Introduction to signal processing: sampled signals

Abstract

The article introduces the theoretical foundations of the modern method of storing, transmitting and processing signals: digital processing. It’s a way to use relatively small number of values instead of continuous real signal. For example, when transmitting information in telephony, speech is concentrated in the bandwidth up to 4 kHz. But we need doubled frequency 8 kHz sampling in digital form. This is a fundamental requirement. The reason is that the sampled signal is not just a set of quantities, but a set of short scaled pulses of large value. Resulting spectrum has multiple copies of original one infinitely duplicated on sampling frequency steps. If these copies do not overlap significant (due to the limited original useful spectrum) we could restore initial signal with filtering just one of them. That’s why doubled sampling frequency is needed. If the number of samples used is finite (as in the real cases), then we can use only an equal number of samples of the spectrum (or even a half of them). It’s enough for restoring. As in the rest parts of the series, all theoretical ideas are illustrated by mathematical rationales and Matlab programs that demonstrate the work “in life”.