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标题: MATLAB —— 信号处理工具箱之 ifft 的案例分析 [打印本页]
作者: mytomorrow 时间: 2019-12-11 09:00
标题: MATLAB —— 信号处理工具箱之 ifft 的案例分析
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案例分析
Inverse Transform of Vector
Padded Inverse Transform of Matrix
Conjugate Symmetric Vector
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9 p% k5 M0 W$ a3 D: U, ^ t案例分析
$ \5 O2 l N: u6 V; h$ b( M# XInverse Transform of Vector3 Q. d: b, Z! g: `: g' J" s1 P- F
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- % The Fourier transform and its inverse convert between data sampled in time and space and data sampled in frequency.
- %
- % Create a vector and compute its Fourier transform.
- X = [1 2 3 4 5];
- Y = fft(X)
- % Y = 1×5 complex
- %
- % 15.0000 + 0.0000i -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i -2.5000 - 3.4410i ⋯
- %
- % Compute the inverse transform of Y, which is the same as the original vector X.
- ifft(Y)
- % ans = 1×5
- %
- % 1 2 3 4 51 j4 a7 [" D; L3 V7 s$ E! h
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结果如下：
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9 U; r& N/ Q: D. a ifft_vector
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- T. t# T5 d0 H; c6 V4 b7 g+ T% ~Y =
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, M l8 ]* |" ?7 q n4 b/ R 1 至 4 列9 i; z/ E' Q: ]+ Z! l8 ^1 i+ |7 ?
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15.0000 + 0.0000i -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i# p) C& L/ E x9 E4 v8 g( Y
6 w9 Z3 w) a5 h! s: d+ B 5 列
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-2.5000 - 3.4410i
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* c$ Z4 b- P% S7 t: tans =
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- G& I: l7 _' L; h" ~ 1 2 3 4 5
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Padded Inverse Transform of Matrix
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- clear
- close all
- % The ifft function allows you to control the size of the transform.
- %
- % Create a random 3-by-5 matrix and compute the 8-point inverse Fourier transform of each row.
- % Each row of the result has length 8.
- Y = rand(3,5)
- n = 8;
- X = ifft(Y,n,2)
- size(X)
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结果如下：3 x) Y' D! a# b* k
& A8 I9 R0 e+ W6 iY =& D4 y$ A. U) U
4 y# D* ]. ~9 g O 0.8147 0.9134 0.2785 0.9649 0.9572
p. b1 C5 r) K4 X8 x& z4 S y 0.9058 0.6324 0.5469 0.1576 0.4854; I3 x9 l8 c1 {" e
0.1270 0.0975 0.9575 0.9706 0.8003
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: ^) J9 u. e/ i; }. J+ bX =8 Q5 b) A7 ]) H5 p0 u2 |# s
4 { f& m+ [: Z0 P/ L 1 至 4 列
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* g d# C Q& x5 m( e 0.4911 + 0.0000i -0.0224 + 0.2008i 0.1867 - 0.0064i -0.0133 + 0.1312i* V9 P, }3 I: f
0.3410 + 0.0000i 0.0945 + 0.1382i 0.1055 + 0.0593i 0.0106 + 0.0015i
( J. k) _3 K( y8 P$ x% N5 R8 l; m0 k 0.3691 + 0.0000i -0.1613 + 0.2141i -0.0038 - 0.1091i -0.0070 - 0.0253i7 w0 x* B4 \3 Q; w4 _
% M. I D; Z4 J& U 5 至 8 列% R# D. B8 r: ^2 ?8 C+ c
7 @$ y! o- n9 o& ~; }9 V& O 0.0215 + 0.0000i -0.0133 - 0.1312i 0.1867 + 0.0064i -0.0224 - 0.2008i* p% j- D; c6 @$ K# \" d
0.1435 + 0.0000i 0.0106 - 0.0015i 0.1055 - 0.0593i 0.0945 - 0.1382i; Y) a5 | ?; S4 G
0.1021 + 0.0000i -0.0070 + 0.0253i -0.0038 + 0.1091i -0.1613 - 0.2141i
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. j$ n% K0 f3 _3 b8 ?( y1 mans =0 h; u3 }& i) o5 P
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) S' @% p+ w2 Y2 Y! ~! r上面的程序是计算矩阵每一行的8点ifft，故结果是每一行的ifft有8个元素，而计算矩阵 Y 每一行的 ifft，关键语句为：
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X = ifft(Y,n,2)，里面的2，如果去掉2，则是对矩阵Y的每一列计算ifft，测试如下：4 G: k; D4 ?' P! G! \
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- clear
- close all
- % The ifft function allows you to control the size of the transform.
- %
- % Create a random 3-by-5 matrix and compute the 8-point inverse Fourier transform of each row.
- % Each row of the result has length 8.
