8.1. SEQUENCES
455
called the Nyquist-Shannon Sampling Theorem that says that human perception
is limited, which allows that replacement of a continuous signal with a digital
one without any perceived loss of information. This theorem also provides the
lowest rate at which a signal can be sampled (called the Nyquist rate) without
such a loss of information. The theorem states that we should sample at double
the maximum desired frequency so that every cycle of the original signal will
be sampled at at least two points.
Recall that the frequency of a sinusoidal function is the reciprocal of the period.
Identify the frequency of the function f and determine the number of partitions
of the interval [0, 10] that give us the Nyquist rate.
(c) Humans cannot typically pick up signals above 20 kHz. Explain why, then, that
information on a compact disk is sampled at 44,100 Hz.
455
called the Nyquist-Shannon Sampling Theorem that says that human perception
is limited, which allows that replacement of a continuous signal with a digital
one without any perceived loss of information. This theorem also provides the
lowest rate at which a signal can be sampled (called the Nyquist rate) without
such a loss of information. The theorem states that we should sample at double
the maximum desired frequency so that every cycle of the original signal will
be sampled at at least two points.
Recall that the frequency of a sinusoidal function is the reciprocal of the period.
Identify the frequency of the function f and determine the number of partitions
of the interval [0, 10] that give us the Nyquist rate.
(c) Humans cannot typically pick up signals above 20 kHz. Explain why, then, that
information on a compact disk is sampled at 44,100 Hz.