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There is a frequency-domain ambiguity associated with discrete-time signal samples that does not exist in the continuous signal world, and we can appreciate the effects of this uncertainty by understanding the sampled nature of discrete data. By way of example, suppose you were given the following sequence of values,

and were told that they represent instantaneous values of a time-domain sinewave taken at periodic intervals. Next, you were asked to draw that sinewave. You'd start by plotting the sequence of values shown by the dots in Figure 2-1(a) . Next, you'd be likely to draw the sinewave, illustrated by the solid line in Figure 2-1(b) , that passes through the points representing the original sequence.

Figure 2-1 Frequency ambiguity: (a) discrete-time sequence of values; (b) two different sinewaves that pass through the points of the discrete sequence.

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There is a frequency-domain ambiguity associated with discrete-time signal samples that does not exist in the continuous signal world, and we can appreciate the effects of this uncertainty by understanding the sampled nature of discrete data. By way of example, suppose you were given the following sequence of values,

and were told that they represent instantaneous values of a time-domain sinewave taken at periodic intervals. Next, you were asked to draw that sinewave. You'd start by plotting the sequence of values shown by the dots in Figure 2-1(a) . Next, you'd be likely to draw the sinewave, illustrated by the solid line in Figure 2-1(b) , that passes through the points representing the original sequence.

Figure 2-1 Frequency ambiguity: (a) discrete-time sequence of values; (b) two different sinewaves that pass through the points of the discrete sequence.


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