed carrier” merely implies that there is no discrete component of the carrier frequency. Since no discrete component exists, the DSB-SC spectrum does not have impulses at ±ωc, which further implies that the modulated signal m(t) cos ωct does not contain a term of the form k cos ωct [assuming that m(t) has a zero mean value].

Figure 7.38 Demodulation of DSB-SC: (a) demodulator and (b) spectrum of e(t).

the modulated signal, we must retranslate the spectrum to its original position. The process of recovering the signal from the modulated signal (retranslating the spectrum to its original position) is referred to as demodulation, or detection. Observe that if the modulated signal spectrum in Fig. 7.36c is shifted to the left and to the right by ω*^c* (and halved), we obtain the spectrum illustrated in Fig. 7.38b, which contains the desired baseband spectrum in addition to an unwanted spectrum at ±2ωc. The latter can be suppressed by a lowpass filter. Thus, demodulation, which is almost identical to modulation, consists of multiplication of the incoming modulated signal m(t) cos ωct by a carrier cos ωct followed by a lowpass filter, as depicted in Fig. 7.38a. We can verify this conclusion directly in the time domain by observing that the signal e(t) in Fig. 7.38a is

$$e(t) = m(t)\cos^2\omega_c t = \frac{1}{2}[m(t) + m(t)\cos 2\omega_c t]$$

Therefore, the Fourier transform of the signal e(t) is

$$E(\omega) = \frac{1}{2}M(\omega) + \frac{1}{4}[M(\omega + 2\omega_c) + M(\omega - 2\omega_c)]$$

Hence, e(t) consists of two components (1/2)m(t) and (1/2)m(t) cos 2ωct, with their spectra, as illustrated in Fig. 7.38b. The spectrum of the second component, being a modulated signal with carrier frequency 2ωc, is centered at ±2ωc. Hence, this component is suppressed by the lowpass filter in Fig. 7.38a. The desired component (1/2)M(ω), being a lowpass spectrum (centered at ω = 0), passes through the filter unharmed, resulting in the output (1/2)m(t).

A possible form of lowpass filter characteristics is depicted (dotted) in Fig. 7.38b. In this method of recovering the baseband signal, called synchronous detection, or coherent detection, we use a carrier of exactly the same frequency (and phase) as the carrier used for modulation. Thus, for demodulation, we need to generate a local carrier at the receiver in frequency and phase coherence (synchronism) with the carrier used at the modulator. We shall demonstrate in Ex. 7.22 that both phase and frequency synchronism are extremely critical.

EXAMPLE 7.22 Frequency and Phase Incoherence in DSB-SC

Discuss the effect of lack of frequency and phase coherence (synchronism) between the carriers at the modulator (transmitter) and the demodulator (receiver) in DSB-SC.

Let the modulator carrier be cos ωct (Fig. 7.36a). For the demodulator in Fig. 7.38a, we shall consider two cases: with carrier cos(ωct+θ ) (phase error of θ) and with carrier cos(ωc+ω)t (frequency error ω).

(a) With the demodulator carrier cos(ωct + θ ) (instead of cos ωct) in Fig. 7.38a, the multiplier output is e(t) = m(t) cos ωct cos(ωct + θ ) instead of m(t) cos2ωct. From the trigonometric identity, we obtain

$$e(t) = m(t)\cos\omega_c t \cos(\omega_c t + \theta)$$

= $\frac{1}{2}m(t)[\cos\theta + \cos(2\omega_c t + \theta)]$

The spectrum of the component (1/2)m(t) cos(2ωct + θ ) is centered at ±2ωc. Consequently, it will be filtered out by the lowpass filter at the output. The component (1/2)m(t) cos θ is the signal m(t) multiplied by a constant (1/2) cos θ. The spectrum of this component is centered at ω = 0 (lowpass spectrum) and will pass through the lowpass filter at the output, yielding the output (1/2)m(t) cos θ.

