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41 The term “sequence” may be used to refer to a discretetime signal. What is the
reason(s)? Also, terms such as wave, waveform, signal, and function are used for
referring to CT and DT entities. Make a table listing terms, including sequence, are
used in this context and give very brief explanations for each.
Because a discretetime signal contains actually a set of points or samples, they are
forming a sequence.
42 Briefly discuss the difference between an ideal continuous to discrete
converter and a practical analogue to digital converter. Include corresponding
block diagram representations for both systems in your explanations.
Solution
:
A Continuous to Discrete Converter (CtoD) are used to convert a continuously
varying signal such as speech or audio to a discrete time signal. This process is called
sampling. The discrete time signal is obtained by taking values of the continuous time
signal at equally spaced time instants.
x[n] = x(nTs) ; Where Ts is the sampling period.
The AtoD conversion is a physical approximation to the ideal CtoD converter. An
AtoD converter produces only finite precision numbers as samples of the input
signal (quantized to a limited number of bits), while the ideal CtoD converter
produces samples with infinite precision.
AtoD converters differ from ideal CtoD converters because of realworld problems
such as:
1. Amplitude quantization to number of bits available (12 or 16 bits)
2. Jitter in the sampling times
3. Other factors those are difficult to analyse
These factors can be made negligible with careful design, and hence a practical A/D
converter offers sufficiently accurate operation as an ideal CtoD converter.
An Ideal CtoD converter
Wave
An entity describes changes of natural phenomenon
Waveform
A curve presents wave visually
Signal
A kind of information that can be processed and transmitted
Function
An entity obtains and processes inputs and give outputs
sequence
A set of points or samples that contain information
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View Full DocumentAn AtoD converter
43 Discretetime frequency is dimensionless. Provide some explanations through
comparing it with angular frequency (circular or radian frequency) and show how an
identical discretetime frequency could be resulted from an infinite number of
continuoustime sinusoid waves.
Discretetime frequency is a dimensionless quantity; consistent with the fact that the
index “n” in x[n] is dimensionless. The unit of discretetime frequency is radian and
the unit of angular frequency is radians/sec. Suppose that identical discretetime
frequency is ω(hat), ω(hat) =ω*Ts.
44 Aliasing is solely due to the fact that trigonometric functions are periodic with
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