Tutorial9_ans - EE 3008. AD and DA Conversion Tutorial...

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EE 3008. AD and DA Conversion Tutorial Solutions Q1) m ( t ) = 6sin(2 π t ). 4 bit PCM. Midriser type quantizer The quantization levels are ± 0.5, ± 1.5, ± 2.5, . ... The binary representations can be 0.5->0000 -0.5->1000 1.5->0001 -1.5->1001 ... 4.5->0100 -4.5->1100 . .. The closest levels 0f ± 4.24 are ± 4.5. Therefore the quantized outputs are 0100, 0100, 1100, 1100, . .. Q2) 16 levels of quantization need 4 bits. 4 µ s spacing is required for one sample. Since the input bandwidth is 3kHz, sampling rate should 2 × 3k=6kHz. The sampling interval should 1/6k=167 µ s. Number of signals that can be multiplexed = N=167/4=41. Q3) (a) The spectrums before and after sampling are shown in the figure below. Denote “+” as the positive part of the original spectrum and “ ” its negative part. We first determine the total duplicates (denoted by N ) of “+” within [-18, 18] (Hz) after sampling. From the figure below, 2 12 36 1 s f N −∆ == + . To avoid overlapping, we have -4.24 -4.24 1 2 0.5 1.5 1/8 3/8 5/8 7/8 6 4.24 m(t) t 4.24 4.24 v i v o 1
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1 10 Hz, 2 10 Hz.
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Tutorial9_ans - EE 3008. AD and DA Conversion Tutorial...

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