If θ is constant, the phase asynchronism merely yields an output that is attenuated (by a factor cos θ). Unfortunately, in practice, θ is often the phase difference between the carriers generated by two distant generators and varies randomly with time. This variation would result in an output whose gain varies randomly with time.

(b) In the case of frequency error, the demodulator carrier is cos(ωc+ω)t. This situation is very similar to the phase error case in part (a) with θ replaced by (ω)t. Following the analysis in part (a), we can express the demodulator product e(t) as

$$e(t) = m(t)\cos\omega_c t \cos(\omega_c + \Delta\omega)t$$

= $\frac{1}{2}m(t)[\cos(\Delta\omega)t + \cos(2\omega_c + \Delta\omega)t]$

The spectrum of the component (1/2)m(t) cos(2ω*^c* + ω)t is centered at ±(2ω*^c* + ω). Consequently, this component will be filtered out by the lowpass filter at the output. The component (1/2)m(t) cos(ω)t is the signal m(t) multiplied by a low-frequency carrier of frequency ω. The spectrum of this component is centered at ±ω. In practice, the frequency error (ω) is usually very small. Hence, the signal (1/2)m(t) cos(ω)t (whose spectrum is centered at ±ω) is a lowpass signal and passes through the lowpass filter at the output, resulting in the output (1/2)m(t) cos(ω)t. The output is the desired signal m(t) multiplied by a very-low-frequency sinusoid cos(ω)t. The output in this case is not merely an attenuated replica of the desired signal m(t), but represents m(t) multiplied by a time-varying gain cos(ω)t. If, for instance, the transmitter and the receiver carrier frequencies differ just by 1 Hz, the output will be the desired signal m(t) multiplied by a time-varying signal whose gain goes from the maximum to 0 every half-second. This is like a restless child fiddling with the volume control knob of a receiver, going from maximum volume to zero volume every half-second. This kind of distortion (called the beat effect) is beyond repair.

7.7-2 Amplitude Modulation (AM)

For the suppressed-carrier scheme just discussed, a receiver must generate a carrier in frequency and phase synchronism with the carrier at a transmitter that may be located hundreds or thousands of miles away. This situation calls for a sophisticated receiver, which could be quite costly. The other alternative is for the transmitter to transmit a carrier A cosωct [along with the modulated signal m(t) cosωct] so that there is no need to generate a carrier at the receiver. In this case, the transmitter needs to transmit much larger power, a rather expensive procedure. In point-to-point communications, where there is one transmitter for each receiver, substantial complexity in the receiver system can be justified, provided there is a large enough saving in expensive high-power transmitting equipment. On the other hand, for a broadcast system with a multitude of receivers for each transmitter, it is more economical to have one expensive high-power transmitter and simpler, less expensive receivers. The second option (transmitting a carrier along with the modulated signal) is the obvious choice in this case. This is amplitude modulation (AM), in which the transmitted signal ϕAM (t) is given by

$$\varphi_{AM}(t) = A\cos\omega_c t + m(t)\cos\omega_c t = [A + m(t)]\cos\omega_c t \tag{7.50}$$

Recall that the DSB-SC signal is m(t) cos ωct. From Eq. (7.50) it follows that the AM signal is identical to the DSB-SC signal with A+m(t) as the modulating signal [instead of m(t)]. Therefore, to sketch ϕAM (t), we sketch A + m(t) and −[A + m(t)] as the envelopes and fill in between with the sinusoid of the carrier frequency. Two cases are considered in Fig. 7.39. In the first case, A is large enough so that A + m(t) ≥ 0 (is nonnegative) for all values of t. In the second case, A is not large enough to satisfy this condition. In the first case, the envelope (Fig. 7.39d) has the same shape as m(t) (although riding on a dc of magnitude A). In the second case, the envelope shape is not m(t), for some parts get rectified (Fig. 7.39e). Thus, we can detect the desired signal m(t) by detecting the envelope in the first case. In the second case, such a detection is not possible. We shall see that envelope detection is an extremely simple and inexpensive operation, which does not require generation of a local carrier for the demodulation. But as just noted, the envelope of AM has the information about m(t) only if the AM signal [A+m(t)] cos ωct satisfies the condition A+m(t) > 0 for all t. Thus, the condition for envelope detection of an AM signal is

$$A + m(t) \ge 0 \qquad \text{for all } t \tag{7.51}$$

If mp is the peak amplitude (positive or negative) of m(t), then Eq. (7.51) is equivalent to

$$A\geq m_p$$

Thus, the minimum carrier amplitude required for the viability of envelope detection is mp. This point is clearly illustrated in Fig. 7.39.

