Time Division Multiplexing (TDM) MCQ Quiz - Objective Question with Answer for Time Division Multiplexing (TDM) - Download Free PDF

Explanation:

Signaling Rate of Time Division Multiplexing (TDM) Signal

Definition: Time Division Multiplexing (TDM) is a digital multiplexing technique used to combine multiple data streams or signals into one stream by assigning each signal a different time slot in the sequence. The signaling rate of a TDM signal refers to the rate at which the multiplexed data is transmitted over the communication channel. This rate depends on the number of input channels (M), the sampling frequency (fs), and the bandwidth of the input signals (W).

Explanation of the Correct Option:

The correct option is:

Option 1: r = Mfs ≥ 2MW

In a TDM system, each input channel has a specific sampling rate (fs). According to the Nyquist sampling theorem, the minimum sampling rate for any signal must be at least twice its highest frequency component (2W) to ensure accurate signal reconstruction. Thus, for M input channels, the total signaling rate (r) must satisfy the condition:

r = M × fs, where fs ≥ 2W

Therefore:

r = M × fs ≥ 2M × W

This equation ensures that the TDM system operates effectively without aliasing and that all the input signals are sampled and transmitted correctly. The signaling rate must be at least 2M × W to accommodate all M channels, as each channel requires a bandwidth of W and a sampling rate of at least 2W.

Key Points:

• M: Number of input channels in the TDM system.
• fs: Sampling frequency of each channel, which must be at least twice the bandwidth (2W) to satisfy the Nyquist criterion.
• W: Bandwidth of each input channel.
• The total signaling rate (r) ensures that all channels are multiplexed and transmitted without loss of information.

Conclusion: The signaling rate of a TDM signal for M input channels is given by r = Mfs ≥ 2MW, as stated in Option 1. This ensures that the system adheres to the Nyquist sampling theorem and can effectively transmit all input signals.

Additional Information:

To further understand the analysis, let’s evaluate the other options:

Option 2: r = Mfs ≤ 2MW

This option is incorrect because the signaling rate cannot be less than or equal to 2MW. The condition r = Mfs ≥ 2MW ensures that the Nyquist criterion is satisfied and that all input signals are accurately sampled and transmitted. If r ≤ 2MW, the system would not meet the minimum requirements for sampling and could result in aliasing or loss of information.

Option 3: r = Mfs ≤ MW

This option is incorrect as it violates the Nyquist sampling theorem. If the signaling rate is less than or equal to MW, the sampling frequency (fs) for each channel would be less than 2W, leading to aliasing and inaccurate signal reconstruction. Such a scenario is not feasible for a TDM system.

Option 4: r = Mfs ≥ MW

While this condition might seem plausible at first glance, it is insufficient to ensure accurate signal reconstruction for all channels. The Nyquist theorem requires the sampling frequency to be at least twice the bandwidth (fs ≥ 2W). Therefore, the signaling rate must satisfy r = Mfs ≥ 2MW, not just MW, to avoid aliasing and ensure proper operation.

Conclusion:

Option 1 (r = Mfs ≥ 2MW) is the correct choice as it ensures that the TDM system adheres to the Nyquist criterion, allowing accurate sampling and transmission of all input signals. The other options fail to meet this critical requirement and would result in improper operation of the TDM system.

Explanation:

Frequency Division Multiplexing (FDM)

Definition: Frequency Division Multiplexing (FDM) is a technique used in communication systems to transmit multiple signals over a single communication channel by dividing the total available bandwidth into non-overlapping frequency bands. Each signal is modulated onto a different carrier frequency, and guard bands are placed between them to prevent interference.

Baseband Bandwidth in FDM:

In FDM, the baseband bandwidth is defined as the total bandwidth required to transmit multiple modulated signals, including the guard bands. This ensures that the signals do not interfere with each other during transmission. The correct formula for calculating the baseband bandwidth in FDM is:

Baseband Bandwidth = (Modulated message bandwidths) + (Guard bands)

This formula accounts for the bandwidth occupied by all the modulated signals and the additional frequency spacing (guard bands) required to prevent overlapping and interference between adjacent signals. The inclusion of guard bands is essential for maintaining the integrity of the transmitted signals.

Correct Option Analysis:

The correct option is:

Option 2: (Modulated message bandwidths) + (Guard bands)

This option accurately represents the baseband bandwidth in the case of FDM. The bandwidth of the modulated messages is summed up, and the guard bands are added to ensure proper spacing and prevent interference. This ensures the effective separation of multiple signals during transmission.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: (Modulated message bandwidths) - (Guard bands)

This option is incorrect because subtracting the guard bands would result in a bandwidth smaller than the actual baseband bandwidth required for FDM. Guard bands are essential components of the total bandwidth, as they prevent interference between adjacent signals.

