discrete fourier transform examples and solutions
The Discrete Fourier Transform
Ngày tải lên :
13/09/2012, 09:49
... The Discrete Fourier Transform 145
Type of Transform Example Signal
Fourier Transform
Fourier Series
Discrete Time Fourier Transform
Discrete Fourier Transform
signals that are continious and ... 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 ... continious and periodic
signals that are discrete and aperiodic
signals that are discrete and periodic
FIGURE 8-2
Illustration of the four Fourier transforms. A signal may be continuous or discrete, and...
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mathematics of the discrete fourier transform
Ngày tải lên :
31/03/2014, 15:21
... Warshofsky, and the Editors of Time-Life Books,
Sound and Hearing, Life Science Library, Time-Life Books, Alexandria, VA, 1965, p.
173.
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” ... Matlab to analyze and display signals and their
spectra.
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O.
Smith, CCRMA, Stanford, Winter 2002. The latest draft and linked HTML
version ... random variable v is given by
E{f (v)}
∆
=
∞
−∞
f(x)p
v
(x)dx
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O.
Smith, CCRMA, Stanford, Winter 2002. The latest draft and...
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The discrete fourier transform
Ngày tải lên :
08/06/2014, 20:19
... most important transforms:
continuous time: Laplace, Fourier, Fourier Series,
discrete time: Z, DTFT, DTFS, DFT/FFT
The first six are for pencil and paper analysis/intuition/understanding. The DFT/FFT ... above time domain recipe, or manually compute X[k] and H[k] and multiply, and
then manually compute inverse DFT.
Chapter 5
The Discrete Fourier Transform
Contents
Overview . . . . . . . . . . . ... of
[0, 2π)
with sample locations and values, and around unit circle too.
Questions arise:
• I. How is
X
2π
N
k
N−1
k=0
related to DTFS (both involve unit circle) and to DFT {X[k]}
N−1
k=0
.
•...
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Báo cáo sinh học: " Research Article Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform" potx
Ngày tải lên :
21/06/2014, 16:20
... “The discrete
fractional Fourier transform, ” IEEE Transactions on Signal
Processing, vol. 48, no. 5, pp. 1329–1337, 2000.
[7] S C. Pei, W L. Hsue, and J J. Ding, Discrete fractional
Fourier transform ... and T. S. Santhanam, Discrete Gauss-Hermite
functions and eigenvectors of the centered discrete Fourier
transform, ” in Proceedings of the IEEE International Conference
on Acoustics, Speech and ... Article
Eigenvectors of the Discrete Fourier Transform Based on
the Bilinear Transform
Ahmet Serbes and Lutfiye Durak-Ata (EURASIP Member)
Department of Electronics and Communications Engineering,...
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báo cáo hóa học:" Discrete fourier transform-based TOA estimation in UWB systems" potx
Ngày tải lên :
21/06/2014, 17:20
... CRLB of f
0
and f
k
).
In Figure 4, we show the local baseband and passband
CRLBs (
c
bb
k
, c
pb
k
), and the MSEs of the local baseband
and passband TOA estimators (
∈
2
˜τ
bb
k
and
∈
2
˜τ
pb
k
) ... s
pb
(−ς)}
where s
pb
(t)andr
pb
(t) denote the real passband trans-
mitted and received signals and ⊗ the convolution
operator.
In Figure 5, we show the b aseband and passband
CRLBs (c
bb
and c
pb
)ofτ,theMSEs(
∈
2
˜τ
bb
k
and
∈
2
˜τ
pb
k
)of
the ... minimum-variance
Figure 4 Local baseband and passband CRLBs (
c
bb
k
, c
pb
k
), and
MSEs (
∈
2
˜τ
bb
k
and
∈
2
˜τ
pb
k
) of the local baseband and passband
TOA estimators versus f
k
+ f
c
.
Mallat...
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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
... 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 ... Add the command file exp7.cmd, the
functions epx7a.c, fft_a.c,andibit_rev.c, and the header file
icomplex.h from the software package into the project.
340
FAST FOURIER TRANSFORM AND ITS APPLICATIONS
Table ... ifft(x,N);
The characteristics and usage of ifft are the same as those for fft.
FAST FOURIER TRANSFORMS
321
[2] N. Ahmed and T. Natarajan, Discrete- Time Signals and Systems, Englewood Cliffs,...
