#### Question 1.4

## Spectrum of a baseband binary data stream

#### The spectrum (frequency domain representation) of a random data stream can be obtained by simply overlaying the instantaneous spectra for each individual pulse. We thus know that it will be bounded by the sinc envelope, and at any instance in time, the location and density of frequency components will depend on the particular pattern of data bits. |
#### By shaping the data pulses, so that they have smooth edges, we would expect to reduce significantly the high frequency spectral content of the waveform. A commonly used pulse-shaping method is to pass the data stream through a low pass filter having a raised cosine response. The raised cosine filter belongs to a family of filters called Nyquist filters which have particularly useful properties in data communications. |