![3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/10/3-2.png?w=1170&ssl=1 "3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)")
![3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/10/3.-1.png?w=1170&ssl=1 "3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)")
![3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/10/3..-1.png?w=1170&ssl=1 "3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)")
3. This problem is on the quantization and encoding. Answer to the following: Assume round-off rule for uniform quantization. We have 10 samples from the analog signal and their quantization error qε are found to be distributed as, qε =[0.33, 0.36, -0.38, 0.22, -0.4, 0.07, 0.4, -0.18, -0.25, 0.38] (a) Decide the suitable value of quantization step size ∆. Give reasoning for your answer (3) (b) We assume that qε are uniformly distributed with its probability density function f ∆ (∆) =1 /∆ for the interval [-∆/2, +∆/2]. Calculate the quantization noise power Pqε for the value of ∆ you found in part (a). (3) (c) Per the quantization noise power you calculated in part (b), calculate the signal power S [Watt] if output Signal to Q-zation noise power ratio SNRo = 30 dB. (3) (d) If we encode the quantizer output with binary code with length ‘n’(integer), decide the minimum code length ‘n’ based on the condition given in part (c) (1)
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