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Frequency-division multiplexing

Frequency-division multiplexing (FDM) is an analog multiplexing technique that enables the simultaneous transmission of multiple signals over a single by dividing the available into non-overlapping bands, with each band assigned to a separate signal modulated onto a distinct carrier . The core principle of FDM involves modulating each input signal—typically signals like audio or voice—onto a unique carrier frequency using techniques such as (AM) or single-sideband (), then combining these modulated signals into a composite for . At the receiver end, bandpass filters separate the bands, and demodulators recover the original signals, with guard bands—unused frequency spaces between channels—preventing and interference. This method contrasts with (TDM) by allocating frequency resources rather than time slots, making it suitable for continuous analog signals. FDM traces its origins to the late , with early experimental systems in the and attempting acoustic and to send multiple messages over wires using different tones, though practical implementation awaited advancements in . By the early , Guglielmo Marconi's 1900 patent for tuned circuits laid foundational technology for frequency separation in radio, enabling basic FDM. Commercial viability emerged in with vacuum tube-based carrier systems, revolutionizing by allowing multiple voice channels over single lines. Key milestones include the 1957 Kineplex system for military radio, which used 20 tones for data transmission, highlighting FDM's role in parallel signaling. Historically, dominated long-distance , , and microwave relay systems from the mid-20th century, supporting up to thousands of in hierarchies like voice-frequency groups (12 at 48 kHz) and supergroups (60 at 240 kHz) and mastergroups (600 at 2.4 MHz). Applications extended to , where it distributed multiple TV signals over cables, and early communications. In open-wire carrier systems, FDM transmitted calls at around 100 kHz with 4 kHz per , facilitating transcontinental networks until phased out by technologies in the . While traditional FDM has largely been supplanted by digital methods like TDM and in fiber optics due to higher efficiency and lower noise susceptibility, its legacy persists in modern variants such as (OFDM), which eliminates guard bands through subcarrier orthogonality and underpins standards like , , and digital TV. FDM's emphasis on spectral allocation remains fundamental to multi-user systems, ensuring robust signal separation in bandwidth-constrained environments.

Fundamental Principles

Core Concept

Frequency-division multiplexing (FDM) is an analog multiplexing technique that enables the simultaneous of multiple signals over a shared communication medium by allocating each signal to a distinct, non-overlapping band within the available of the medium. This approach divides the total into narrower sub-bands, separated by guard bands to minimize , allowing efficient use of the medium's capacity for applications like and data . In FDM, baseband signals—such as audio or low-frequency data—are first modulated onto separate carrier frequencies to shift them into their assigned spectral slots, ensuring no overlap and thus preventing crosstalk between channels. The modulation process typically employs techniques such as amplitude modulation (AM) or, more efficiently, single-sideband suppressed-carrier (SSB-SC) modulation, particularly in telephony to minimize bandwidth usage by transmitting only one sideband along with a suppressed carrier. In AM, the amplitude of a high-frequency carrier wave is varied in accordance with the baseband signal, while the carrier's frequency remains constant; this produces sidebands around the carrier that occupy the designated band without altering the baseband content. The modulated signals are then combined linearly into a composite multiplexed signal for transmission over the medium, such as a cable or radio link. The basic FDM transmission process can be illustrated by the following simplified of the multiplexing stage: 
Input Signal 1 ──► Modulator (Carrier f1) ──┐
Input Signal 2 ──► Modulator (Carrier f2) ──┤
Input Signal N ──► Modulator (Carrier fN) ──┤
                                           │
                                           ▼
                                       Linear Combiner
                                           │
                                           ▼
                                    [Multiplexed Output Signal](/page/Multiplexing)
Here, each input is modulated onto its unique frequency, and the outputs are summed to form the composite signal. At the end, bandpass filters isolate each , followed by to recover the original signals. A practical example of FDM is the transmission of multiple voice channels over a single , where each voice signal (occupying a of about 4 kHz) is modulated to a separate and combined, allowing dozens or more channels to share the cable's efficiently.

