Consider a random variable X which is zero mean Gaussian distributed with unit variance o = 1. Suppose X is applied to the uniform quantization with the output Y shown below in Figure 1. [PYP AY2021-22] a. b. C. Y (volts) Output +3 -2 +1 -1 X (volts) Input Figure 1 Evaluate and sketch the probability density function (PDF) of the output Y. Determine the mean and variance of the output Y. Design a suitable symbol mapping for the source encoder above. If a source message m(t) is applied to this input quantizer in Figure 1. If it is sent PCM transmission with available bit rate 50 x 106 bits per sec (bps), determine the maximum message bandwidth W Hz for the system to work satisfactory. A binary channel with the bit rate R = 36000 bits per second (bps) is available for PCM audio transmission. Find the appropriable values of the sampling rate fs, the uniform quantization level L, and the binary digits n, assuming the maximum frequency contents of the source message is fM= 3.2 kHz. Calculate the peak Signal-to-quantization Noise Ratio (SNR) for uniform quantization in terms of dB units. Explain the modification required for SNR, when the average power of sinusoidal tone signal is used instead and evaluate this value.