Suppose that we have a signal X(t), of which its samples X follow a uniform PDF overrange (-3,7). We are sampling a second signal Y (t), of which its samples follow thefunction Y = (X – 1)². We want to quantize Y(t) with a uniform PCM scheme, bytheusing the maximum bit number possible and a step size bigger than 1.a) Derive the PDF of Y.b) What is the maximum bit number we can use?c) What is the corresponding step size?d) Calculate the SQNR of this quantization process. Table 1: Values of Q(x) for 0 < a<9Q(x)2.6823x10-62.1125x10-61.6597x10-61.3008x10-64.75 1.0171x10-67.9333x10-76.1731x 10-74.7918x 10-7Q(x)Q(z)Q(z)5.231x10-26.85 3.6925x10-126.90 2.6001x 10–126.95 1.8264x 10-127.00 1.2798x 10-127.05 8.9459x10-137.10 6.2378x10-137.15 4.3389x10-137.20 3.0106x10-7.25 2.0839x 10-137.30 1.4388x10-137.35 9.9103x 10-147.40 6.8092x10-144.667×10-147.50 3.1909x 10-147.55 2.1763x10-147.60 1.4807x 10-140.000.52.300.0107244.556.800.050.480062.350.00938674.600.100.460172.400.00819754.650.150.440382.450.00714284.700.200.420742.500.00620970.250.401292.550.00538614.800.300.382092.600.00466124.850.350.363172.650.00402464.903.7107x10-72.8665x 10-72.2091x 10-71.6983x10-71.3024x10-70.400.344582.700.0034674.95-130.450.326362.750.00297985.000.500.308542.800.00255515.050.550.291162.850.0021865.100.600.274252.900.00186585.155.20 9.9644x10-87.605x10-85.7901x10-84.3977x10-80.650.257852.950.00158897.450.700.241963.000.00134995.250.750.226633.050.00114425.300.800.211863.100.00096765.353.332x10-82.5185x10-87.65 1.0049x 10-147.70 6.8033x10-157.75 4.5946x 10-157.80 3.0954×10-157.85 2.0802x10-157.90 1.3945x 10-157.95 9.3256x10-160.850.197663.150.000816355.400.900.184063.200.000687145.451.899x 10-81.4283x10-81.0718x10-88.0224x10-95.70 5.9904x10-90.950.171063.250.000577035.501.000.158663.300.000483425.551.050.146863.350.000404065.601.100.135673.400.000336935.651.150.125073.450.000280294.4622x10-95.80 3.3157x 10-92.4579x10-91.8175x10-91.3407x10-96.221 x10-168.05 4.1397x10-168.10 2.748x10-161.200.115073.500.000232635.758.001.250.105653.550.000192621.300.09683.600.000159115.858.15 1.8196x 10-168.20 1.2019x10-168.25 7.9197x 10-178.30 5.2056x10-178.35 3.4131x10-171.350.0885083.650.000131125.901.40 0.080757 3.700.00010785.951.45 0.073529 | 3.75 8.8417x10-53.80 7.2348 x10-53.85 5.9059x 10-53.90 4.8096 x10-53.95 3.9076x10-56.00 9.8659x10-107.2423x10-106.10 5.3034×10-106.15 3.8741 x10-106.20 2.8232x10-106.25 2.0523x10-106.30 1.4882x10-106.35 1.0766x10-16.40 7.7688x10-116.45 5.5925x10-114.016x10-116.55 2.8769 x10-112.0558x10-116.65 1.4655x10-116.70 1.0421 x10-116.75 7.3923x10-121.50 0.0668076.051.550.0605718.40 2.2324x10-178.45 1.4565x 10-171.60 0.0547991.650.0494718.50 9.4795x 10-188.55 6.1544x10-184.00 3.1671 x 10-54.05 2.5609x 10-54.10 2.0658x10-54.15 1.6624x10-51.90 0.028717 | 4.20 1.3346× 10-51.95 0.025588 4.25 1.0689x 10-54.30 8.5399x 10-64.35 6.8069 x 10-62.10 0.017864 4.40 5.4125x10-61.70 0.0445651.75 0.0400598.60 3.9858x 10-182.575x10-188.70 1.6594x10-11.800.035931.85 0.0321578.656.508.75 1.0668x10-188.80 6.8408x 10-194.376x10-198.90 2.7923x10-198.95 1.7774x10-191.1286x10-192.000.022752.05 0.0201826.608.854.2935 x 10-64.50 3.3977x 10-62.15 0.0157784.42.20 0.0139039.002.250.012224

Hi, since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Suppose that we have a signal X(t), of which its samples X follow a uniform PDF over the range (-3,7). We are sampling a second signal Y(t), of which its samples follow the function Y = (X – 1)². We want to quantize Y(t) with a uniform PCM scheme, by using the maximum bit number possible and a step size bigger than 1. a) Derive the PDF of Y. b) What is the maximum bit number we can use? c) What is the corresponding step size?

Suppose that we have a signal X(t), of which its samples X follow a uniform PDF over the range (-3,7). We are sampling a second signal Y(t), of which its samples follow the function Y = (X – 1)². We want to quantize Y(t) with a uniform PCM scheme, by using the maximum bit number possible and a step size bigger than 1. a) Derive the PDF of Y. b) What is the maximum bit number we can use? c) What is the corresponding step size?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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