数字信号处理实验报告Word下载.docx
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p=input（'
是否需要补0？
1（是）/0（否）:
'
%是否需要补0%
ifp==1%如果需要补0%
m=input（'
需要补多少个0？
%输入需要补0的个数%
M=N+m;
forj=N:
M-1
x（j+1）=0;
%给采样点后补0%
end
N=M;
%修正采样点数%
n=log（N）/log
（2）;
%计算总级数n%
forj=1:
N%码位倒置%
k=dec2bin（j-1,n）;
（注意到matlab中矩阵下标从1
k=fliplr（k）;
开始，而码位倒置需从0开始，
k=bin2dec（k）;
因此特别把下标作以修改（程序
y（k+1）=x（j）;
中红色部分）。
）
x=y;
forl=1:
n%按时间抽取的FFT蝶形运算%
j=1;
%将FFT分为n级进行%
m=0;
forp=2^l:
2^l:
N%将每一级分为计算方法相同的几块%
k=0;
z=j;
forq=m+（（p-m）/2+1）:
p%计算每一块里面的FFT%
y（j）=x（j）+exp（（-i*2*pi*k）/N）*x（j+2^（l-1））;
y（j+2^（l-1））=x（j）-exp（（-i*2*pi*k）/N）*x（j+2^（l-1））;
k=k+N/（2^l）;
m=p;
ifq<
p%判断该块是否计算完毕%
j=j+1;
%没有计算完继续计算%
elsej=z+2^l;
%计算完后进入下一块%
x=y;
x=abs（x）;
%将所得频谱取模值%
%模值归一化%
y=max（x）;
x=x/y;
N
stem（j,x（j））;
%绘制棒状图%
holdon
二、实验内容记录及分析
1、信号频率F=50Hz，采样长N=32，采样时间T=0.000625s
得到采样点为：
x（n）=[00.19510.38270.55560.70710.83150.92390.9808
1.00000.98080.92390.83150.70710.55560.38270.1951
0.0000-0.1951-0.3827-0.5556-0.7071-0.8315-0.9239-0.9808
-1.0000-0.9808-0.9239-0.8315-0.7071-0.5556-0.3827-0.1951]
对应的X（k）值为：
X（k）=[0.00000.0000-16.0000i0.0000+0.0000i-0.0000+0.0000i
-0.0000-0.0000i-0.0000+0.0000i0.0000-0.0000i0.0000+0.0000i0.0000+0.0000i-0.0000-0.0000i-0.0000+0.0000i-0.0000-0.0000i-0.0000+0.0000i-0.0000-0.0000i-0.0000-0.0000i0.00000.00000.0000+0.0000i-0.0000+0.0000i-0.0000+0.0000i
-0.0000-0.0000i-0.0000-0.0000i-0.0000-0.0000i0.0000+0.0000i
0.0000-0.0000i0.0000+0.0000i0.0000+0.0000i-0.0000-0.0000i
-0.0000+0.0000i-0.0000-0.0000i0.0000-0.0000i-0.0000+16.0000i]
归一化后的频谱模特性如下：
分析：
采样频率fs=
=
=1600Hz>
2F
所以频谱无混叠
信号周期T0=
=0.02s
采样持续时间t=NT=32×
0.000625=0.02s
一个周期内的采样点数n=
×
T0=32
X（k）可以采到频谱的峰点和谷点，故频谱不会出现栅栏效应。
频谱中未出现新的频率分量，故无频谱泄露。
2、信号频率F=50Hz，采样长N=32，采样时间T=0.005s
x（n）=[01.00000.0000-1.0000-0.00001.00000.0000-1.0000
-0.00001.0000-0.0000-1.0000-0.00001.0000-0.0000-1.0000
-0.00001.00000.0000-1.00000.00001.0000-0.0000-1.0000
-0.00001.0000-0.0000-1.00000.00001.0000-0.0000-1.0000]
X（k）=[-0.00000.0000+0.0000i0.0000-0.0000i-0.0000+0.0000i
-0.0000-0.0000i0.0000-0.0000i-0.0000-0.0000i0.0000-0.0000i
0.0000-16.0000i0.0000+0.0000i-0.0000+0.0000i0.0000+0.0000i
-0.0000+0.0000i-0.0000-0.0000i0.0000+0.0000i0.0000-0.0000i
-0.00000.0000+0.0000i0.0000-0.0000i-0.0000+0.0000i
0.0000+16.0000i0.0000+0.0000i-0.0000+0.0000i0.0000+0.0000i
-0.0000+0.0000i-0.0000-0.0000i0.0000+0.0000i0.0000-0.0000i]
=200Hz>
0.005=0.16s
