Uniform quantization provides better quantization for

1. Weak signals
2. Strong signals
3. Weak & Strong signals
4. None of the mentioned

Solution

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Correct option is B. Strong signals

Uniform quantization provides better quantization for strong signals.

Explanation: Uniform quantization is a process in which the range of the continuous amplitude signal is divided into equal-sized intervals or steps, and each interval is assigned a discrete amplitude value. In this type of quantization, the step size remains constant across the entire range of the signal.

For weak signals, which have low amplitudes, uniform quantization may not provide the best representation because the quantization error (difference between the original signal and the quantized signal) can be relatively high compared to the signal amplitude. This can result in a poor signal-to-noise ratio (SNR), as the quantization noise becomes more prominent.

In contrast, strong signals with higher amplitudes are better represented by uniform quantization. The quantization error is relatively smaller compared to the signal amplitude, resulting in a better SNR.

Example: Consider an 8-bit analog-to-digital converter (ADC) that has a range of -1 V to 1 V. The step size for uniform quantization would be (1 – (-1)) / (2^8) = 2 / 256 ≈ 0.0078 V. If a weak signal has an amplitude of 0.01 V, the quantization error could be as high as 78% of the signal amplitude. On the other hand, for a strong signal with an amplitude of 0.5 V, the quantization error would be only about 1.56% of the signal amplitude.

Facts: Non-uniform quantization techniques, such as logarithmic or companding quantization, can provide better quantization for weak signals. These methods allocate more quantization levels to smaller amplitude values, which improves the representation of weak signals and reduces the quantization noise. In non-uniform quantization, the step size is variable and depends on the signal amplitude.

For example, the μ-law and A-law companding techniques are commonly used in telecommunication systems for audio signal compression. These methods allocate more quantization levels to lower-amplitude signals, which improves the representation of weak signals and reduces the quantization noise.

Relevant Stats: To further illustrate the difference between uniform and non-uniform quantization, let’s consider the signal-to-quantization noise ratio (SQNR). SQNR is a metric that indicates the quality of the quantized signal, with higher values indicating better representation.

In uniform quantization, the SQNR is given by the following formula:

SQNR = (Peak Signal Power) / (Quantization Noise Power) = (3 * 2^(2 * n)) / (1) dB, where n is the number of bits.

For an 8-bit ADC, the SQNR would be around 49.93 dB.

In non-uniform quantization using μ-law or A-law companding, the SQNR can be significantly higher for weak signals. For instance, the μ-law companding can provide an SQNR of around 34 dB for weak signals, which is a considerable improvement compared to uniform quantization.

In summary, uniform quantization provides better quantization for strong signals, while non-uniform quantization techniques, such as logarithmic or companding quantization, offer improved representation for weak signals. Choosing the appropriate quantization method can significantly impact the quality of the quantized signal and its subsequent processing and transmission.