Digital Signal Processing Lab
2
Sampling
1. Objective
1.1 Speech sampling
1.2 Generation of sinusoid at different sampling rates
1.3 Reconstruction of sampled sinusoid using low pass filter
2. Overview
Under certain conditions a continuous tim e signal can be com pletely represented
by and recoverable from knowledge of its values or samples at points equally spaced in
time. It is exploited, for exam ple, in m oving pictures, which consist of a sequence of
individual fram es each of which represents an instantaneous view of a continuously
changing scene. When these samples are viewed in sequence at a sufficiently fast rate,
we perceive an accurate representation of the original continuously moving scene.
The only way that a com puter can handl e a continuous (analog) signal is by
sampling them . The sam pling frequency ha s to be at least TW ICE the m aximum
frequency in the continuous signal, that is the ABSOLUTE m aximum frequency, not
just the twice the maximum frequency that you are interested in. More formally this is:
fs > 2·fmax
Sampling at this rate will not result in any loss of inform ation, but if you sam ple
at less than this then you will not be able to reconstruct the signal as it first appeared.
The reason f or this is that sam pling a signal is equivalent to m ultiplying it by a series
of delta functions.
In real life continuous signals have frequencies that are beyond any sam pling
frequency possible, they m ight even contain infinite frequencies!! One way round this
is to pass the signal through a low pass filte r that stops any frequencies ABOVE half
the sampling frequency. This is still not perfect, but is a practical method.
So, sam pling rate can be reduced up to above discussed rate. Now, the
reconstruction process is possible by m ean of low pass filter. Low pass filter works as
an interpolator. In this lab we will study the reconstruction process.
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