Spectrum Allocation and Filtering

In frequency-division multiplexing (FDM), the total available bandwidth B is divided into N non-overlapping sub-bands, each allocated a width b such that B \approx N \times b, with provisions for guard bands to accommodate practical implementation. This division enables multiple signals to share the medium by assigning each to a distinct range, ensuring efficient utilization while maintaining . Guard bands, consisting of unused frequency portions between sub-bands, play a critical role in preventing by providing separation that minimizes overlap from filter imperfections or signal leakage. Guard bands typically occupy a portion of the sub-band width, often around 20-25% in applications, allowing for the use of less sharp (and thus more cost-effective) filters without excessive inter-channel . For instance, in FDM systems, the standard voice channel bandwidth is 4 kHz, spanning 300 Hz to 3400 Hz, with guard bands positioned at 0-300 Hz and 3400-4000 Hz to isolate adjacent channels. Filtering techniques are essential at both the transmitter and receiver ends to isolate signals within their assigned sub-bands. At the (transmitter), each signal is first modulated onto a unique carrier frequency, then the modulated signals are combined, with bandpass filters ensuring that each occupies its designated without encroaching on others. At the demultiplexer (), a bank of bandpass filters separates the composite signal back into individual modulated components, followed by for each. The mathematical foundation of signal placement in FDM relies on to shift signals to their s. A signal s(t) is modulated to a frequency f_c using the equation x(t) = s(t) \cos(2\pi f_c t), which produces a double-sideband suppressed- (DSB-SC) signal centered at f_c (for illustration; SSB variants one for efficiency). at the receiver involves mixing the received signal with a at f_c (i.e., multiplying by \cos(2\pi f_c t)) and applying a to recover s(t), rejecting higher-frequency components. Non-ideal filters in FDM systems introduce , degrading through from neighboring sub-bands. The attenuation of this is approximately 6 per of frequency separation beyond the , arising from the roll-off characteristics of practical bandpass filters (e.g., +6 / in the passband transition for high-pass sections). This necessitates careful sizing to achieve sufficient , typically targeting levels below -50 in high-fidelity applications.

Historical Development

Origins and Early Innovations

Building on 19th-century acoustic and harmonic telegraphy experiments in the 1860s and 1870s to send multiple messages over wires using different tones, the concept of frequency-division multiplexing (FDM) emerged from early efforts to separate signals using distinct frequencies in telegraphy. In 1898, Karl Ferdinand Braun introduced tuned circuits in wireless telegraphy systems, enabling frequency selectivity to reduce interference and allow multiple signals to coexist without overlap, providing a foundational principle for later multiplexing techniques. Similarly, Émile Baudot's pioneering work in the 1870s on multiplexing for telegraphy demonstrated the feasibility of sharing a communication channel among multiple users, though his approach relied on time-division methods rather than frequency separation. The true invention of FDM for telephony is credited to Major George Owen Squier of the U.S. Signal Corps, who in 1910 patented a carrier multiplexing system that modulated multiple voice signals onto different carrier frequencies for transmission over a single wire pair, effectively creating the first practical frequency-based telephony multiplex. AT&T licensed Squier's technology and advanced its development through the 1910s. A key milestone came in 1918, when engineers Lloyd Espenschied and Herman Affel at AT&T demonstrated the first multi-channel carrier system over open-wire lines, transmitting multiple voice channels using a five-carrier setup between Baltimore, Maryland, and Pittsburgh, Pennsylvania, spanning approximately 250 miles. This early system employed double-sideband amplitude modulation, allocating 4 kHz voice channels spaced at 8 kHz centers to incorporate guard bands that minimized crosstalk between adjacent signals. The motivation for shifting from single-channel to multi-channel transmission intensified after , as surging demand for long-distance telephone service—driven by and —strained existing open-wire , necessitating more efficient use of toll circuits to handle the volume of interstate calls without laying vast new lines. In the 1920s, pre-commercial laboratory tests at further refined FDM, achieving 12-channel multiplexing over open-wire routes, which validated the technology's scalability for broader deployment while building on the basic carrier modulation principles.

Key Milestones in the 20th Century

In the late 1930s, commercialized frequency-division multiplexing through the introduction of the Type J carrier system in 1938, which enabled the transmission of 12 voice channels over a single pair of open-wire lines using analog FDM techniques. This system marked a significant step in scaling capacity without requiring new physical infrastructure, building on earlier experimental work. By 1942, completed the first transcontinental underground cable route from to , enhancing long-distance connectivity during wartime demands. Following , expanded FDM capabilities with the L-carrier series in the 1950s, starting with enhancements to the L-1 system and introducing the L-3 carrier in 1953, which supported up to 1,860 voice channels per through hierarchical of groups and supergroups. A key deployment occurred in 1951 with the New York-to-San Francisco microwave relay system, an FDM-based link that initially handled hundreds of circuits and was later expanded to over 2,000 voice equivalents, facilitating transcontinental broadcasts and telephony. The 1960s saw international standardization of FDM hierarchies under the CCITT (now ), with recommendations establishing the mastergroup as 600 voice channels and the supermastergroup as 3,600 channels, enabling interoperable global networks for analog telephony. These standards, formalized in CCITT Fascicle III.2, promoted widespread adoption in international submarine cables and terrestrial links. A notable application was the 1964 Tokyo Olympics, where FDM and cable relays supported the first satellite-assisted international TV transmission, relaying live color footage to audiences worldwide. By the 1970s and 1980s, FDM began declining as fiber optics and time-division multiplexing (TDM) technologies offered higher capacity and lower costs, with initiating widespread digital conversions in long-haul networks. Despite this shift, analog FDM persisted in legacy systems through the , particularly in developing regions and for compatibility with existing infrastructure.

