discrete fourier transform matlab function
The Discrete Fourier Transform
Ngày tải lên :
13/09/2012, 09:49
... decomposed.
Chapter 8- The Discrete Fourier Transform 145
Type of Transform Example Signal
Fourier Transform
Fourier Series
Discrete Time Fourier Transform
Discrete Fourier Transform
signals that ... term: transform, is extensively used in Digital Signal
Processing, such as: Fourier transform, Laplace transform, Z transform,
Hilbert transform, Discrete Cosine transform, etc. Just what is a transform?
To ... ]
141
CHAPTER
8
The Discrete Fourier Transform
Fourier analysis is a family of mathematical techniques, all based on decomposing signals into
sinusoids. The discrete Fourier transform (DFT) is...
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Fourier Transform Properties
Ngày tải lên :
13/09/2012, 09:49
... frequency
domain multiplexing.
The Discrete Time Fourier Transform
The Discrete Time Fourier Transform (DTFT) is the member of the Fourier
transform family that operates on aperiodic, discrete signals. The ... four members of the Fourier
transform family (Fourier transform, Fourier Series, DFT, and DTFT).
Figure 10-1 provides an example of how homogeneity is a property of the
Fourier transform. Figure ... properties of the Fourier Transform, how a mathematical change in one
domain results in a mathematical change in the other domain.
Linearity of the Fourier Transform
The Fourier Transform is linear,...
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Fourier Transform Pairs
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13/09/2012, 09:49
... called Fourier transform pairs. Several common
pairs are presented in this chapter.
Delta Function Pairs
For discrete signals, the delta function is a simple waveform, and has an
equally simple Fourier ... of the general form: , i.e., a sinc function. Forsin(x)/x
continuous signals, the rectangular pulse and the sinc function are Fourier
transform pairs. For discrete signals this is only an approximation, ... will be zero.
The sinc function is widely used in DSP because it is the Fourier transform pair
of a very simple waveform, the rectangular pulse. For example, the sinc
function is used in spectral...
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The Fast Fourier Transform
Ngày tải lên :
13/09/2012, 09:50
... with zeros to make it an
Chapter 12- The Fast Fourier Transform 235
TABLE 12-4
The Fast Fourier Transform in BASIC.
1000 'THE FAST FOURIER TRANSFORM
1010 'Upon entry, N% contains the ... the far right
column in Fig. 12-3).
225
CHAPTER
12
The Fast Fourier Transform
There are several ways to calculate the Discrete Fourier Transform (DFT), such as solving
simultaneous linear equations ... signal with a shifted delta function. This multiplies the signal's spectrum
with the spectrum of the shifted delta function. The spectrum of a shifted delta
function is a sinusoid (see Fig...
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The Complex Fourier Transform
Ngày tải lên :
13/09/2012, 10:20
... continuous or discrete, and it can be either
periodic or aperiodic. This defines four types of Fourier transforms: the
Discrete Fourier Transform (discrete, periodic), the Discrete Time
Fourier Transform ... the complex Fourier transform, they are
introduced by the real Fourier transform. In the world of mathematics, the
complex Fourier transform is a greater truth than the real Fourier transform.
This ... Laplace and z-transforms. These complex transforms
are the foundation of theoretical DSP.
The Real DFT
All four members of the Fourier transform family (DFT, DTFT, Fourier
Transform & Fourier Series)...
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Các phương pháp xử lý tín hiệu dùng bộ lọc, phương pháp Fourier Transform, STFT( Short Time Fourier Transform)
Ngày tải lên :
01/04/2013, 16:14
... Trong miền tần số: phương pháp Fourier Transform.
- Trong miền thời gian và tần số: STFT( Short Time Fourier Transform) .
2.4.1. Phương pháp Fourier:
2.4.1.1. Biến đổi Fourier:
Cho một hàm f(t) ... kết thúc của sự
kiện thì Fourier không phát hiện được.
2.4.2. Phương pháp STFT:
Để đạt được một biến đổi Fourier cục bộ, chúng ta có thể định nghĩa một biến đổi
Fourier cửa sổ. Tín hiệu đầu ... đổi Fourier của nó được định nghĩa:
() () ()
tfedtetfF
titj
,
ωω
ω ==
∫
∞
∞−
−
(2.14)
Biến đổi Fourier ngược là:
() ()
∫
∞
∞−
= ωω
π
ω
deFtf
tj
2
1
(2.15)
Giả sử rằng biến đổi Fourier...
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MATLAB Functions
Ngày tải lên :
29/09/2013, 22:20
... features, compare
these MATLAB statements with a C, Fortran, or Java
routine to do the same operation.
5. MATLAB Functions
MATLAB has a wide assortment of built-in functions.
You have already ... gallery('parter', 6)
svd(A)
The
eig
,
eigs
, and
svd
functions are discussed below.
5.2 Scalar functions
Certain MATLAB functions operate essentially on scalars
but operate entry-wise ... manipulation functions. For a more complete list,
see Chapter 22, or
Help
:
MATLAB
:
Functions
Categorical
List
.
5.1 Constructing matrices
Convenient matrix building functions include:...
