Question:
A TDM system is used to multiplex four independent voice signals each sampled at the rate of 8 kHz using PAM. The system incorporates a synchronizing pulse train for its proper operation. Calculate the transmission bandwidth?
A TDM system is used to multiplex four independent voice signals each sampled at the rate of 8 kHz using PAM. The system incorporates a synchronizing pulse train for its proper operation. Calculate the transmission bandwidth?
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For TDM-PAM:
\[
B=(N+\text{sync pulses})f_s
\]
Always include synchronization slots when calculating transmission rate.
Updated On: Jun 25, 2026
- \(8~kHz\)
- \(16~kHz\)
- \(32~kHz\)
- \(40~kHz\)
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The Correct Option is D
Solution and Explanation
Concept:
In TDM-PAM, one frame contains samples from all channels plus one synchronization pulse.
The pulse transmission rate determines the bandwidth.
Step 1: Determine pulses per frame.
Number of voice channels \[ N=4 \] One synchronizing pulse is added. Therefore, \[ \text{Pulses per frame}=4+1=5 \]
Step 2: Determine frame repetition rate.
Each channel is sampled at \[ f_s=8~kHz \] Hence frame rate is also \[ 8~kHz \]
Step 3: Compute pulse rate.
\[ R_p=5\times8~kHz \] \[ R_p=40~kHz \] Transmission bandwidth approximately equals pulse rate. \[ B=40~kHz \]
Step 4: Final Answer.
\[ \boxed{40~kHz} \] Hence, \[ \boxed{\text{Correct Option (D)}} \]
Step 1: Determine pulses per frame.
Number of voice channels \[ N=4 \] One synchronizing pulse is added. Therefore, \[ \text{Pulses per frame}=4+1=5 \]
Step 2: Determine frame repetition rate.
Each channel is sampled at \[ f_s=8~kHz \] Hence frame rate is also \[ 8~kHz \]
Step 3: Compute pulse rate.
\[ R_p=5\times8~kHz \] \[ R_p=40~kHz \] Transmission bandwidth approximately equals pulse rate. \[ B=40~kHz \]
Step 4: Final Answer.
\[ \boxed{40~kHz} \] Hence, \[ \boxed{\text{Correct Option (D)}} \]
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