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Understanding digital signal processing - Chapter 2

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Tài liệu tham khảo giáo trình tìm hiểu xử lý tín hiệu số bằng tiếng anh ( Understanding digital signal processing ) Chương 2. Preodic lấy mẫu | CHAPTER TWO Periodic Sampling Periodic sampling the process of representing a continuous signal with a sequence of discrete data values pervades the field of digital signal processing. In practice sampling is performed by applying a continuous signal to an analog-to-digital A D converter whose output is a series of digital values. Because sampling theory plays an important role in determining the accuracy and feasibility of any digital signal processing scheme we need a solid appreciation for the often misunderstood effects of periodic sampling. With regard to sampling the primary concern is just how fast must a given continuous signal be sampled in order to preserve its information content. We can sample a continuous signal at any sample rate we wish and we ll get a series of discrete values but the question is how well do these values represent the original signal Let s learn the answer to that question and in doing so explore the various sampling techniques used in digital signal processing. 2.1 Aliasing Signal Ambiguity in the Frequency Domain 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 x 0 0 x l 0.866 x 2 0.866 x 3 0 x 4 -0.866 x 5 -0.866 x 6 0 23 24 Periodic Sampling Figure 2-1 Frequency ambiguity a discrete-time sequence of values b two different sinewaves that pass through the points of the discrete sequence. 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-l 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 .