We define the modulation index μ as

$$\mu = \frac{m_p}{A} \tag{7.52}$$

where A is the carrier amplitude. Note that mp is a constant of the signal m(t). Because A ≥ mp and because there is no upper bound on A, it follows that

0 ≤ μ ≤ 1

Figure 7.39 An AM signal (a) for two values of A (b, c) and the respective envelopes (d, e).

as the required condition for the viability of demodulation of AM by an envelope detector.

When A < mp, Eq. (7.52) shows that μ > 1 (overmodulation, shown in Fig. 7.39e). In this case, the option of envelope detection is no longer viable. We then need to use synchronous demodulation. Note that synchronous demodulation can be used for any value of μ (see Prob. 7.7-7). The envelope detector, which is considerably simpler and less expensive than the synchronous detector, can be used only when μ ≤ 1.

EXAMPLE 7.23 Amplitude Modulation

Sketch ϕAM (t) for modulation indices of μ = 0.5 (50% modulation) and μ = 1 (100% modulation), when m(t) = Bcos ωmt. This case is referred to as tone modulation because the modulating signal is a pure sinusoid (or tone).

744 CHAPTER 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM

In this case, mp = B and the modulation index according to Eq. (7.52) is

$$\mu = \frac{B}{A}$$

Hence, B = μA and

$$m(t) = B\cos\omega_m t = \mu A\cos\omega_m t$$

Therefore,

$$\varphi_{AM}(t) = [A + m(t)] \cos \omega_c t = A[1 + \mu \cos \omega_m t] \cos \omega_c t$$

The modulated signals corresponding to μ = 0.5 and μ = 1 appear in Figs. 7.40a and 7.40b, respectively.

DEMODULATION OF AM: THE ENVELOPE DETECTOR

The AM signal can be demodulated coherently by a locally generated carrier (see Prob. 7.7-7). Since, however, coherent, or synchronous, demodulation of AM (with μ ≤ 1) will defeat the very purpose of AM, it is rarely used in practice. We shall consider here one of the noncoherent methods of AM demodulation, envelope detection. †

In an envelope detector, the output of the detector follows the envelope of the (modulated) input signal. The circuit illustrated in Fig. 7.41a functions as an envelope detector. During the positive cycle of the input signal, the diode conducts and the capacitor C charges up to the peak voltage of the input signal (Fig. 7.41b). As the input signal falls below this peak value, the diode is cut off, because the capacitor voltage (which is very nearly the peak voltage) is greater than the input signal voltage, a circumstance causing the diode to open. The capacitor now discharges through the resistor R at a slow rate (with a time constant RC). During the next positive cycle,

^† There are also other methods of noncoherent detection. The rectifier detector consists of a rectifier followed by a lowpass filter. This method is also simple and almost as inexpensive as the envelope detector [4]. The nonlinear detector, although simple and inexpensive, results in a distorted output.

Figure 7.41 Demodulation by means of envelope detector.

the same drama repeats. When the input signal becomes greater than the capacitor voltage, the diode conducts again. The capacitor again charges to the peak value of this (new) cycle. As the input voltage falls below the new peak value, the diode cuts off again and the capacitor discharges slowly during the cutoff period, a process that changes the capacitor voltage very slightly.

