Question

Consider a 3 KHz voice signal x(t) (i.e., fₘ=3 KHz). The signal will be sampled with a rate fₛ and quantized using an L-level quantizer. The signal amplitude takes values vetween [-Vₘₐₓ, Vₘₐₓ].

Quantization
a). Consider that the signal is uniformly distributed. Derive the quantization SNR

Answer 1

The quantization SNR for a uniformly distributed signal that is sampled and quantized can be derived using the formula SNR = 1.76 + 6.02 × log2(L) dB, where L is the number of quantization levels.

Step-by-step explanation:

To derive the quantization signal-to-noise ratio (SNR) for a uniformly distributed signal that is sampled and quantized, we use the following formula:

SNR = 1.76 + 6.02 × N dB

where N is the number of bits used in quantization. For an L-level quantizer, N is given by N = log2(L). First, we find N using the L levels provided. Then we substitute N into the equation to find the SNR. It is important to note that an increase in the number of levels L will lead to an increase in SNR, indicating a better quality signal after quantization.

Since the amplitude of the signal is between [-Vmax, Vmax], and the signal is uniformly distributed, the quantization noise power will be (Vmax^2) / (3 × (2^N)^2), while the signal power is (Vmax^2) / 2. The quantization SNR is then the ratio of the signal power to the noise power, which simplifies to the formula provided.