A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

In delta modulation, the slope overload distortion can be reduced by

The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$$p(t) = {{\sin \,4\,\pi \,W\,t} \over \matrix{ 4\,\pi \,W\,t(1 - 16{W^2}{t^2}) \hfill \cr \hfill \cr \hfill \cr} }$$$ The value of p(t) at $$t = {1 \over {4\,W}}$$ is

In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency reuse factor of 1/5, i. e. a five-cell repeat pattern,, the maximum number of simultaneous channels that can exist in one cell is