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Giáo trình toán kỹ thuật 6

Những nội dung trên được dùng làm môn học cơ sở cho các môn học chuyên ngành Điện tử viễn thông đồng thời có thể sử dụng làm tài liệu tham khảo cho các ngành kỹ thuật khác. | 46 47 The quantity sin v -0 sinH -01 is called a scanning funo Hon. Over the range 0 X 2tt it has a very large peak at X t where the amplitude equals 2N 1. See Figure 2.2.1 On either side of this peak there are oscillations which decrease rapidly with distance from the peak. Consequently as jV oo the scanning function becomes essentially a long narrow slit corresponding to the area under the large peak at X t. Tf we neglect for the moment the small area under the minor ripples adjacent to this slit then the integral 2.2.37 essentially equals i times the area of the slit divided by 2tt. ĩf l 2ir times the area of the slit equals unity then the value of Sjv i ft t to a good approximation for large A . For a relatively small value of A r the scanning function deviates considerably from its ideal form and the partial sum Sjv 0 only crudely approximates the given function f t . As the partial sum includes more terms and TV becomes relatively large the form of the scanning function improves and so does the degree of approximation bet ween S v O and f t . The improvement in the scanning function is due to the large hump becoming taller and narrower. At the same time the adjacent ripples become larger in number and hence also become narrower in the same proportion as the large hump becomes narrower. The reason why S v i and i will never become identical even in the limit of N oc is the presence of the positive and negative side lobes near the large peak. Because sin W z-ỉ .A _ __ sin l J-01 1 2Z sH - 2.2.38 .