04-07-2012, 10:53 AM
Digital Processing of Continuous-Time Signals
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• Digital processing of a continuous-time
signal involves the following basic steps:
(1) Conversion of the continuous-time
signal into a discrete-time signal,
(2) Processing of the discrete-time signal,
(3) Conversion of the processed discretetime
signal back into a continuous-time
signal
The Sampling Process
• Many natural phenomena produce analogue
signals
• Signal processors are inherently digital
systems.
• In order to process analogue signals with
digital processors the analogue signals must be
converted to digital.
• The process whereby analogue signals are
converted to digital involves sampling and
quantization.
The Sampling Theorem
For any baseband signal that is bandlimited to
a frequency f the sampling fm, rate fs must be
selected to be greater or equal to twice the
highest frequency fm in order for the original
baseband signal to be recovered without
distortion using an ideal lowpass filter with a
cut-off frequency fc such that f £ f £ f - f
m c s m.
Digital Processing of
Continuous-Time Signals
• Since the A/D conversion takes a finite
amount of time, a sample-and-hold (S/H)
circuit is used to ensure that the analog
signal at the input of the A/D converter
remains constant in amplitude until the
conversion is complete to minimize the
error in its representation.
• To prevent aliasing, an analog anti-aliasing
filter is employed before the S/H circuit
• To smooth the output signal of the D/A
converter, which has a staircase-like
waveform, an analog reconstruction filter
is used
Effect of Sampling in the
Frequency Domain
• In high-quality analog music signal
processing, a bandwidth of 20 kHz has been
determined to preserve the fidelity
• Hence, in compact disc (CD) music
systems, a sampling rate of 44.1 kHz, which
is slightly higher than twice the signal
bandwidth, is used