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1. What is the quantization level ( q ) for a digitized signal that ranges from

ID: 2080964 • Letter: 1

Question

1. What is the quantization level (q) for a digitized signal that ranges from -5.00 to 5.00 volts when using …

(a) 12-bit representation?

q = ( Vmax – Vmin ) / ( 2N )

q = ( 5 – (-5) ) / ( 212 )

q = 5 / 2048

q = 2.4 (10-3)

(b) 8-bit representation?

q = ( Vmax – Vmin ) / ( 2N )

q = ( 5 – (-5) ) / ( 28 )

q = 5 / 128

q = 0.039

(c) Assume that the digital system assigns the closest available value. For the case in (a), what digital value (to 5 decimal places) would be assigned and stored if the continuous time voltage was 3.02000 V?

(d) Your answer to (c) above is the voltage assigned in the system; thus, the system never captures the actual voltage. Thus, you know that the actual voltage is probably not the voltage that you calculated in (c). What range of voltage values could this data point have?

Explanation / Answer

Quantization levels , L = 2N

where N = number of bits

(a) N = 8, L = 28 =256

(b) N = 12, L = 212= 4096

(c) L = Vmax - Vmin /(2.4 * 10-3) = [3.02 - (-3.02)] / (2.4 * 10-3) =2516.667

L = 2N = 2516.67

N = 12

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