Ïðèëîæåíèå 5
Òàáëèöà z-èçîáðàæåíèé íåêîòîðûõ ðåøåò÷àòûõ ôóíêöèé
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f[k] |
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Îáùèé âèä |
ßâíîå âûðàæåíèå |
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1 |
1 ïðè k = 0, 0 ïðè ïðî÷èõ k |
1, 0, 0, 0, 0, 0,… |
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(α — ëþáîå êîìïëåêñíîå ÷èñëî) |
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1,
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1 |
1, 1, 1, … |
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(– 1)k |
1, – 1, 1, – 1,… |
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k |
0, 1, 2, 3, … |
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(ω — âåùåñòâåííîå) |
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(ω — âåùåñòâåííîå) |
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0, 1, 0, – 1, … ñ ïåðèîäè÷åñêèì ïîâòîðåíèåì |
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1, 0, – 1, 0,… ñ ïåðèîäè÷åñêèì ïîâòîðåíèåì |
Ïðè k < 0 äëÿ âñåõ ñëó÷àåâ f[k] = 0. Ïðèâåäåííûå ôîðìóëû F(z) îïðåäåëÿþò ïðè ïîäñòàíîâêå z = ejωT ñïåêòðàëüíóþ ïëîòíîñòü îäíîñòîðîííåãî ïðåîáðàçîâàíèÿ Ôóðüå F(jω) ñîîòâåòñòâóþùåé ðåøåò÷àòîé ôóíêöèè f[k].
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