Pulse Modulation MCQ Quiz - Objective Question with Answer for Pulse Modulation - Download Free PDF

The correct answer is 2f.

Key Points

• The bandwidth requirement for simulating an analog signal is determined by the Nyquist criterion.
  • According to the Nyquist theorem, the sampling rate must be at least twice the highest frequency of the analog signal to accurately reconstruct the signal without aliasing.
  • If the frequency of the analog signal is f" id="MathJax-Element-147-Frame" role="presentation" style="position: relative;" tabindex="0">ff $f$ , the minimum sampling rate required is 2f" id="MathJax-Element-148-Frame" role="presentation" style="position: relative;" tabindex="0">2f2f $2f$ .
  • This ensures that the signal can be accurately digitized and reconstructed.

Additional Information

• Aliasing occurs when the sampling rate is less than twice the signal frequency, leading to distortion in the reconstructed signal.
• To avoid aliasing, a low-pass filter is often used before sampling to limit the bandwidth of the analog signal to f" id="MathJax-Element-149-Frame" role="presentation" style="position: relative;" tabindex="0">ff $f$ .
• In practical systems, the sampling rate is often slightly higher than 2f" id="MathJax-Element-150-Frame" role="presentation" style="position: relative;" tabindex="0">2f2f $2f$ to provide a margin of safety.
• This principle is widely used in digital audio, communications, and other fields involving analog-to-digital conversion.

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.

Calculation:

The total modulation index is the square root of the sum of the squares of the individual modulation indices. If the modulation indices for the two waves are 0.3 and 0.4, then the total modulation index is:

m_total = √(0.3² + 0.4²)

m_total = √(0.09 + 0.16) = √0.25 = 0.5

Therefore, the total modulation index is 0.5.

Concept

The total transmitted power for an AM system is given by:

\(P=P_c({1+{μ\over 2}^2})\)

where, P_c = Carrier Power

μ = Modulation index

Calculation

Given, Pc = 10 kW

μ = 0.6

\(10=P_c({1+{0.6\over 2}^2})\)

P_c = 8.47 kW

Explanation:

Quantisation Error in an 8-bit A/D Converter

Definition: Quantisation error in an Analog to Digital (A/D) converter is the difference between the actual analog input value and the digitized output value. It arises due to the finite resolution of the A/D converter, which cannot represent all possible values of the analog input precisely.

Working Principle: An A/D converter transforms an analog voltage into a corresponding digital value. The range of the analog input is divided into discrete levels, and each level is assigned a unique digital code. The resolution of the A/D converter is determined by the number of bits it uses to represent the analog input. An 8-bit A/D converter, for instance, divides the input range into 28 = 256 discrete levels.

Calculating Quantisation Error:

The quantisation error can be approximated by determining the size of the smallest step (Least Significant Bit - LSB) that the A/D converter can resolve. For an 8-bit A/D converter with an input voltage range from -1 to +1 volt, the steps can be calculated as follows:

The total voltage range = 1 - (-1) = 2 volts

The number of discrete levels = 2⁸ = 256

The voltage step size (LSB) = Total voltage range / Number of levels = 2 volts / 256 ≈ 0.0078125 volts = 7.8125 mV

The quantisation error is typically ±1/2 LSB, hence:

Quantisation error = ± (7.8125 mV / 2) ≈ ± 3.90625 mV

Since the error is typically considered as the absolute value, the quantisation error is approximately 3.90625 mV per step for an 8-bit A/D converter. This means the correct answer is closest to 4 mV. However, since the question specifies "approximately equal to," the answer would be rounded to the closest given option.

The correct option is: Option 3: 2 mV

In TV transmission:

• A video is Vestigial sideband modulated, which is a type of amplitude modulated waveform
• The Video signals are thus encoded in amplitude variations of the carriers
• The Audio signal is encoded in FM waveform
• Thus, the audio signals are encoded as frequency variations of the carrier

Noise is the signal that affects amplitude majorly. Thus, the video signal is distorted from amplitude variations.

Quantization: 

• It is the process through which a range of continuous analog values are quantized or rounded off to a single value, thereby forming samples of a discrete digital signal.
• Quantization Error occurs when there is a difference between an input value and it’s quantized value. 
• Quantization occurs when an analog signal is converted into it’s digital form, thus it occurs in Pulse Code modulation (PCM).

PCM:

• PCM stands for Pulse Code Modulation.
• It is a technique by which an analog signal gets converted into digital form to have signal transmission through a digital network.

• The major steps involved in PCM are sampling, quantizing, and encoding.

• With PCM, the amplitude of the analog signal is sampled at regular intervals and translated into a binary number.
• The difference between the original signal and the translated digital signal is called the quantizing error.

Some Advantages associated with PCM are:

• Immunity to transmission noise and interference.
• It is possible to regenerate the coded signal along the transmission path.
• The Quantization Noise depends on the number of quantization levels and not on the number of samples produced per second.
• The storage of Coded signals is easy.

The disadvantages of PCM includes:

• Requires larger Bandwidth.
• Need synchronization
• Not compatible with analog systems.

PCM:

• PCM stands for Pulse Code Modulation.
• With PCM, the amplitude of the analog signal is sampled at regular intervals and translated into a binary number.
• The difference between the original signal and the translated digital signal is called the quantizing error.