T0=4
3、信号频率F=50Hz，采样长N=32，采样时间T=0.0046875s
x（n）=[00.99520.1951-0.9569-0.38270.88190.5556-0.7730
-0.70710.63440.8315-0.4714-0.92390.29030.9808-0.0980
-1.0000-0.09800.98080.2903-0.9239-0.47140.83150.6344
-0.7071-0.77300.55560.8819-0.3827-0.95690.19510.9952]
X（k）=[1.10331.1273-0.0000i1.2050-0.0000i1.3568-0.0000i
1.6339-0.0000i2.1750+0.0000i3.4960+0.0000i10.2519-0.0000i
-10.1532+0.0000i-3.3953+0.0000i-2.0703+0.0000i-1.5226+0.0000i-1.2361-0.0000i-1.0707-0.0000i-0.9739+0.0000i-0.9225-0.0000i-0.9063-0.9225+0.0000i-0.9739-0.0000i-1.0707+0.0000i
-1.2361+0.0000i-1.5226-0.0000i-2.0703-0.0000i-3.3953-0.0000i
-10.1532-0.0000i10.2519+0.0000i3.4960-0.0000i2.1750-0.0000i1.6339+0.0000i1.3568+0.0000i1.2050+0.0000i1.1273+0.0000i]
=213.33Hz>
0.0046875=0.15s
T0=4.27
X（k）不会采到频谱的峰点和谷点，故频谱会出现栅栏效应。
频谱中出现了新的频率分量，故有频谱泄露。
4、信号频率F=50Hz，采样长N=32，采样时间T=0.004s
x（n）=[00.95110.5878-0.5878-0.95110.00000.95110.5878
-0.5878-0.95110.00000.95110.5878-0.5878-0.9511-0.0000
0.95110.5878-0.5878-0.95110.00000.95110.5878-0.5878
-0.9511-0.00000.95110.5878-0.5878-0.9511-0.00000.9511]
X（k）=[0.95110.9867-0.0854i1.1052-0.1829i1.3526-0.3125i
1.8670-0.5220i3.1952-0.9911i11.3836-3.6858i-7.8447+2.5301i
-3.0777+0.9511i-2.0004+0.5718i-1.5376+0.3925i-1.2889+0.2826i
-1.1405+0.2045i-1.0482+0.1432i-0.9916+0.0912i-0.9608+0.0445i
-0.9511-0.9608-0.0445i-0.9916-0.0912i-1.0482-0.1432i
-1.1405-0.2045i-1.2889-0.2826i-1.5376-0.3925i-2.0004-0.5718i
-3.0777-0.9511i-7.8447-2.5301i11.3836+3.6858i3.1952+0.9911i
1.8670+0.5220i1.3526+0.3125i1.1052+0.1829i0.9867+0.0854i]
=250Hz>
0.004=0.128s
T0=5
5、信号频率F=50Hz，采样长N=64，采样时间T=0.000625s
x（n）=[00.19510.38270.55560.70710.83150.92390.9808
0.0000-0.1951-0.3827-0.5556-0.7071-0.8315-0.9239-0.9808
-1.0000-0.9808-0.9239-0.8315-0.7071-0.5556-0.3827-0.1951
-0.00000.19510.38270.55560.70710.83150.92390.9808
X（k）=[-0.0000-0.0000-0.0000i0.0000-32.0000i-0.0000+0.0000i
0.0000+0.0000i0.0000-0.0000i0.0000+0.0000i0.0000+0.0000i
-0.0000-0.0000i0.0000+0.0000i-0.0000+0.0000i-0.0000+0.0000i
-0.0000+0.0000i-0.0000+0.0000i-0.0000-0.0000i0.0000-0.0000i
0.0000+0.0000i-0.0000-0.0000i-0.0000-0.0000i0.0000-0.0000i
0.0000+0.0000i-0.0000+0.0000i-0.0000-0.0000i-0.0000-0.0000i
0.0000+0.0000i-0.0000+0.0000i-0.0000-0.0000i0.0000-0.0000i
0.0000-0.0000i0.0000-0.0000i0.00000.0000+0.0000i
-0.00000.0000-0.0000i0.0000-0.0000i0.0000+0.0000i
0.0000+0.0000i0.0000+0.0000i-0.0000+0.0000i-0.0000-0.0000i