Applications in Telephony

Analog Telephone Multiplexing

In analog telephone networks, frequency-division multiplexing (FDM) enabled the efficient transmission of multiple voice channels over shared long-haul facilities by combining signals from local lines at central offices into a single composite signal suitable for transmission on fewer physical lines. Central office multiplexers served as the key components in this architecture, aggregating individual 4 kHz voice channels—typically derived from subscriber loops—into higher-frequency bands to form the composite signal, which was then routed through toll networks for inter-city or long-distance connectivity. This setup minimized the infrastructure demands of early telephone systems by leveraging a single pair of copper wires or open-wire lines to carry dozens or hundreds of simultaneous conversations, a significant advancement over dedicated lines per call. The primary equipment in these FDM systems included modulators, such as balanced modulators designed for suppression to eliminate redundant and power while preserving the voice information in a 3-4 kHz per . These modulators translated each voice signal to its assigned , after which combiners or adders summed the modulated channels into the composite signal, and line amplifiers boosted the power for transmission over cable or open-wire routes. At the receiving end, demultiplexing occurred using banks of tunable bandpass filters to isolate individual channels, followed by demodulators to recover the original signals for distribution to local lines. Operationally, the process began in channel banks at the transmitting central office, where each voice channel's baseband signal (0-4 kHz) was modulated to an (IF) band, such as 60-108 kHz for a basic group of channels, using techniques to optimize spectrum use. The IF composite was then further translated to a final line frequency compatible with the , such as or cable carriers, and amplified for dispatch. This hierarchical translation ensured minimal between channels while accommodating the limited of analog facilities. FDM found widespread application in toll networks during the mid-20th century, particularly from onward, to drastically reduce the need for wire pairs in long-haul routes; for instance, a single pair could support up to 12 voice channels in a basic group with a typical composite of 48 kHz, including guard bands to prevent . This efficiency was crucial for scaling national infrastructures without proportional increases in cabling costs. To manage and inherent in analog , equalizers were integrated into the FDM to counteract frequency-dependent and shifts in cables, which could otherwise degrade higher-frequency channels more severely than lower ones. These devices applied compensatory across the , ensuring uniform signal quality across all multiplexed channels and maintaining acceptable signal-to-noise ratios over extended distances.

Group and Supergroup Hierarchies

In frequency-division multiplexing (FDM) systems for , channels are organized into hierarchical levels to efficiently aggregate multiple voice circuits into higher- aggregates for long-haul transmission. The lowest level is the basic group, which combines 12 voice channels, each allocated a 4 kHz slot (with small guard bands to prevent ), for a total bandwidth of 48 kHz. These channels are modulated onto frequencies ranging from 60 kHz to 108 kHz, with the first channel at 64 kHz and subsequent channels spaced at 4 kHz intervals. This basic group structure is common to both international and North American standards. The next level assembles five basic groups into a supergroup, supporting 60 voice channels with a total of 240 kHz. In the CCITT (now ) standard, as well as North American systems, this is achieved by modulating each basic group onto intermediate carriers (e.g., at 316 kHz for the first group), resulting in the supergroup occupying the frequency band from 312 kHz to 552 kHz. Further aggregation differs by standard. In the North American () hierarchy, a mastergroup combines 10 supergroups, accommodating 600 voice channels across a bandwidth of 2.52 MHz in the 564-3084 kHz . This upper-sideband configuration (often denoted as U-600) allows efficient use of or media. The hierarchy progresses to larger units, such as the jumbogroup in AT&T's L5 carrier system, which multiplexes six mastergroups for 3600 channels, enabling high-capacity transcontinental links introduced in the 1970s. In contrast, the CCITT international standard defines a mastergroup as 5 supergroups (300 voice channels, approximately 1.3 MHz bandwidth). The hierarchy continues to a supermastergroup combining 3 mastergroups (900 channels). This stepwise assembly process involves successive stages: individual voice channels are first translated to form a basic group using channel , then groups are upconverted via group to build supergroups, and higher-level multiplexers (e.g., supergroup and mastergroup equipment) shift these aggregates to non-overlapping bands using stable carriers and sharp filters. The CCITT Recommendation G.232, established in and revised in subsequent years, standardized the basic group and higher hierarchies for international consistency, ensuring across global networks with the 4 kHz spacing integral to all levels. In practice, these hierarchies built upon 1950s innovations like AT&T's L-carrier systems, which adapted similar grouping for domestic microwave and coaxial transmission.

