A zero-mean stationary information source X(t) has a power spectral density given by The...

Question

A zero-mean stationary information source X(t) has a power spectral density given by

The amplitude of this source is limited to 10 in magnitude. This source is sampled at the Nyquist rate and the samples are coded using an 8 bit/sample uniform PCM system.

1. Determine the resulting SQNR in decibels.

2. If we want to increase the SQNR by at least 20 dB, how should the required number of quantization levels change?

3. In Part 2, what is the minimum required bandwidth for the transmission of the PCM signal?

David · Accepted Answer

1. PX = 1π
∫ 200
−200
1
1+f 2 df =
1
π tan
−1 f
]200
−200 ≈ 1 where we have used the approximations tan
−1 200 =
π
2 and tan
−1(−200) = −π2 . To find the SQNR, we have SQNRdB = 6 × 8 + 4.8 + 10 log
1
100 =
48+ 4.8− 20 = 32.8 dB.
2. To increase the SQNR by 20 dB, we need at least 4 more bits per sample (each bit improved
the SQNR by 6 dB).

A zero-mean stationary information source X(t) has a power spectral density given by The amplitude of this source is limited to 10 in magnitude. This source is sampled at the Nyquist rate and the...

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