Option 3: (Modulated message bandwidths) ÷ (Guard bands)

This option is incorrect because dividing the modulated message bandwidths by the guard bands does not provide a meaningful representation of the baseband bandwidth in FDM. The bandwidth calculation in FDM involves summing the modulated message bandwidths and the guard bands, not dividing them.

Option 4: (Modulated message bandwidths) × (Guard bands)

This option is incorrect because multiplying the modulated message bandwidths by the guard bands does not represent the actual baseband bandwidth in FDM. The bandwidth calculation requires the addition of the guard bands to the modulated message bandwidths.

Conclusion:

In Frequency Division Multiplexing (FDM), the baseband bandwidth is the sum of the bandwidths of all modulated signals and the guard bands. This ensures proper signal separation and prevents interference. Option 2 accurately describes this concept, making it the correct choice. Understanding the role of guard bands and their impact on the total bandwidth is crucial for designing efficient FDM systems.

The correct answer is Option 2: TDM requires the transmitter and receiver to be synchronized periodically.

Key Points

• Time Division Multiplexing (TDM) is a method of transmitting and receiving independent signals over a common signal path by means of synchronized switches.
• TDM divides the available time on a channel into time slots and allocates these slots to different data streams.
• Synchronization between the transmitter and receiver is crucial in TDM to ensure that the correct data is received in the correct time slot.
• If the transmitter and receiver are not synchronized, data meant for one slot could be received in another, causing data loss or corruption.
• Effective synchronization involves periodic checks and adjustments to maintain alignment between the transmitter and receiver.

Additional Information

• TDM is used in various communication systems such as telephone networks, where multiple calls are transmitted over a single line.
• There are different types of TDM, including Synchronous TDM and Statistical TDM.
• Synchronous TDM assigns fixed time slots to each data stream, whether or not there is data to send, leading to potential inefficiency.
• Statistical TDM, on the other hand, dynamically allocates time slots based on demand, improving efficiency.
• TDM systems often include mechanisms for error detection and correction to ensure data integrity.

Concept:

In time division multiplexing bandwidth (R_b)is given as: 

Rb = (nN+a)F_s ;

where n is no of bits,

N is no of signals multiplexed,

a is synchronized bit per frame

F_s is sampled frequency

Calculation:

Quantization level 64 is given so,

n =  \(log_{2} 64\) = 6​;

N = 10; a = 5; F_s = 8 kHz

 Rb = (nN+a)Fs 

=  (6 × 10 + 5) × 8000

= 520 kHz 

correct option is 4

Concept:

For TDM

Bit rate (R_b) = N(n + a)f_s

Where;

N → Number of channels 

n → Number of bits

a → Number of additional synchronization bits

f_s → Sampling frequency

Calculation:

Given;

N = 20 

n = 7 

a = 1

fs = 8 kHz

Bit rate (Rb) = N(n + a)fs = 20×(7 + 1)× 8 = 1280 kbps

TDM (Time Division Multiplexing):

It is a multiplexing technique that allows the transmission of multiple signals over a common channel but in different time slots.

Each signal will get transmitted very quickly over the channel but at a time only one signal will be transmitted.

FDM (Frequency Division Multiplexing):

It is also a multiplexing technique like TDM, in which multiple transmitted signals use a common channel but the total available bandwidth is utilized among the various signals.

This implies that over a complete channel a particular frequency slot is allotted to only one signal.

In FDM, a different frequency band is used to modulate different data signals. This means that different carrier frequency modulates the various signals that are to be transmitted over the channel.

Key differences between FDM and TDM:

Time Division Multiplexing:

• Time-division multiplexing (TDM) is a method of putting multiple data streams in a single signal by separating the signal into many segments, each having a very short duration. Each individual data stream is reassembled at the receiving end based on the timing.
• In Time Division Multiplexing (TDM), the time frame is divided into slots. This technique is used to transmit a signal over a single communication channel, by allotting one slot for each message.
• For separating channels in TDM, it is necessary to use  Time slots. For this purpose AND gates are used.
• Time Division Multiplexing (TDM) can be classified into Synchronous TDM and Asynchronous TDM.

• Synchronous TDM
  •    In Synchronous TDM, the input is connected to a frame. If there are ‘n’ number of connections, then the frame is divided into ‘n’ time slots. One slot is allocated for each input line.
  • In this technique, the sampling rate is common for all signals and hence the same clock input is given. The MUX allocates the same slot to each device at all times.

• Asynchronous TDM
  • In Asynchronous TDM, the sampling rate is different for each of the signals and a common clock is not required.
  • If the allotted device for a time slot transmits nothing and sits idle, then that slot can be allotted to another device, unlike synchronous
  • This type of TDM is used in Asynchronous transfer mode networks.

