Signals, Systems, and Signal Processing

This chapter introduces bandlimited signals, sampling theory, and the method of reconstruction from samples. Uniform sampling with a Dirac delta train is considered, and the Fourier transform of the sampled signal is derived. The reconstruction from samples is based on the use of a linear filter called an interpolator. When the sampling rate is not sufficiently large, the sampling process leads to a phenomenon called aliasing. This is discussed in detail and several real-world manifestations of aliasing are also discussed. In practice, the sampled signal is typically processed by a digital signal processing device, before it is converted back into a continuous-time signal. The building blocks in such a digital signal processing system are discussed. Extensions of the lowpass sampling theorem to the bandpass case are also presented. Also proved is the pulse sampling theorem, where the sampling pulse is spread out over a short duration, unlike the Dirac delta train. Bandlimited channels are discussed and it is explained how the data rate that can be transmitted over a channel is limited by channel bandwidth.