Group Members
Muhammad Naveed
07-CP-06
Hamza Khalid
07-CP-08
Umer Aziz Malik
07-CP-56
Nyquist Frequency &
Nyquist Rate
Sampling
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Sampling is the reduction of a continuous
signal to a discrete signal
A sample refers to a value or set of values at
a point in time and/or space.
A sampler is a subsystem or operation that
extracts samples from a continuous signal
Sampling Frequency
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The sampling rate, sample rate, or sampling
frequency defines the number of samples per
second (or per other unit) taken from a
continuous signal to make a discrete signal
Sampling Frequency (contd.)
Bandwidth
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Bandwidth is the difference between the
upper and lower cutoff frequencies of, for
example, a filter, a communication channel,
or a signal spectrum, and is typically
measured in hertz
Undersampling & Oversampling
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Undersampling is a technique where one
samples a signal below the usual twice the
bandwidth or highest frequency of the signal
being sampled, but is still able to reconstruct
the signal
Oversampling is the process of sampling a
signal with a sampling frequency significantly
higher than twice the bandwidth or highest
frequency of the signal being sampled
Aliasing
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Aliasing refers to an effect that causes
different continuous signals to become
indistinguishable (or aliases of one another)
when sampled
It also refers to the distortion or artifact that
results when the signal reconstructed from
samples is different than the original
continuous signal
Aliasing-An example
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Here's a sine wave signal
The dashed vertical lines are sample intervals, and
the blue dots are the crossing points - the actual
samples taken by the conversion process. When we
reconstruct the waveform we see the problem quite
readily
Nyquist Frequency
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Nyquist Frequency or the Nyquist–Shannon
sampling theorem is half the sampling
frequency of a discrete signal processing
system
It is sometimes called the folding frequency,
or the cut-off frequency of a sampling system
Nyquist Frequency (contd.)
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The sampling theorem shows that aliasing can be
avoided if the Nyquist frequency is greater than
the bandwidth, or maximum component frequency,
of the signal being sampled.
In principle, a Nyquist frequency just larger than the
signal bandwidth is sufficient to allow perfect
reconstruction of the signal from the samples
If the signal contains a frequency component at
precisely the Nyquist frequency then the
corresponding component of the sample values
cannot have sufficient information to reconstruct the
Nyquist component in the continuous-time signal
because of phase ambiguity
Nyquist rate
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In signal processing, the Nyquist rate is two
times the bandwidth of a bandlimited signal
or a bandlimited channel
This term means it is a lower bound for the
sample rate for alias-free signal sampling(not
to be confused with the Nyquist Frequency,
which is half the sampling rate of a discreettime system)
.
Nyquist rate relative to sampling
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The Nyquist rate is the minimum sampling
rate required to avoid aliasing, equal to twice
the highest frequency contained within the
signal
where B is the highest frequency component of
the signal
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To avoid aliasing, the sampling rate must
exceed the Nyquist rate:
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