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TDM vs FDM for voice; 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.

Compare TDM and FDM. Show that for voice application. Compare E1 and T1 hierarchies.

Comparison of TDM and FDM

PointFDMTDM
Sharing basisEach signal gets its own frequency bandEach signal gets its own time slot
Time useAll signals sent at the same timeSignals sent one after another
Signal typeMainly analogMainly digital (PAM/PCM samples)
HardwareModulators, sharp band-pass filters, oscillators per channelSampler, commutator, mostly digital circuits
GuardGuard bands between channelsGuard times between slots
Crosstalk causeNon-linearity, poor filtersPulse spreading (ISI), poor sync
SynchronisationNot criticalFrame sync is essential
Fading effectNarrow-band fading hits only some channelsFading during a slot hits one channel
ExampleRadio/TV broadcast, old analog telephone trunksT1/E1 digital telephony, GSM slots

Voice application

The question asks for the comparison to be shown for voice channels. Take N=24N = 24 telephone channels, each band-limited to 3.4 kHz.

FDM (SSB, 4 kHz slot per channel including guard band):

BFDM=N×4 kHz=24×4=96 kHzB_{FDM} = N \times 4\ \text{kHz} = 24 \times 4 = 96\ \text{kHz}

TDM-PCM (8 kHz sampling, 8 bits/sample, T1 frame):

Bits per frame=24×8+1=193 bitsFrames per second=fs=8000 frames/sRb=193×8000=1 544 000 b/s=1.544 Mb/s\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 Rb/2=772R_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

PointT1 (North America, Japan)E1 (Europe, ITU-T, Nepal)
Voice channels2430 (+2 overhead slots)
Time slots per frame24 + 1 framing bit32
Bits per frame24×8+1=19324 \times 8 + 1 = 19332×8=25632 \times 8 = 256
Frame duration125 µs125 µs
Bit rate1.544 Mb/s2.048 Mb/s
Framing1 F-bit per frame, pattern over 12/24 framesTS0 carries frame alignment word
SignallingRobbed-bit (LSB of frames 6 and 12)Separate slot TS16 (CAS)
MultiframeSuperframe 12 frames / ESF 24 frames16 frames (2 ms)
Companding lawµ-law, μ=255\mu = 255A-law, A=87.6A = 87.6
Line codeAMI / B8ZSHDB3
Higher levels6.312, 44.736, 274.176 Mb/s8.448, 34.368, 139.264, 564.992 Mb/s

✓ Answer checked by Claude Opus 5.5 (high effort)

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