Other Applications

Broadcasting Systems

Frequency-division multiplexing (FDM) plays a central role in broadcasting systems, enabling the simultaneous transmission of multiple audio and video signals over shared frequency spectra in radio and television applications. In FM radio, stereo broadcasting employs a multiplexing scheme where the main channel carries the sum (L+R) of left and right audio signals within a 15 kHz bandwidth, while a 19 kHz pilot tone allows receivers to detect stereo content and regenerate a 38 kHz suppressed subcarrier for the difference (L-R) signal, all modulated onto carriers in the 88-108 MHz band. This configuration ensures backward compatibility with monaural receivers, which ignore the subcarrier components, and has been the standard since the mid-20th century for high-fidelity audio delivery. In AM radio, particularly on (3-30 MHz), analog FDM facilitates multi-station by assigning discrete carrier frequencies to individual programs, allowing multiple services to operate without within the allocated . This approach contrasts with digital standards like , which can embed multiple programs into sidebands around a single carrier, but analog shortwave relies on traditional FDM for global propagation of diverse content, such as international news and cultural programs. Television broadcasting leverages FDM through vestigial sideband (VSB) modulation in analog systems, where the video signal occupies 0-4.2 MHz around the carrier, and the audio signal is frequency-modulated at a 4.5 MHz offset in standards like NTSC, fitting within a 6 MHz channel to optimize bandwidth usage. In cable television networks, FDM stacks these 6 MHz channels across a coaxial spectrum from 50-550 MHz for downstream delivery, enabling dozens of video and audio services to reach subscribers via a single cable without crosstalk. The approval of FM stereo multiplexing in 1961 marked the first widespread application of FDM beyond , revolutionizing broadcast audio by enabling spatial sound reproduction over the airwaves. In , systems like NICAM built on these analog FDM foundations by adding a subcarrier at 728 kbit/s, providing near-CD quality stereo or bilingual sound alongside the primary analog video and mono audio signals in analog TV transmissions. For distribution, FDM supports microwave relay links in broadcast networks, where multiple and radio channels are combined into high-capacity trunks for between studios and transmitters. Satellite downlinks similarly employ FDM to deliver up to 100 channels, with transponders modulating video carriers in bands like C-band (4-8 GHz) to serve wide-area audiences efficiently.

Data and Cable Transmission

Frequency-division multiplexing (FDM) found early applications in data transmission beyond voice telephony, particularly in telegraphy and teletype systems during the mid-20th century. In the 1950s, military communications leveraged FDM carriers to multiplex telegraph and teletype signals over radio links, enabling multiple low-speed channels—such as 250 baud frequency-shift keying (FSK) streams—within a shared bandwidth of around 1.5 kHz. These systems, often using independent sideband techniques, standardized FDM for flexible, multi-channel data relay in tactical environments. FDM also enabled full-duplex operation in early s by splitting the available into distinct frequency bands for upstream and downstream , often alongside signals. This voice/ separation allowed simultaneous transmission over two-wire circuits, with FDM reducing effective per direction but supporting bidirectional flow without . For instance, modems modulated into higher frequency bands while reserving lower ones for analog , a technique that became foundational for hybrid voice- links in the post-World War II era. In cable infrastructure, FDM underpinned the evolution of community antenna television (CATV) systems starting in the 1970s, where coaxial cables carried dozens of analog video channels by assigning each a 4-6 MHz band within the total spectrum. Early CATV networks, initially limited to 12 channels, expanded to support 20-50 channels by the mid-1970s through FDM, distributing broadcast signals to remote areas with poor over-the-air reception. These analog FDM setups served as precursors to modern data services, with cable operators later overlaying bidirectional data on the same infrastructure before transitioning to hybrid fiber-coax (HFC) architectures in the . Beyond terrestrial links, FDM facilitated transmission in challenging environments, such as underwater cables. The transatlantic cable, operational from 1956, employed analog FDM over conductors to support 36 voice-grade channels, each with 4 kHz , for reliable long-haul telegraph and early relay across 3,600 km. In satellite communications, FDM multiplexed streams—such as sensor readings and control signals—into separate frequency sub-bands for uplink and downlink, allowing multiple low-rate channels to share transponder efficiently. A prominent example of FDM in data modems persists in asymmetric digital subscriber line () technology, where the plain old telephone service () band (0-4 kHz) is isolated from data bands via frequency splitting. In , voice occupies 0-4 kHz, a spans 4-25 kHz, upstream data uses 25-138 kHz (covering sub-channels 6-31), and downstream extends to 1.1 MHz, enabling simultaneous voice and over existing twisted-pair lines without cross-talk. Although largely supplanted by digital alternatives, legacy FDM-based systems like remain in use for rural , providing data rates up to several Mbps where deployment is uneconomical. Phase-outs of these copper-based FDM infrastructures have accelerated in the 2020s, with many countries targeting completions between 2025 and 2030 driven by regulatory pushes for upgrades; as of November 2025, some remote networks continue to support them.

