discrete fourier transform example mathematica
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 ... there.
The mathematical term: transform, is extensively used in Digital Signal
Processing, such as: Fourier transform, Laplace transform, Z transform,
Hilbert transform, Discrete Cosine transform, ... ]
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...
- 28
- 677
- 0
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 ... 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, ... 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...
- 24
- 477
- 0
Fourier Transform Pairs
Ngày tải lên :
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 ... one domain is discrete, the other domain must
be periodic, and vice versa. This holds for all four members of the Fourier
transform family. Since the DFT views both domains as discrete, it must ... real part of the
209
CHAPTER
11
Fourier Transform Pairs
For every time domain waveform there is a corresponding frequency domain waveform, and vice
versa. For example, a rectangular pulse in...
- 16
- 495
- 1
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 ... synthesized into a single frequency
spectrum.
Figure 12-2 shows an example of the time domain decomposition used in the
FFT. In this example, a 16 point signal is decomposed through four
The Scientist...
- 18
- 555
- 1
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 ... complex Fourier transform was
introduced, the problems vanished. Wonderful, we said, the complex Fourier
transform has solved the difficulties.
While this is true, it does not give the complex Fourier...
- 14
- 651
- 0
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...
- 11
- 1.5K
- 5
Real-Time Digital Signal Processing - Chapter 7: Fast Fourier Transform and Its Applications
Ngày tải lên :
28/10/2013, 05:15
... Circular 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 ... 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 ... increment
f
s
=N, and is sometimes referred to as the bin spacing of the DFT outputs. The spacing
DISCRETE FOURIER TRANSFORM
307
± Segment the input sequence of length M with L À 1zeros padded at the end.
±...
- 47
- 634
- 0
Tài liệu Table of Fourier Transform Pairs ppt
Ngày tải lên :
13/12/2013, 12:15
... )(
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 & Systems - Reference Tables
4
Some Useful Mathematical Relationships
2
)cos(
jxjx
ee
x
-
+
=
j
ee
x
jxjx
2
)sin(
-
-
=
)sin()sin()cos()cos()cos( ... 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
...
- 5
- 453
- 0
Tài liệu Fast Fourier Transform part 1 doc
Ngày tải lên :
21/01/2014, 18:20
... This result shows that multiplyingthe Fourier transform
of one function by the complex conjugate of the Fourier transform of the other gives
the Fourier transform of their correlation. The correlation ... a simple transform pair
g ∗ h ⇐⇒ G ( f ) H ( f ) “ConvolutionTheorem” (12.0.9)
In other words, the Fourier transform of the convolution is just the product of the
individual Fourier transforms.
The ... North America).
Chapter 12. Fast Fourier Transform
12.0 Introduction
A very large class of important computational problems falls under the general
rubric of Fourier transform methods” or “spectral...
- 5
- 305
- 0
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 ... equation (12.1.6) is called the discrete Fourier transform of the N
points h
k
. Let us denote it by H
n
,
H
n
≡
N−1
k=0
h
k
e
2πikn/N
(12.1.7)
The discrete Fourier transform maps N complex numbers...
- 5
- 292
- 0
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 ... in these
transforms, and the fact that the Winograd transform cannot be done “in place.”
Finally, an interesting class of transforms for doing convolutions quickly are
number theoretic transforms. ... 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...
- 7
- 387
- 0
Tài liệu Fast Fourier Transform part 4 pdf
Ngày tải lên :
21/01/2014, 18:20
... 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, the real
and ... 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 ... stepsanalogous
to those leading up to equation (12.3.11), you will find that the Fourier transform is
520
Chapter 12. Fast Fourier Transform
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
- 12
- 414
- 0
Tài liệu Fast Fourier Transform part 5 pptx
Ngày tải lên :
21/01/2014, 18:20
... 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 ... rows. If
isign is input as −1, data is replaced by its inverse
transform times the product of the lengths of all dimensions.
12.5 Fourier Transforms of Real Data in Two and Three Dimensions
525
Sample...
- 5
- 309
- 0
Tài liệu Fast Fourier Transform part 6 pdf
Ngày tải lên :
21/01/2014, 18:20
... 1974,
The Fast Fourier Transform
(Englewood Cliffs, NJ: Prentice-Hall).
Swartztrauber, P. N. 1986,
Mathematics of Computation
, vol. 47, pp. 323–346.
530
Chapter 12. Fast Fourier Transform
Sample ... 6f
2
/f
2
c
, 0). The second program example illustrates a three-dimensional
transform, where the three dimensions have different lengths. The third program
example is an example of convolution, as it ... 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...
- 8
- 260
- 0