0.0000-0.0000i-0.0000+0.0000i-0.0000+0.0000i-0.0000-0.0000i
0.0000-0.0000i0.0000+0.0000i-0.0000+0.0000i-0.0000+0.0000i
0.0000-0.0000i0.0000+0.0000i-0.0000-0.0000i-0.0000-0.0000i
-0.0000-0.0000i-0.0000-0.0000i-0.0000-0.0000i0.0000-0.0000i
-0.0000+0.0000i0.0000-0.0000i0.0000-0.0000i0.0000+0.0000i
0.0000-0.0000i-0.0000-0.0000i-0.0000+32.0000i-0.0000+0.0000i]
采样持续时间t=NT=64×
0.000625=0.04s
T0=16
6、信号频率F=250Hz，采样长N=32，采样时间T=0.005s
x（n）=[01.00000.0000-1.0000-0.00001.0000-0.0000-1.0000
-0.00001.00000.0000-1.00000.00001.00000.0000-1.0000
-0.00001.00000.0000-1.0000-0.00001.00000.0000-1.0000
0.00001.00000.0000-1.0000-0.00001.00000.0000-1.0000]
X（k）=[0.00000.0000+0.0000i-0.0000+0.0000i0.0000-0.0000i
0.0000+0.0000i-0.0000+0.0000i-0.0000+0.0000i-0.0000+0.0000i
-0.0000-16.0000i-0.0000-0.0000i-0.0000-0.0000i-0.0000-0.0000i
0.0000-0.0000i0.0000+0.0000i-0.0000-0.0000i0.0000-0.0000i
0.00000.0000+0.0000i-0.0000+0.0000i0.0000-0.0000i
-0.0000+16.0000i-0.0000-0.0000i-0.0000-0.0000i-0.0000-0.0000i
0.0000-0.0000i0.0000+0.0000i-0.0000-0.0000i0.0000-0.0000i]
虽然采样频率不同，但各采样点上的值与2中的采样点上的值是一致的，因此经FFT后频谱与2中的频谱一致。
但采样频率fs=
=200Hz<
所以频谱会混叠
=0.004s
T0=0.8
7、信号频率F=50Hz，采样长N=32，采样时间T=0.0046875s，采样点后补32个0
-0.7071-0.77300.55560.8819-0.3827-0.95690.19510.9952
00000000
00000000]
X（k）=[1.10330.0000+0.0000i1.1273-0.0000i-0.0000+0.0000i
1.2050-0.0000i-0.0000+0.0000i1.3568-0.0000i-0.0000+0.0000i
1.6339-0.0000i-0.0000-0.0000i2.1750+0.0000i0.0000+0.0000i
3.4960+0.0000i0.0000+0.0000i10.2519-0.0000i-0.0000-16.0000i
-10.1532+0.0000i0.0000-0.0000i-3.3953+0.0000i0.0000-0.0000i
-2.0703+0.0000i-0.0000+0.0000i-1.5226+0.0000i0.0000-0.0000i
-1.2361-0.0000i0.0000+0.0000i-1.0707-0.0000i-0.0000-0.0000i
-0.9739+0.0000i0.0000-0.0000i-0.9225-0.0000i0.0000+0.0000i
-0.90630.0000-0.0000i-0.9225+0.0000i0.0000+0.0000i
-0.9739-0.0000i-0.0000+0.0000i-1.0707+0.0000i0.0000-0.0000i
-1.2361+0.0000i0.0000+0.0000i-1.5226-0.0000i-0.0000-0.0000i
-2.0703-0.0000i0.0000+0.0000i-3.3953-0.0000i0.0000+0.0000i
-10.1532-0.0000i-0.0000+16.0000i10.2519+0.0000i0.0000-0.0000i
3.4960-0.0000i0.0000-0.0000i2.1750-0.0000i-0.0000-0.0000i
1.6339+0.0000i-0.0000-0.0000i1.3568+0.0000i-0.0000-0.0000i
1.2050+0.0000i-0.0000-0.0000i1.1273+0.0000i0.0000-0.0000i]
T0=8.53
增加了32个零点后，对X（ejw）每个周期内的采样点数增加，X（k）可以采到频谱的峰点和谷点，故频谱不会出现栅栏效应
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