FFT補(bǔ)0 - 簡書

通過補(bǔ)0，F(xiàn)FT可提高計(jì)算速度和提供頻域的分辨率遇西。時(shí)域補(bǔ)0相當(dāng)于頻域插值馅精。

原始信號(hào)采樣點(diǎn)數(shù)480個(gè)，補(bǔ)了480個(gè)0之后粱檀，變?yōu)?60個(gè)洲敢。(這里沒有按照2個(gè)整次冪進(jìn)行補(bǔ)0，而是按照speex中補(bǔ)0的邏輯進(jìn)行仿真)

時(shí)域信號(hào)

頻譜比較

FFT補(bǔ)0

clear
Fs = 48000;       % 采樣頻率
T  = 1/Fs;       % 采樣時(shí)間
L  = 480;        % 信號(hào)長度

t  = (0:L-1)*T; % 時(shí)間

L2  = 960;        % 信號(hào)長度
t2  = (0:L2-1)*T; % 時(shí)間

y  = textread('far.txt');
y2 = textread('far_zero_padding.txt');

%N  = 2^nextpow2(L); %采樣點(diǎn)數(shù)茄蚯，采樣點(diǎn)數(shù)越大压彭，分辨的頻率越精確睦优，N>=L，超出的部分信號(hào)補(bǔ)為0
%N2 = 2^nextpow2(L2); %采樣點(diǎn)數(shù)壮不，采樣點(diǎn)數(shù)越大汗盘，分辨的頻率越精確，N>=L询一，超出的部分信號(hào)補(bǔ)為0
N = L;
N2 = L2;

% y
Y = fft(y,N)/N*2;   %除以N乘以2才是真實(shí)幅值隐孽，N越大，幅值精度越高
f = Fs/N*(0:1:N-1); %頻率
A = abs(Y);     %幅值
P = angle(Y);   %相值

% y的功率譜
%Pyy = Y.*conj(Y)/N;%power spectrum %conj()共軛
%plot(f, Pyy(1:N));
%title('功率譜');
%xlabel('頻率（Hz）');

% y2
Y2 = fft(y2,N2)/N2*2;   %除以N乘以2才是真實(shí)幅值健蕊，N越大菱阵，幅值精度越高
f2 = Fs/N2*(0:1:N2-1); %頻率
A2 = abs(Y2);     %幅值
P2 = angle(Y2);   %相值

figure;
subplot(411);
plot(t, y, 'k')
hold on
plot(t2, y2, 'r')

legend('原始數(shù)據(jù)','補(bǔ)0之后的數(shù)') %為圖片添加圖例

title('時(shí)域信號(hào)')
xlabel('時(shí)間(s)')

subplot(412); 
plot(f(1:N/2), A(1:N/2),'k');   
hold on
plot(f2(1:N2/2), A2(1:N2/2), 'r');   

title('比較 幅值頻譜(前半部分)')
xlabel('頻率(Hz)')
ylabel('幅值')

subplot(413); 
plot(f(1:N/2), A(1:N/2),'k');   

title('原始數(shù)據(jù) 幅值頻譜(前半部分)')
xlabel('頻率(Hz)')
ylabel('幅值')

subplot(414); 
plot(f2(1:N2/2), A2(1:N2/2), 'r');   

title('補(bǔ)0之后 幅值頻譜(前半部分)')
xlabel('頻率(Hz)')
ylabel('幅值')