- Y = rand(3,5)
- n = 8;
- X = ifft(Y,n)
- size(X)/ P- _8 s& ~! b6 P
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Y =
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0.1419 0.7922 0.0357 0.6787 0.39228 _1 V$ J2 E3 u3 F3 `1 `; a
0.4218 0.9595 0.8491 0.7577 0.6555: |* a3 N" R; N1 p0 `
0.9157 0.6557 0.9340 0.7431 0.1712
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X =
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1 至 4 列7 s; x$ ~9 m6 ?3 @0 r9 J9 b
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0.1849 + 0.0000i 0.3009 + 0.0000i 0.2274 + 0.0000i 0.2725 + 0.0000i- |& P6 Y; [ B! t; {: F
0.0550 + 0.1517i 0.1838 + 0.1668i 0.0795 + 0.1918i 0.1518 + 0.1599i! w& E- E$ b# g# L
-0.0967 + 0.0527i 0.0171 + 0.1199i -0.1123 + 0.1061i -0.0080 + 0.0947i# ~7 w0 b" L, A& y# s1 |6 v
-0.0195 - 0.0772i 0.0142 + 0.0028i -0.0706 - 0.0417i 0.0179 - 0.0259i$ |& {6 w) W5 T3 b; |
0.0795 + 0.0000i 0.0611 + 0.0000i 0.0151 + 0.0000i 0.0830 + 0.0000i$ _+ F }# R. y/ {# j
-0.0195 + 0.0772i 0.0142 - 0.0028i -0.0706 + 0.0417i 0.0179 + 0.0259i
: H. S! E' \6 c& i. {) h -0.0967 - 0.0527i 0.0171 - 0.1199i -0.1123 - 0.1061i -0.0080 - 0.0947i" [: B8 A& D5 s2 M- A$ t
0.0550 - 0.1517i 0.1838 - 0.1668i 0.0795 - 0.1918i 0.1518 - 0.1599i$ W' \! U- j2 K, R: B
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5 列
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+ H$ w6 T7 L( M4 }5 X6 W' U/ n 0.1524 + 0.0000i+ Z7 [5 _& | |- Z# o, }
0.1070 + 0.0793i J- G. I6 z5 Y, {4 C# G8 k
0.0276 + 0.0819i4 j1 V# ]( r; j' V( ^# l9 Z
-0.0089 + 0.0365i
! O( Y L2 V+ e2 m2 V1 F, t* S -0.0115 + 0.0000i
5 A! W6 ~$ ^ }. E) \% v -0.0089 - 0.0365i/ ?$ ]8 T, U( k
0.0276 - 0.0819i
* j" f% d! G- p+ ~# j6 U 0.1070 - 0.0793i
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ans =
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Conjugate Symmetric Vector
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For nearly conjugate symmetric vectors, you can compute the inverse Fourier transform faster by specifying the 'symmetric' option, 2 i2 L3 [, `9 N0 g
which also ensures that the output is real. Nearly conjugate symmetric data can arise when computations introduce round-off error.
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Create a vector Y that is nearly conjugate symmetric and compute its inverse Fourier transform.
( [9 d" M1 T* v2 f! T0 O1 dThen, compute the inverse transform specifying the 'symmetric' option, which eliminates the nearly 0 imaginary parts.
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1 L& v* e9 ^, x9 Y$ v3 H" k对于近似共轭对称矢量，您可以通过指定“symmetric”选项来更快地计算逆傅里叶变换，这也确保了输出是真实的。 当计算引入舍入误差时，可能出现几乎共轭的对称数据。5 u) T# r/ |; n* r1 p2 D% ?; B+ t
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创建几乎共轭对称的向量Y并计算其逆傅里叶变换。然后，计算指定'对称'选项的逆变换，它消除了近0虚部。) M5 S3 Y9 ]1 _7 r
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- clear
- close all
- % For nearly conjugate symmetric vectors, you can compute the inverse Fourier transform faster by specifying the 'symmetric' option,
- % which also ensures that the output is real. Nearly conjugate symmetric data can arise when computations introduce round-off error.
- %
- % Create a vector Y that is nearly conjugate symmetric and compute its inverse Fourier transform.
- % Then, compute the inverse transform specifying the 'symmetric' option, which eliminates the nearly 0 imaginary parts.
- Y = [1 2:4+eps(4) 4:-1:2]
- % Y = 1×7
- %
- % 1.0000 2.0000 3.0000 4.0000 4.0000 3.0000 2.0000 ⋯
- X = ifft(Y)
- % X = 1×7 complex
- %
- % 2.7143 + 0.0000i -0.7213 + 0.0000i -0.0440 - 0.0000i -0.0919 + 0.0000i -0.0919 - 0.0000i -0.0440 + 0.0000i -0.7213 - 0.0000i ⋯
- Xsym = ifft(Y,'symmetric')
- % Xsym = 1×7
- %
- % 2.7143 -0.7213 -0.0440 -0.0919 -0.0919 -0.0440 -0.7213 ⋯
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结果如下：
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Y =
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[ @0 t- S! e) m5 nX =
" [ u( g/ H4 b% ]
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C$ e8 q7 [- i 2.7143 + 0.0000i -0.7213 + 0.0000i -0.0440 - 0.0000i -0.0919 + 0.0000i
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6 V4 b3 S% n/ u 5 至 7 列. j- W4 E' z/ D& V" Y
( C& e* B8 i9 K" C4 _# s -0.0919 - 0.0000i -0.0440 + 0.0000i -0.7213 - 0.0000i- o4 ^( s% N7 `4 A: Q
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Xsym =; n9 B+ f- }! K' Y- z( ^- }
! R# |) J; ^0 z: Z. z 2.7143 -0.7213 -0.0440 -0.0919 -0.0919 -0.0440 -0.7213
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作者: Neken 时间: 2019-12-11 19:22
谢谢分享
作者: sharkN 时间: 2019-12-12 18:58
学习咯
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