--- title: "TDM vs FDM for voice; E1 and T1 hierarchies" subject: "Communication Systems" chapter: 5 key: "semester_6/communication_systems:tdm-fdm-voice-e1-t1" source: https://www.bctengineer.com/q/semester_6/communication_systems/tdm-fdm-voice-e1-t1 site: BCT Engineering --- # TDM vs FDM for voice; E1 and T1 hierarchies Communication Systems · Chapter 5: Multiplexing Techniques - Asked in: 2079 Chaitra, 3+2+5 marks - Video: [Communication Engineering - Multiplexing Hierarchy for Digital Communication](https://www.youtube.com/watch?v=DrPbb3cDvFE) — Dr. Sapna Katiyar - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/tdm-fdm-voice-e1-t1 - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-5 ## Question Compare TDM and FDM. Show that for voice application. Compare E1 and T1 hierarchies. ## Short answer FDM assigns different frequency bands, TDM assigns time slots. For 24 voice channels, FDM-SSB needs 96 kHz, while T1 PCM needs 1.544 Mbps (~772 kHz Nyquist). E1 carries 30 voice at 2.048 Mbps with TS0/TS16 overhead, T1 carries 24 voice at 1.544 Mbps with a framing bit; E1 uses A-law, T1 µ-law. ## Answer #### Comparison of TDM and FDM | Point | FDM | TDM | |---|---|---| | Sharing basis | Each signal gets its own frequency band | Each signal gets its own time slot | | Time use | All signals sent at the same time | Signals sent one after another | | Signal type | Mainly analog | Mainly digital (PAM/PCM samples) | | Hardware | Modulators, sharp band-pass filters, oscillators per channel | Sampler, commutator, mostly digital circuits | | Guard | Guard bands between channels | Guard times between slots | | Crosstalk cause | Non-linearity, poor filters | Pulse spreading (ISI), poor sync | | Synchronisation | Not critical | Frame sync is essential | | Fading effect | Narrow-band fading hits only some channels | Fading during a slot hits one channel | | Example | Radio/TV broadcast, old analog telephone trunks | T1/E1 digital telephony, GSM slots | #### Voice application The question asks for the comparison to be shown for voice channels. Take $N = 24$ telephone channels, each band-limited to 3.4 kHz. **FDM (SSB, 4 kHz slot per channel including guard band):** $$ B_{FDM} = N \times 4\ \text{kHz} = 24 \times 4 = 96\ \text{kHz} $$ **TDM-PCM (8 kHz sampling, 8 bits/sample, T1 frame):** $$ \begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frames per second} &= f_s = 8000\ \text{frames/s} \\ R_b &= 193 \times 8000 = 1\,544\,000\ \text{b/s} = 1.544\ \text{Mb/s} \end{aligned} $$ The minimum (Nyquist) bandwidth is $R_b/2 = 772$ kHz. So for voice, FDM needs only about one-eighth of the bandwidth of TDM-PCM. TDM-PCM is still preferred because: - regenerative repeaters remove noise at each hop, - digital switching and circuits are cheap, - it can carry speech and data together. FDM was used in older analog trunks. TDM (T1/E1) is used in today's digital telephone networks. #### Comparison of E1 and T1 hierarchies | Point | T1 (North America, Japan) | E1 (Europe, ITU-T, Nepal) | |---|---|---| | Voice channels | 24 | 30 (+2 overhead slots) | | Time slots per frame | 24 + 1 framing bit | 32 | | Bits per frame | $24 \times 8 + 1 = 193$ | $32 \times 8 = 256$ | | Frame duration | 125 µs | 125 µs | | Bit rate | 1.544 Mb/s | 2.048 Mb/s | | Framing | 1 F-bit per frame, pattern over 12/24 frames | TS0 carries frame alignment word | | Signalling | Robbed-bit (LSB of frames 6 and 12) | Separate slot TS16 (CAS) | | Multiframe | Superframe 12 frames / ESF 24 frames | 16 frames (2 ms) | | Companding law | µ-law, $\mu = 255$ | A-law, $A = 87.6$ | | Line code | AMI / B8ZS | HDB3 | | Higher levels | 6.312, 44.736, 274.176 Mb/s | 8.448, 34.368, 139.264, 564.992 Mb/s | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What bandwidth does FDM-SSB need for 24 voice channels at 4 kHz each? A. 48 kHz B. 96 kHz C. 772 kHz D. 1.544 MHz Answer: B. 24 x 4 kHz = 96 kHz. (Key point: FDM bandwidth for 24 voice channels) 2. For 24 voice channels in T1, how is the bit rate found? A. 24 x 8 x 8000 = 1.536 Mb/s with no extra bits B. (24 x 8 + 1) x 8000 = 1.544 Mb/s C. 24 x 8 x 6800 = 1.306 Mb/s D. (24 x 8 + 8) x 8000 = 1.6 Mb/s Answer: B. 193 bits per frame at 8000 frames/s is 1.544 Mb/s. (Key point: TDM-PCM rate) 3. For voice, how do the bandwidths of FDM and TDM-PCM (Nyquist, 772 kHz) compare? A. TDM needs about 8 times less B. FDM needs about 8 times less C. They are equal D. FDM needs twice as much Answer: B. 96 kHz versus 772 kHz: FDM needs about 8 times less bandwidth, yet TDM is preferred for other reasons. (Key point: Bandwidth comparison) 4. Why is TDM-PCM preferred despite needing more bandwidth? A. Regenerative repeaters remove noise, digital switching is cheap, speech and data can be carried together B. It needs no synchronisation C. It uses sharper filters D. It has lower sampling rate Answer: A. Regeneration, cheap digital switching and mixed voice/data carriage outweigh the bandwidth cost. (Key point: Why TDM still preferred) ## Related in Communication Systems - [T1 and E1 TDM-PCM hierarchy with frame diagrams](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-e1-frame-diagrams) — Communication Systems, chapter 5 - [Constellation diagram significance; E1 vs T1](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aconstellation-significance-e1-t1) — Communication Systems, chapter 5 - [Short note: FDM vs TDM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashort-note-fdm-vs-tdm) — Communication Systems, chapter 5 - [FDM vs TDM; FDM telephone hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afdm-vs-tdm-fdm-hierarchy) — Communication Systems, chapter 5 - [FDMA vs TDMA; T1 and E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afdma-tdma-t1-e1) — Communication Systems, chapter 5 - [E1 frame, TDM hierarchy and signaling rate](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-frame-hierarchy) — Communication Systems, chapter 5 ## Related in other subjects - [Compare FDM, WDM and TDM](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acompare-fdm-wdm-tdm) — Data Communication, chapter 6 - [TDM and T1/E1 carrier standards](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atdm-t1-e1-carriers) — Telecommunications, chapter 3 - [North American T1 vs European E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3At1-e1-hierarchy-compare) — Telecommunications, chapter 3, asked 2× - [Comparison of FDM, TDM and WDM](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultiplexing-fdm-tdm-wdm) — Telecommunications, chapter 3, asked 2×