far.txt中的數(shù)據(jù)（480個(gè)采樣數(shù)據(jù)）

-1122
-121.2
-123.1
-125.1
-130.2
-131.7
-132.2
-130.6
-129.7
-124.6
-121.9
-119.9
-122.7
-120.8
-118.7
-119.4
-124.2
-127.5
-124.1
-125.3
-130.6
-128.4
-118.9
-109.4
-109
-114.7
-113.1
-103.4
-99.8
-102
-97.6
-89.9
-89.6
-83.5
-77
-75.1
-65.3
-66.8
-71.8
-71.6
-70.6
-63.7
-59.3
-56.7
-51.1
-50.2
-51.5
-51.2
-44.1
-40.5
-43.8
-43.7
-36.8
-29.4
-24.5
-19.4
-14.1
-9.6
-3
-3.1
-0.6
5.8
1.5
2.4
10.1
15.3
24.7
29.7
32.8
41.8
48.3
54
58.8
59.6
65
72.5
80.3
92.4
92.2
87.4
92.6
102.9
97.8
95.7
108
114.2
108.6
111
119.3
122.1
114.8
114.4
119.7
135.3
145.2
149.7
165.2
178.8
173.2
172.4
180
180.9
180.4
185.4
192.5
200.9
210.7
207
207.4
205.4
206.8
215
218.7
218.4
213.7
214.2
217.5
229.9
241.3
244.5
240.6
237.9
236.6
233.9
236.7
248.6
252.5
245.5
236.5
237.4
235.3
224.9
225.4
240
235.1
219.6
210.5
213.6
218.2
214.4
208.3
211.7
223.6
218.8
212.5
209.6
212.5
203.8
198.3
210.4
211.9
196.6
188.8
192.4
200.6
205.8
185.6
165.4
177.4
182
170.3
173.6
175.5
159.8
152.7
167.2
167.5
160
166.9
174.7
166.4
154.3
143.1
145
155.4
159.1
154.3
137.1
133.3
135.4
129
123.2
123.1
119.3
116.4
119.5
115.2
103.7
89.3
76.8
87.5
98.8
86.6
71.4
70
62.9
58.5
72.1
76.5
68.6
67.1
75.7
77.4
61.4
44.9
45
48.5
38.7
32.2
26.4
12.4
4.4
7.1
0.6
-8.1
-6.2
-3.6
1.7
-0.1
-12.8
-24.5
-35
-38.1
-37
-40.3
-45.5
-45.8
-41.7
-39.8
-40.4
-52.8
-58.2
-52.8
-55.5
-64.2
-71.5
-79.2
-92.3
-100.3
-94.6
-84.8
-80.6
-84.7
-85
-81.1
-86.6
-94.5
-96
-92.4
-82.2
-77.8
-90.9
-102.3
-93.7
-86
-81.4
-78.3
-77.9
-86.5
-93
-89.1
-79.7
-78.3
-89.8
-96.5
-90.8
-92.4
-106.1
-113.1
-105.6
-95.1
-85.4
-88.7
-96.4
-97.9
-92.5
-93.5
-89.6
-87.3
-94.8
-93.1
-84.2
-76.4
-81.9
-93.1
-97.5
-92.3
-93.5
-100.8
-98.8
-91.5
-94.4
-98.6
-106.2
-117.5
-115.8
-97.7
-84.6
-85.2
-91
-91.5
-90.1
-84.6
-80.6
-73.3
-70.4
-68.4
-65.4
-61.3
-68
-74.6
-67
-60.7
-66.9
-83.9
-84.7
-73.5
-72.1
-71.6
-62.1
-57.7
-68
-80.5
-87.3
-82.7
-77.5
-77.7
-70.9
-52.4
-38.1
-48.6
-65.5
-71.3
-68.7
-64.8
-66.5
-69.4
-64.6
-63.3
-69.9
-67.2
-66.2
-77.1
-82.1
-69.5
-59.5
-68.5
-88.5
-102.5
-95.7
-86.9
-88
-94.1
-96.7
-99.4
-99.2
-103.8
-107.7
-102.8
-100.2
-104.2
-103.5
-105.6
-122.8
-137.6
-123.6
-108.8
-114.3
-131.3
-133.9
-129.5
-135.4
-144.7
-147.7
-149.7
-144.6
-129.7
-120.1
-130.5
-153
-159.7
-148.8
-144.5
-147.6
-152.9
-156.6
-152.5
-139.8
-131.7
-128.8
-135.7
-136.4
-122.2
-110.6
-119
-129.5
-120.2
-105
-104.4
-111
-106.5
-93.7
-89.8
-99.8
-105.1
-108.1
-103.5
-91.5
-81.4
-77.5
-86.5
-95.7
-99
-88.7
-79.4
-81.3
-88.6
-77.8
-53
-38.9
-46.8
-61
-61
-50.2
-38.5
-24.9
-17.3
-18.4
-14.1
-8.8
-5.4
-4.1
1.9
6.1
12.3
16.7
11.1
17.5
25.2
26.3
27.1
38.6
44.9
47.4
47.7
43.6
40.7
45.2
42.9
50.1
64.8
78.7
78.6
75
75.6
78.9
85.2
95.8
100.1
98.4
96.1
100.2
108.4
118.1
117.4
116.2
126.5
136.5
134.1
127
122.8
126.9
138.2
150.4
156.5
158.8
161.9
158.9
152.2
151.5

far_zero_padding.txt中的數(shù)據(jù)(480個(gè)0 + 480個(gè)采樣數(shù)據(jù)):