II- (20 pts) If the analog signal to be quantized is a...

II- (20 pts) If the analog signal to be quantized is a sinusoidal waveform, that is, x(t) = 9.5 sin (3,000?t) and if the bipolar quantizer uses 6 bits, determine a. number of quantization levels; b. the quantization step size or resolution, ?, assuming the signal range is from -10 to 10 volts; c. quantization level when the analog voltage is 1.611 volts; d. binary code produced by the ADC; e. quantization error. Is it acceptable? Justify your answer f. the signal power to quantization noise power ratio (SNR).

Transcript

00:01 Hello students, here we have a sinusoidal waveform of the analog signal as x of t equal to 9 .5 sin of 3000 pi of t.

00:14 This is equation number 1.

00:17 And from this we have to calculate the first number of quantization level.

00:25 Number of quantization level.

00:33 So here the number of quantization level is related to the bipolar quantization bits.

00:45 So here we have a bipolar that uses 6 bits.

00:52 So we can write the number of quantization as 2 power 6 that is equal to 64 levels.

01:06 And in section b we have to calculate the quantization step size.

01:17 Quantization step size.

01:23 So here the formula is step size equal to signal range divided by number of quantization levels minus 1.

01:47 Number of levels minus 1.

01:53 So we will get the step size as 10 minus of 10 divided by 64 minus 1.

02:06 So we will get 20 divided by 63 that is approximately equal to 0 .3175 volt.

02:15 And third we have to calculate the quantization level when the analog signal is 1 .611 volt.

02:21 So when analog signal is 1 .611 volt the quantization level is quantization level that is equal to analog voltage minus nearest quantization value.

02:59 Nearest quantization value.

03:09 So here we can get the nearest quantization value as nearest quantization value equal to step size into absolute value of analog voltage divided by analog voltage divided by step size.

03:40 So substitute the values we will get 0 .3175 into absolute value of 1 .611 divided by 0 .3175 that is equal to 0 .3175 into 5...

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