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Real-Time Digital Signal Processing - Chapter 7: Fast Fourier Transform and Its Applications
Ngày tải lên :
28/10/2013, 05:15
... Convolution
The Fourier transform, the Laplace transform, and the z -transform of the linear con-
volution of two time functions are simply the products of the transforms of the
individual functions. ... frequencies
f
k
kf
s
N
, k 0, 1, , N À 1: 7:3:1
322
FAST FOURIER TRANSFORM AND ITS APPLICATIONS
DFT and z -transform
Consider a sequence x(n) having the z -transform X(z) with an ROC that includes
the unit ... implemented in the MATLAB function ifft, which can be
used as
y ifft(x);
or
y ifft(x,N);
The characteristics and usage of ifft are the same as those for fft.
FAST FOURIER TRANSFORMS
321
[2]...
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Tài liệu Table of Fourier Transform Pairs ppt
Ngày tải lên :
13/12/2013, 12:15
... waw
w
j++
t
e
a-
22
2
wa
a
+
)2/(
22
s
t
e
-
2/
22
2
ws
ps
-
e
t
etu
a-
)(
wa
j
+
1
t
tetu
a-
)(
2
)(
1
wa
j
+
Ø Trigonometric Fourier Series
()
å
¥
=
++=
1
000
)sin()cos()(
n
nn
ntbntaatf
ww
where
ò
òò
=
==
T
n
T
T
n
dtnttf
T
b
dtnttf
T
adttf
T
a
0
0
0
0
0
0
)sin()(
2
... Series
()
å
¥
=
++=
1
000
)sin()cos()(
n
nn
ntbntaatf
ww
where
ò
òò
=
==
T
n
T
T
n
dtnttf
T
b
dtnttf
T
adttf
T
a
0
0
0
0
0
0
)sin()(
2
and, )cos()(
2
, )(
1
w
w
Ø Complex Exponential Fourier Series
ò
å
-
¥
-¥=
==
T
ntj
n
n
ntj
n
dtetf
T
FeFtf
0
0
)(
1
where, )(
w
w
Signals &...
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Tài liệu Fast Fourier Transform part 1 doc
Ngày tải lên :
21/01/2014, 18:20
... and h are real functions,so wetakethelibertyof
setting H(−f)=H*(f).] This result shows that multiplyingthe Fourier transform
of one function by the complex conjugate of the Fourier transform of ... is equal to the sum of
the transforms. The transform of a constant times a function is that same constant
times the transform of the function.
In the time domain, function h(t) may happen to ... when we get to discretely
sampled data in §12.1.
From equation (12.0.1) it is evident at once that Fourier transformation is a
linear operation. The transform of the sum of two functions is equal...
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Tài liệu Fast Fourier Transform part 2 ppt
Ngày tải lên :
21/01/2014, 18:20
... showed
that a discrete Fourier transform of length N can be rewritten as the sum of two
discrete Fourier transforms, each of length N/2. One of the two is formed from the
12.1 Fourier Transform of Discretely ... generate the
required powers of W . So, the discrete Fourier transform appears to be an O(N
2
)
process. These appearances are deceiving! The discrete Fourier transform can,
in fact, be computed in ... a
continuous function has been competently sampled, then, when we come to estimate
its Fourier transform from the discrete samples, we can assume (orratherwemight
as well assume) that its Fourier transform...
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Tài liệu Fast Fourier Transform part 3 docx
Ngày tải lên :
21/01/2014, 18:20
... isign)
Replaces
data[1 2*nn] by its discrete Fourier transform, if isign is input as 1; or replaces
data[1 2*nn] by nn times its inverse discrete Fourier transform, if isign is input as −1.
data ... Frameworks for the Fast Fourier Transform
(Philadelphia:
S.I.A.M.).
Beauchamp, K.G. 1984,
Applications of Walsh Functions and Related Functions
(New York:
Academic Press) [non -Fourier transforms].
Heideman, ... a slow
Fourier transform, of order N
2
instead of order N log
2
N. Our advice is to stay clear
of such FFT implementations, with perhaps one class of exceptions, the Winograd
Fourier transform...
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Tài liệu Fast Fourier Transform part 4 pdf
Ngày tải lên :
21/01/2014, 18:20
... 12.3.1. Basis functionsused by the Fourier transform( a), sine transform( b), and cosine transform
(c), are plotted. The first five basis functions are shown in eachcase. (For the Fourier transform, ... Frameworks for the Fast Fourier Transform
(Philadelphia:
S.I.A.M.).
Beauchamp, K.G. 1984,
Applications of Walsh Functions and Related Functions
(New York:
Academic Press) [non -Fourier transforms].
Heideman, ... the components of the
discrete Fourier transform satisfy
F
N−n
=(F
n
)* (12.3.1)
where the asterisk denotes complex conjugation. By the same token, the discrete
Fourier transform of a purely...
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Tài liệu Fast Fourier Transform part 5 pptx
Ngày tải lên :
21/01/2014, 18:20
... a complex function h(k
1
,k
2
) defined over the two-dimensional grid
0 ≤ k
1
≤ N
1
− 1, 0 ≤ k
2
≤ N
2
− 1, we can define its two-dimensional discrete
Fourier transform as a complex function H(n
1
,n
2
), ... REFERENCES AND FURTHER READING:
Nussbaumer, H.J. 1982,
Fast Fourier Transform and Convolution Algorithms
(New York: Springer-
Verlag).
12.5 Fourier Transforms of Real Data in Two
and Three Dimensions
Two-dimensional ... data[], unsigned long nn[], int ndim, int isign)
Replaces
data by its ndim-dimensional discrete Fourier transform, if isign is input as 1.
nn[1 ndim] is an integer array containing the lengths...
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