In this manner, during each positive cycle, the capacitor charges up to the peak voltage of the input signal and then decays slowly until the next positive cycle. Thus, the output voltage vC(t) follows closely the envelope of the input. The capacitor discharge between positive peaks, however, causes a ripple signal of frequency ω*^c* in the output. This ripple can be reduced by increasing the time constant RC so that the capacitor discharges very little between the positive peaks (RC 1/ωc). Making RC too large, however, would make it impossible for the capacitor voltage to follow the envelope (see Fig. 7.41b). Thus, RC should be large in comparison to 1/ω*^c* but small in comparison to 1/2πB, where B is the highest frequency in m(t). Incidentally, these two conditions also require that ω*^c* 2πB, a condition necessary for a well-defined envelope.

The envelope-detector output vC(t) is A + m(t) plus a ripple of frequency ωc. The dc term A can be blocked out by a capacitor or a simple RC highpass filter. The ripple is reduced further by

746 CHAPTER 7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER TRANSFORM

another (lowpass) RC filter. In the case of audio signals, the speakers also act as lowpass filters, which further enhances suppression of the high-frequency ripple.

7.7-3 Single-Sideband Modulation (SSB)

Now consider the baseband spectrum M(ω) (Fig. 7.42a) and the spectrum of the DSB-SC modulated signal m(t) cos ωct (Fig. 7.42b). The DSB spectrum in Fig. 7.42b has two sidebands: the upper and the lower (USB and LSB), both containing complete information on M(ω) [see Eq. (7.12)]. Clearly, it is redundant to transmit both sidebands, a process that requires twice the bandwidth of the baseband signal. A scheme in which only one sideband is transmitted is known

Figure 7.42 Spectra for single-sideband transmission: (a) baseband, (b) DSB, (c) USB, (d) LSB, and (e) synchronously demodulated signal.

as single-sideband (SSB) transmission, which requires only half the bandwidth of the DSB signal. Thus, we transmit only the upper sidebands (Fig. 7.42c) or only the lower sidebands (Fig. 7.42d).

An SSB signal can be coherently (synchronously) demodulated. For example, multiplication of a USB signal (Fig. 7.42c) by 2 cos ωct shifts its spectrum to the left and to the right by ωc, yielding the spectrum in Fig. 7.42e. Lowpass filtering of this signal yields the desired baseband signal. The case is similar with an LSB signal. Hence, demodulation of SSB signals is identical to that of DSB-SC signals, and the synchronous demodulator in Fig. 7.38a can demodulate SSB signals. Note that we are talking of SSB signals without an additional carrier. Hence, they are suppressed-carrier signals (SSB-SC).

EXAMPLE 7.24 Single-Sideband Modulation

Find the USB (upper sideband) and LSB (lower sideband) signals when m(t) = cos ωmt. Sketch their spectra, and show that these SSB signals can be demodulated using the synchronous demodulator in Fig. 7.38a.

The DSB-SC signal for this case is

$$\varphi_{\text{DSB-SC}}(t) = m(t)\cos\omega_c t = \cos\omega_m t \cos\omega_c t \qquad = \frac{1}{2} [\cos(\omega_c - \omega_m)t + \cos(\omega_c + \omega_m)t]$$

As pointed out in Ex. 7.21, the terms (1/2) cos(ω*^c* + ωm)t and (1/2) cos(ω*^c* − ωm)t represent the upper and lower sidebands, respectively. The spectra of the upper and lower sidebands are given in Figs. 7.43a and 7.43b. Observe that these spectra can be obtained from the DSB-SC spectrum in Fig. 7.37b by using a proper filter to suppress the undesired sidebands. For instance, the USB signal in Fig. 7.43a can be obtained by passing the DSB-SC signal (Fig. 7.37b) through a highpass filter of cutoff frequency ωc. Similarly, the LSB signal in Fig. 7.43b can be obtained by passing the DSB-SC signal through a lowpass filter of cutoff frequency ωc.

