Question

Communication systems theory:

Exercise 6: Consider an audio signal with an amplitude that ranges over the interval [-10,10] and with spectral components limited to the frequency band of 300 Hz to 3300 Hz. The signal is sampled at a rate of 8000 samples/second and used to generate a PCM signal. The signal-to-quantization- noise ratio (SQNR) is required to be maintained at 43.9 dB a) What is the minimum number of uniform quantization levels needed, and what is the minimum number of bits per sample needed? (State you results to the nearest integer) b) Determine the required step size if a uniform quantizer is employed c) Calculate the transmission rate in bits/sec (bps) and the minimum bandwidth (in Hz) required for this transmission d) Determine the smallest and the largest effective separation (or voltage range) between levels if a non-uniform u-law quantizer with 255 is employed. Note that the smallest effective separation will be the one closest to the origin with the level Vin being when Vou.-2V,n/L, where Kn is the maximum input voltage (amplitude) and L is the number of levels out Nonuniform Largest Separation Smallest Separation Figure 6.1: Characteristics of the compressor for u-law companding. Half of the levels are used for positive amplitudes and half for negative amplitudes.

Answer 1

176 +6 02 h2 43, d B No.of level = 2y= 127 ievuss-イ No. f level 127 : 2D