ݷʱ : 2024/12/24 7:50:28һ µȫĶ
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M?1ϣz任X(z)?j2?kN?nx(n)zڵλԲNȼ?n?0ijz?e,k?0,1,?N?1ϵijN?Mʱ
ҳֻһNDFTܼX(z)Nķ֤֮ ⣺N?Mɽx(n)㵽N㣬 x0(n)??? X(ejx(n),0?n?M?1?0,M?n?N?12?kN
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)??x0(n)en?0N?1?j2?nkN1,0,1,1,0,1?Z任X(z)ڵλԲϽ5ȷ10x(n)??ȡõȡֵX(k)X(k)?X(z)X(k)渵Ҷ任x1(n) ⣺
X(z)??x(n)z?n?1?z?2?z?3?z?5n?05z?W5?k,k?0,1,2,3,4
X(k)?X(z)z?W?k5?1?W52?W53?W55?2?W52?W53
??x1(n)Wn?04kn5
x1(n)??2,0,1,1,0?
11ͼʾx(n)Z任ΪX(z)X(z)ڵλԲϵȼ4ȡõX(k)X(k)?X(z)z?e2?k4j,k?0,1,2,3
X(k)4ɢҶ任x1(n)x1(n)ͼΡ?P379?
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x?n?1-2-101234567
⣺ΪX(z)ڵλԲϵȼ4ȡʹx(n)4Ϊڽأx1(n)?Σͼʾ
x1?n?21r????x((n?4r))ʽɻx(n)ͼ
1?-2-101234567n
ġɢҶ任ʱźűƽ
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1DFTźƵгֵԼЩķ? ⣺
2źųȶкӰ죿ǷƵֱ?
⣺ʱźųȣʹƵܣƵֱʡ
3˵Ҷ任X(f)ķֵɢҶ任X(k)word
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ֵʲôϵ ⣺ֵһ
4DFTƵƵй©ԭο˷ ⣺ƵʹͣDFTƵֻԣγƵʧ棻߲Ƶ˷ʧ档
й©ڼ𣬿˷ǾСխĴ
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5ij̨FFTʹøʱѡõijN2ݡ֪źУƵ?1025kHzҪֱ?5Hzȷв1.һ¼еٳ2.ʱ3.źŵС¼ʱ䡣 ⣺ΪźƵfm?1.25kHz ԳƵӦ㣺fs?2fm?2.5kHz ΪҪֱ
fs2.5?1000?5kHzN??500 N5ΪѡõijN2ݣһ¼еٳN?512
ʱT?1fsmin?11?ms?0.4ms 2fs2.5źŵС¼ʱTpmin?N?T?512?0.4ms?204.8ms
61ģ10.24ǧȡҼ1024ȡɢ
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Ҷ任Ƶȡ֮Ƶʼ
2ݾԺֽɢҶ任
ɢҶ任ļΪ٣1024ʱΪ٣
10240?10գ ⣺1Ƶʼ?F?10242ļ?T?1?97.66?s 10.24 1024ʱT=97.66?1024=100ms
7Ƶģź8kHz512DFTȷƵ׳֮Ƶʼ֤Ļش
?s?,F0?02?2? fs??s
F0?0֤ fs?
?sԽƵΪƵڣ?0Ƶ׳֮Ƶ
fs?s??N F0?0 F0?fs Nڱ fs?8kHz,N?512 F0?8000?15.625Hz 5128һõźŴΪ2ݣٶûвκݴʩҪƵʷֱ?10HzõijʱΪ0.1msȷ1С¼ȣ2
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źŵƵʣ3һ¼еٵ ⣺
1 ΪT0?1F,F0?10Hz 0 T10?10s
С¼Ϊ0.1s 2 Ϊfs?1T?10.1?103?10kHz fs?2fh f1h?2fs?5kHz źƵΪ5kHz
3N?T00.1T?0.1?103?1000N Ϊ2ݣһ¼еٵΪN?210?1024
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