If we apply the LSB signal (1/2) cos(ω*^c* − ωm)t to the synchronous demodulator in Fig. 7.38a, the multiplier output is

$$e(t) = \frac{1}{2}\cos{(\omega_c - \omega_m)t}\cos{\omega_c t} = \frac{1}{4}[\cos{\omega_m t} + \cos{(2\omega_c - \omega_m)t}]$$

The term (1/4) cos(2ωc−ωm)t is suppressed by the lowpass filter, producing the desired output (1/4) cos ωmt [which is m(t)/4]. The spectrum of this term is π[δ(ω+ωm)+δ(ω−ωm)]/4, as depicted in Fig. 7.43c. In the same way, we can show that the USB signal can be demodulated by the synchronous demodulator.

In the frequency domain, demodulation (multiplication by cos ωct) amounts to shifting the LSB spectrum (Fig. 7.43b) to the left and the right by ω*^c* (times 0.5) and then suppressing the high frequency, as illustrated in Fig. 7.43c. The resulting spectrum represents the desired signal (1/4)m(t).

GENERATION OF SSB SIGNALS

Two methods are commonly used to generate SSB signals. The selective-filtering method uses sharp cutoff filters to eliminate the undesired sideband, and the second method uses phase-shifting networks to achieve the same goal [4].† We shall consider here only the first method.

Selective filtering is the most commonly used method of generating SSB signals. In this method, a DSB-SC signal is passed through a sharp cutoff filter to eliminate the undesired sideband.

To obtain the USB, the filter should pass all components above ω*^c* unattenuated and completely suppress all components below ωc. Such an operation requires an ideal filter, which is unrealizable. It can, however, be realized closely if there is some separation between the passband and the stopband. Fortunately, the voice signal provides this condition, because its spectrum shows little power content at the origin (Fig. 7.44). Moreover, articulation tests show that for speech signals, frequency components below 300 Hz are not important. In other words, we may suppress all speech components below 300 Hz without appreciably affecting intelligibility.‡ Thus, filtering of the unwanted sideband becomes relatively easy for speech signals because we have a 600 Hz transition region around the cutoff frequency ωc. For some signals, which have considerable power

^† Yet another method, known as Weaver’s method, is also used to generate SSB signals.

^‡ Similarly, suppression of components of a speech signal above 3500 Hz causes no appreciable change in intelligibility.

at low frequencies (around ω = 0), SSB techniques cause considerable distortion. Such is the case with video signals. Consequently, for video signals, instead of SSB, we use another technique, the vestigial sideband (VSB), which is a compromise between SSB and DSB. It inherits the advantages of SSB and DSB but avoids their disadvantages at a cost of slightly increased bandwidth. VSB signals are relatively easy to generate, and their bandwidth is only slightly (typically 25%) greater than that of SSB signals. In VSB signals, instead of rejecting one sideband completely (as in SSB), we accept a gradual cutoff from one sideband [4].

7.7-4 Frequency-Division Multiplexing

Signal multiplexing allows transmission of several signals on the same channel. Later, in Ch. 8 (Sec. 8.2-2), we shall discuss time-division multiplexing (TDM), where several signals time-share the same channel, such as a cable or an optical fiber. In frequency-division multiplexing (FDM), the use of modulation, as illustrated in Fig. 7.45, makes several signals share the band of the same channel. Each signal is modulated by a different carrier frequency. The various carriers are adequately separated to avoid overlap (or interference) between the spectra of various modulated signals. These carriers are referred to as subcarriers. Each signal may use a different kind of modulation, for example, DSB-SC, AM, SSB-SC, VSB-SC, or even other forms of modulation, not discussed here [such as FM (frequency modulation) or PM (phase modulation)]. The modulated-signal spectra may be separated by a small guard band to avoid interference and to facilitate signal separation at the receiver.

When all the modulated spectra are added, we have a composite signal that may be considered to be a new baseband signal. Sometimes, this composite baseband signal may be used to further modulate a high-frequency (radio frequency, or RF) carrier for the purpose of transmission.

At the receiver, the incoming signal is first demodulated by the RF carrier to retrieve the composite baseband, which is then bandpass-filtered to separate the modulated signals. Then each modulated signal is individually demodulated by an appropriate subcarrier to obtain all the basic baseband signals.