Bandwidth, SNR and Data Transmission

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Questions and Answers

In the context of channel capacity, how does increasing the signal-to-noise ratio (SNR) affect the channel capacity, assuming bandwidth remains constant?

Increasing the signal-to-noise ratio increases the channel capacity.

Given a fixed channel capacity, what is the effect of increasing the bandwidth on the required signal-to-noise ratio (SNR)?

Increasing the bandwidth reduces the signal-to-noise ratio (SNR).

Explain the relationship between bandwidth, signal-to-noise ratio, and channel capacity based on the Shannon-Hartley theorem.

The channel capacity is directly proportional to the bandwidth and the logarithm of (1 + SNR).

In a communication system, if the signal power is significantly lower than the noise power, what can be said about the channel capacity?

If the signal power is significantly lower than the noise power, the channel capacity will be very low. Signup and view all the answers

Describe a scenario where increasing the bandwidth might not significantly increase the channel capacity.

A scenario where increasing bandwidth might not significantly increase channel capacity is when the SNR is very low. Signup and view all the answers

How does channel capacity influence the maximum achievable data rate in a communication system?

Channel capacity sets the upper limit on the maximum achievable data rate. Signup and view all the answers

What strategies can be employed to improve the SNR in a communication system, and how would this affect channel capacity?

Strategies to improve SNR include increasing signal power, reducing noise levels, and using error correction codes. This increases the channel capacity. Signup and view all the answers

Explain how different modulation techniques can impact the effective signal-to-noise ratio and affect overall system channel capacity.

Different modulation techniques impact the power, bandwidth, and noise immunity. Overall system channel capacity will depend on the effective SNR based on the modulation technique used. Signup and view all the answers

Discuss methods to mitigate the impact of noise on data transmission in the context of maintaining an acceptable signal-to-noise ratio.

Methods include using shielding, equalization, filtering, and error-correcting codes. Signup and view all the answers

If a communication channel's bandwidth is severely limited due to regulatory constraints, what strategies can be adopted to maximize the channel capacity?

Strategies to maximize channel capacity with limited bandwidth include using higher-order modulation schemes, advanced coding techniques, and signal processing methods to improve spectral efficiency. Signup and view all the answers

Flashcards

Channel Capacity (C)

The maximum rate at which information can be transmitted over a communication channel for a specified bandwidth and signal-to-noise ratio.

Shannon's Channel Capacity Formula

Formula to calculate the channel capacity (C) based on bandwidth (B) and signal-to-noise ratio (SNR).

Signal-to-Noise Ratio (SNR)

Ratio of the power of a signal to the power of background noise.

Digital Modulation

Process of converting digital data into a signal suitable for transmission over a communication channel.

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Amplitude Shift Keying (ASK)

A method of representing digital data by varying the amplitude of a carrier signal.

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Study Notes

C = Blog₂(1 + SNR)

Calculating Bandwidth (B)

B = C / log₂(1 + 0.1) = (56 x 10³) / log₂(1 + 0.1) = 405262.64 Hz
B = (56 x 10³) / log₂(1 + 0.01) = 3910001.146 Hz
B = (56 x 10³) / log₂(1 + 0.001) = 55535647 Hz

Calculating SNR (Signal-to-Noise Ratio)

C / B = 1
log₂(1 + SNR) = 1
2¹ = (1 + SNR)
SNR = 2¹ - 1 = 1

Data Representation (Question 2)

Example bit sequences:
(0) 1110010 or 111-1-11-1
(1) 1000110
(2) 1011100
(3) 1010001
(4) 1101000
(5) 0110100
(6) 1100101 or 11-1-11-11

Bit Value Calculation

With example values: 5 + 1 - 1 + 1 + 1 - 1 + 3 = 7, bit value = 1
With example values: 5 + -1 + 1 + 3 + 1 + 3 + 3 = 9, bit value = 1

Data Transmission and Output (Question 4)

A = (-1, 1, -1, 1, -1, 1, -1, 1)
B = (-1, -1, 1, 1, -1, -1, 1, 1)
Data = Da x Ca
Output = Data + Code A

Example Calculation

1 x (-1, 1, -1, 1, -1, 1, -1, 1) = (-1, 1, -1, 1, -1, 1, -1, 1)
Data = 0 x (-1, 1, -1, 1, -1, 1, -1, 1) = (1, -1, 1, -1, 1, -1, 1, -1)
(1, -1) x (1, -1, 1, -1, 1, -1, 1, -1) = -8

Output and Multiplication with Data = 1

Output for A is (-1, 1, 1, -1, 1, -1, 1, -1)
Output for B is (-1, -1, 1, 1, -1, -1, 1, 1)
Received values: (-2, 0, 0, 2, -2, 0, 0, 2)
Multiplication: (2, 0, 0, 2, 2, 0, 0, 2) with a resulting 8

Output at Receiver (Question E)

Conditions: A transmits a data bit 1, B transmits a data bit 0, received power from A and B assumed the same.
With Data A=1 and Data B=0 multiplication results in 8
Receiver output when Data A=0 and Data B=1
Multiplication: (0,-2,-2,0,0,-2,-2,0) results in -8

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