Concept:

Multiplexing:

• Multiplexing is a way of sending multiple signals or streams of information over a communications link at the same time in the form of a single, complex signal.
• When the signal reaches its destination, a process called demultiplexing, recovers the separate signals and outputs them to individual lines.

In TDMA, different users access the transponder in different time slots, not in parallel.

Hence, Option 2 is correct.

Time-division multiple access (TDMA):

• This is a channel access method for shared-medium networks.
• It allows several users to share the same frequency channel by dividing the signal into different time slots.
• The users transmit in rapid succession, one after the other, each using its own time slot. This allows multiple stations to share the same transmission medium (e.g. radio frequency channel) while using only a part of its channel capacity.

Frequency division multiple access (FDMA):

• FDMA is a channel access method used in some multiple-access protocols.
• FDMA allows multiple users to send data through a single communication channel, such as a coaxial cable or microwave beam, by dividing the bandwidth of the channel into separate non-overlapping frequency sub-channels and allocating each sub-channel to a separate user.
• Users can send data through a sub-channel by modulating it on a carrier wave at the sub-channels frequency.

Code division multiple access (CDMA):

• CDMA stands for Code Division Multiple Access.
• CDMA (Code Division Multiple Access) uses a digital modulation technique called Direct Sequence spread spectrum which spreads voice data over a very wide spectrum using a user or cell-specific pseudo-random codes.
• It is a wireless technology used in the transmission of signals from places with high security and Noise reduction.
• The principle of the spread spectrum is used to work with CDMA.
• CDMA is not frequency specific to each user, instead, every channel uses the full available spectrum.
• Each user in a CDMA system uses a different code to modulate their signal.

Time Division Multiplexing (TDM):

• In TDM a single communication channel is used to transmit and receive the information from different sources serially.
• During transmission of information, it is divided into a small-small sample called the TDM frame and then transmitted over the channel.
• In TDM the whole time interval is divided into smaller time slots and each time slots are assigned to a fixed user.
• Each user can use the entire channel bandwidth during allotted time slice, so that channel Bandwidth utilized completely.
• In TDM, synchronization is necessary at the receiver end so fast-changing of data can create inter-symbol interference. So for a high-speed telemetry system, TDM is not the best choice.
• Hence, by considering above points above TDM, statement 1 and 2 is valid but statement 3 is not Valid.

Attenuator :

It decreases the amplitude or any characteristics of signal.

Sample :

It samples analog signal.

Pre-alias filter :

It removes the desired component from the signal.

Modulator

A device which modulates carrier signal.

in TDM non-essential frequency components of the modulating signal are removed by Pre-alias filter.

Given sampling rate of each channel as 6KHz which can be represented as f_c

since 30 signals are multiplexed, the total frequency of the multiplexed signal can be calculated as,

 f_s = n fc

Where n is the number of the signals multiplexed

That is, n = 30

Therefore,  fs = 30*6KHz = 180 KHz

Now each sample is represented by 5 bits and contains an additional bit for synchronization.

The total number of bits per sample is, 

N = 5+1 = 6

The total bit rate of TDM link will be,

R_b = N fs = 6*180 Kbps = 1080 kbps

Explanation:

The bit rate for a PAM/TDM system is given by

Rb = nfs

Where

Rb = Bit rate/Signaling rate

n = number of bits in the encoder

fs = sampling frequency

From Nyquist criteria

fs = 2fm

Where fm = message signal frequency

Minimum transmission Bandwidth (B.W.) = nfm ----(1)

Rb = nfs ----(2)

Given:

f_m = 4 kHz

n = 6

Minimum transmission Bandwidth (B.W.) is given by equation (1)

B.W. = 6 × 4 = 24 kHz

f_s = 2 × 4 = 8 kHz

Signaling rate is given by equation (2):

R_b = 6 × 8 = 48 kHz

During sampling:

We sample at 2W. With this rate signal of bandwidth, W gets sampled properly.

The signal of bandwidth 2W is sampled properly by being fed twice in the commutator switch.

And signal with bandwidth 3W is fed thrice into the commutator switch in order to get sampled at an effective rate of 6W. So, the total bit rate is R_b = 14W

Now, the minimum bandwidth required is: \({{{R_b}} \over 2} = 7W\).

Concept:

In time division multiplexing bandwidth (R_b)is given as: 

Rb = (nN+a)F_s ;

where n is no of bits,

N is no of signals multiplexed,

a is synchronized bit per frame

F_s is sampled frequency

Calculation:

Quantization level 64 is given so,

n =  \(log_{2} 64\) = 6​;

N = 10; a = 5; F_s = 8 kHz

 Rb = (nN+a)Fs 

=  (6 × 10 + 5) × 8000

= 520 kHz 

correct option is 4