## 51. Four independent messages have bandwidths of 100 Hz, 100 Hz, 200 Hz, and 400 Hz, respectively. Each is sampled at the Nyquist rate, and the samples are Time Division Multiplexed (TDM) and transmitted. The transmitted sample rate (in Hz) is

## 52. In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by a factor of

## 53. The line code that has zero dc component for pulse transmission of random binary data is

## 54. In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

## 55. An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

## 56. The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function)

x(t) = 125t(u(t) - u(t - 1)) + (250 - 125t)(u(t - 1) - u(t - 2)) so that slope-overload is avoided, would be

x(t) = 125t(u(t) - u(t - 1)) + (250 - 125t)(u(t - 1) - u(t - 2)) so that slope-overload is avoided, would be