Advantages, Limitations, and Comparisons

Benefits and Technical Challenges

Frequency-division multiplexing (FDM) provides significant benefits due to its analog nature, particularly in of hardware . Unlike time-based schemes, FDM requires no between transmitters and receivers, as each signal occupies a distinct frequency band, allowing independent operation without complex timing mechanisms. This facilitates straightforward using basic analog components like modulators and filters, reducing complexity for systems handling multiple signals. FDM is especially efficient for transmitting continuous signals, such as voice in applications, where constant allocation supports uninterrupted flow without the need for buffering or sampling. Its further enhances utility, as additional carriers can be introduced to expand on existing , enabling cost-effective upgrades to legacy systems without replacing physical lines. For instance, in , FDM carrier systems dramatically increased line capacity—up to twelvefold—over single-channel setups while utilizing the same wires, demonstrating low-cost enhancements for established networks. Despite these advantages, FDM systems face notable technical challenges stemming from their analog foundation. One primary issue is susceptibility to and , which worsens as the number of channels grows, since closely spaced bands are prone to from adjacent signals. utilization is also inefficient, as guard bands—unused intervals between channels to prevent overlap—typically limit overall efficiency to around 70%, wasting that could otherwise carry data. Nonlinearities in amplifiers introduce distortion, where multiple input signals generate unwanted products that fall into other channels, degrading signal quality. These distortion products appear at frequencies given by m f_1 \pm n f_2, where f_1 and f_2 are the input frequencies, and m and n are integers representing the order of nonlinearity, often causing in-band in multi-channel setups. Maintenance poses additional hurdles, as analog filters in FDM systems experience drift due to aging, temperature variations, and environmental factors, necessitating regular to maintain channel separation and performance. Furthermore, high-channel-count configurations lead to power inefficiency, as each requires dedicated , escalating overall and heat generation in along long transmission lines.

Comparison to Time-Division Multiplexing

Frequency-division multiplexing (FDM) and (TDM) represent two fundamental approaches to combining multiple signals for transmission over a shared medium, differing primarily in how they allocate resources. FDM divides the available into separate, non-overlapping frequency bands, each assigned to a different signal, which makes it particularly suitable for analog signals as it avoids the need for precise between transmitters and receivers. In contrast, TDM segments the transmission time into discrete slots, cyclically allocating these to individual signals, a method that aligns well with digital signals but demands accurate timing synchronization to prevent slot overlaps or losses. In terms of performance, FDM excels with variable-rate analog signals by enabling continuous transmission without interruption, though it is susceptible to and if guard bands between frequency channels are insufficient. TDM, however, achieves greater spectrum efficiency—often approaching 100% utilization after accounting for minimal overhead—and provides superior resistance through digital regeneration, which reconstructs signals at without accumulating analog distortions. These attributes make TDM more scalable for high-capacity links, as it multiplexes signals like the 24 channels in a T1 system at 1.544 Mbps, outperforming FDM's analog hierarchies in utilization. The transition from FDM to TDM marked a pivotal shift in during the mid-20th century, driven by the advantages of digital processing. Introduced in the public during the 1960s, T1 systems using TDM began outperforming FDM by enabling efficient over twisted-pair cables, which FDM required more expensive or links to handle. By the , the advent of fiber optics further accelerated this replacement, with TDM-based standards like standardizing high-speed digital transmission and phasing out most analog FDM deployments in core networks. In modern optical networks, (WDM)—an analog to FDM using different light s instead of radio frequencies—coexists with TDM, often in hybrid configurations to maximize capacity. While pure TDM handles time-slot allocation within a single wavelength, WDM parallels FDM by dividing the across multiple wavelengths, allowing TDM to operate independently on each for enhanced scalability in passive optical networks (). This hybrid approach, such as in WDM/TDM , leverages WDM's frequency-like separation for broader while using TDM for fine-grained sharing, sustaining TDM's dominance in digital environments even as FDM recedes.

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