Some Advantages associated with PCM are:

• Immunity to transmission noise and interference.
• It is possible to regenerate the coded signal along the transmission path.
• The Quantization Noise depends on the number of quantization levels and not on the number of samples produced per second.
• The storage of Coded signals is easy.

The disadvantages of PCM includes:

• Requires larger Bandwidth.
• Need synchronization
• Not compatible with analog systems.

Advantages of FM over AM are:

• Improved signal to noise ratio.
• Smaller geographical interference between neighbouring stations.
• Less radiated power.
• Well defined service areas for given transmitter power.

Disadvantages of FM:

• Much more Bandwidth
• More complicated receiver and transmitter.

Concept:

The number of levels for an n-bit PCM system is given by:

L = 2n

We can also state that the number of bits for a given quantization level will be:

n = log2 L

Calculation:

The number of levels given = 4096, i.e. L = 4096

The number of bits used will be:

n = log2 (4096)

= log2 (2¹²)

= 12 log2 (2)

n = 1

The bandwidth of PCM is given by:

\(BW=n{f_s}\)

n = number of bits to encode

fs = sampling frequency

Concept:

The number of levels for an n-bit PCM system is given by:

L = 2n

We can also state that the number of bits for a given quantization level will be:

n = log₂ L

Also, the bandwidth of PCM is given by:

\(BW=n{f_s}\)

n = number of bits to encode

fs = sampling frequency

Calculation:

For L = 4 quantization levels, the number of bits n = log2 4 = 2 bits. The bandwidth is, therefore:

B.W. = 2 fs

Similarly, For L = 64 quantization levels, the number of bits n = log2 64 = 6 bits. The bandwidth is, therefore:

B.W. = 6 fs

Clearly, the Bandwidth is increased by 3 times.

The AM, FM and PM output waveforms are as shown:

In Frequency modulation, the frequency of the carrier is varied according to the amplitude of the message signal and the amplitude of the carrier remains constant.

Concept:

Two types of distortions (Errors) occurs in Delta modulation system i.e.

1) Slope overload error

2) Granular Error

This is explained with the help of the given figure:

To avoid the slope overload error, the optimum or desired condition is:

\(\frac{{\rm{\Delta }}}{{{T_s}}} = \frac{{d\;m\left( t \right)}}{{dt}}\)

i.e. the step rise of the quantized output must follow the input

Slope overload occurs when:

\(\frac{{\rm{\Delta }}}{{{T_s}}} < \frac{{d\;m\left( t \right)}}{{dt}}\)

To prevent/avoid slope overload error, the condition that shall be satisfied is:

\(\frac{{d\;m\left( t \right)}}{{dt}} \le \frac{{\rm{\Delta }}}{{{T_s}}}\)

m(t) is a sinusoidal waveform given as:

m(t) = A_m sin ω_m t

The condition to avoid slope overload, therefore, becomes:

\(\frac{d}{{dt}}({A_m}\sin {\omega _m}t) \le \frac{{\rm{\Delta }}}{{{T_s}}}\)

\({A_m}\cos {\omega _m}t\;\left( {{\omega _m}} \right) \le \frac{{\rm{\Delta }}}{{{T_s}}}\)

A_m cos (2π (mt)).2πf_m ≤ Δ⋅f_s

\({A_m} \le \frac{{{\rm{\Delta }}{f_s}}}{{2\pi {f_m} \cdot \cos \left( {2\pi {f_m}f} \right)}}\)

For maximum Amplitude, the above condition becomes:

\({A_m} \le \frac{{{\rm{\Delta }} \cdot {f_s}}}{{2\pi {f_m}}}\)

• PCM (Pulse Code Modulation) is a digital scheme for transmitting analog data.
• The amplitude of an analog signal can take any value over a continuous range, i.e. it can take on infinite values.
• But, digital signal amplitude can take on finite values.
• Analog signals can be converted into digital by sampling and quantizing.

Advantages of PCM:

• Encoding is possible in PCM.
• Very high noise immunity, i.e. better performance in the presence of noise.
• Convenient for long-distance communication.
• Good signal to noise ratio.

Disadvantage of PCM:

• The circuitry is complex.
• It requires a large bandwidth.
• Synchronization is required between transmitter and receiver.

Concept:

Slope overload distortion: When the maximum slope of the message is more than Δ f_s then there is slope overload distortion in the delta modulator.

condition to prevent slope overload distortion 

\(\vert {\dfrac{d{m(t)}}{dt}} \vert _{MAX} ≤|{Δ × f_s}|\) ,

where m(t)→ message signal, f_s→ sampling frequency

Calculation:

Given f_m = 10 kHz

Input is 1 V_pp so the maximum  input voltage is 0.5 volt

let applied input is sinusoidal than

m(t) = A_msin(2πf_mt)

where 

\(|\frac{dm(t)}{dt}|=2π f_mA_m \space cos(2π f_mt)\)

\(|\frac{dm(t)}{dt}|_{MAX} =2π f_m A_m\)

f_s = 10× (Nyquist rate)

f_s =10×(2f_m)= 20(10k)=200kHZ

 By the condition to prevent slope overload distortion 

\(\vert {\dfrac{d{m(t)}}{dt}} \vert _{MAX} ≤ \space |{Δ × f_s}| \)

2πA_mf_m ≤ Δ (200k)

2π(0.5)(10k) ≤ Δ (200k)

Δ ≥ 0.157

Δ _minimum = 0.157 V