Signals and Stochastic Processes
Module 12: Introduction to Sampling
Objective: To Understand the concept of Sampling a signal its reconstruction and various
methods of Sampling
In the applications of signal processing in real time systems, the mathematical description of
signals will not be available. To find the characteristics of the signals, they must be measured
and analyzed .If the signal is unknown, the process of analysis starts with the acquisition of the
signal, which means measuring and recording the signals over a period of time.Sampling is the
acquisition of a continuous signal at discrete time intervals. After Sampling, the analog signal is
represented at discrete times only, with the values of the samples equal to those of the original
analog signal at the discrete times. In the process of Analog to Digital conversion of a signal,
the signal is first sampled, converting a continuous ,analog signal into a discrete time,
continuous amplitude signal. Next comes the process of Quantization and digitization. The
present Module focuses on the methods of sampling a given low pass signal and its
reconstruction from its sampled version.
A Band-pass signal is a signal containing a band of frequencies i.e. its magnitude
spectrum ranges over two frequency limits i.e. 𝑓𝐿 𝑙𝑜𝑤𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑙𝑖𝑚𝑖𝑡 ≠
0 𝑎𝑛𝑑 𝑓𝐻 𝑢𝑝𝑝𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑙𝑖𝑚𝑖𝑡 ≠ 0 .
A Band-pass Signal is a signal x ( t) whose Fourier transform X( f ) is nonzero only in some
small band around some “central” frequency f o.
A Low pass signal is also a band-pass signal with lower frequency limit 𝑓𝐿 = 0. Then, the
upper frequency limit 𝑓𝐻 (≠ 0) is referred to as Band-limiting frequency of the signal,
and the Low pass signal is also referred to as band-limited signal.