Digital Signal Processing: A Practitioner's Approach

1

Processing of Signals

Any sequence or set of numbers, either continuous or discrete, defines a signal in the broad sense. Signals originate from various sources. They occur in data processing or share markets, human heartbeats or telemetry signals, a space shuttle or the golden voice of the Indian playback singer Lata Mangeshkar, the noise of a turbine blade or submarine, a ship or instrumented signal inside a missile.

Processing of signals, whether analogue or digital, is a prerequisite to understanding and analysing them. Conventionally, any signal is associated with time. Typically, a one-dimensional signal has the form x(t) and a two-dimensional signal has the form f (x, y, t). Understanding the origin of signals or their source is of paramount importance. In strict mathematical form, a signal is a mapping function from the real line to the real line, or in the case of discrete signals, it is a mapping from the integer line to the real line;¹ and finally it is a mapping from the integer line to the integer line.

Typically the measured signal ŷ(t) is different from the emanated signal y(t). This is due to corruption and can be represented as follows:

where γ is the unwanted signal, commonly referred to as noise and most of the time statistical in nature. This is one of the reasons ...