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Báo cáo khoa học: Determination of thioxylo-oligosaccharide binding to family 11 xylanases using electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry and X-ray crystallography pot
Ngày tải lên :
07/03/2014, 17:20
... I
PL
3
Þ
ð4Þ
in which I
P
and I
PLn
are the intensities of a free pro-
tein and different protein–ligand complexes summed
over the charge states and the isotopic distributions.
The free ligand concentration ... Jackson GS (1998)
Fourier transform ion cyclotron resonance mass spec-
trometry: a primer. Mass Spectrom Rev 17, 1–35.
56 Smith RD (2000) Evolution of ESI-mass spectrometry
and Fourier transform ion ... Ward DG & Trayer IP
(2002) Calcium and peptide binding to folded and
unfolded conformations of cardiac troponin C. Electro-
spray ionization and Fourier transform ion cyclotron
resonance mass...
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Comparison between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation
Ngày tải lên :
26/03/2014, 00:29
... case)
For the best estimate, and f
2
0 f
1
Å 0.070 Hz, the
5. THE FOURIER TRANSFORM ESTIMATOR
lower limit is between 5 and 6 dB, as is shown in
Fig. 13.
Figures 14 and 15 have been extracted from ... Matrix Pencil Method
and the Fourier Transform Technique for
High-Resolution Spectral Estimation
Jose
´
Enrique Ferna
´
ndez del Rı
B
o and Tapan K. Sarkar*
Department of Electrical and Computer Engineering, ... The Discrete
that the Standard window offers less bias than the TFBMPM for
Time Fourier Transform (DTFT) was used to obtain H( f ).
SNR below 10 dB, its rmse performance is worse because the
Standard...
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báo cáo hóa học:" Fourier-transform infrared anisotropy in cross and parallel sections of tendon and articular cartilage" pptx
Ngày tải lên :
20/06/2014, 01:20
... Surgery and
Research
Open Access
Research article
Fourier- transform infrared anisotropy in cross and parallel sections
of tendon and articular cartilage
Nagarajan Ramakrishnan, Yang Xia* and Aruna ... TB: Amide I band of IR
spectrum and structure of collagen and related peptides.
Biopol 1985, 24:1449-1478.
16. Potter K, Kidder LH, Levin IW, Lewis EN, Spencer RG: Imaging of
collagen and proteoglycan ... amide I (a) and amide II (b) of tendon in the regular, parallel and cross sectionsFigure 3
Absorption anisotropy of amide I (a) and amide II (b) of tendon in the regular, parallel and cross sections.
Journal...
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Fourier Transform Properties
Ngày tải lên :
13/09/2012, 09:49
... 6
MHz band for display on the screen. This scheme is called frequency
domain multiplexing.
The Discrete Time Fourier Transform
The Discrete Time Fourier Transform (DTFT) is the member of the Fourier
transform ... the Fourier Transform
The Fourier Transform is linear, that is, it possesses the properties of
homogeneity and additivity. This is true for all four members of the Fourier
transform family (Fourier ... sine and cosine waves
making up that waveform must also change by an equal amount.
In mathematical form, if and are a Fourier Transform pair, then x[ ] X[ ] kx[ ]
and are also a Fourier Transform...
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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 ... 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, with the
error being...
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The Fast Fourier Transform
Ngày tải lên :
13/09/2012, 09:50
... Fast Fourier Transform in BASIC.
1000 'THE FAST FOURIER TRANSFORM
1010 'Upon entry, N% contains the number of points in the DFT, REX[ ] and
1020 'IMX[ ] contain the real and imaginary ... The Fast Fourier Transform 233
5000 'COMPLEX DFT BY CORRELATION
5010 'Upon entry, N% contains the number of points in the DFT, and
5020 'XR[ ] and XI[ ] contain the real and imaginary ... 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...
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The Complex Fourier Transform
Ngày tải lên :
13/09/2012, 10:20
... types of Fourier transforms: the
Discrete Fourier Transform (discrete, periodic), the Discrete Time
Fourier Transform (discrete, aperiodic), the Fourier Series (continuous,
periodic), and the Fourier ... 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 ... several ways that the real
Fourier transform is awkward. When the complex Fourier transform was
introduced, the problems vanished. Wonderful, we said, the complex Fourier
transform has solved the...
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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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STRUCTURES,EXAMPLES AND EXERCISES.doc
Ngày tải lên :
14/06/2013, 01:25
... your hands before meals. .
7. Would you like (saw – to see – seeing – see) a movie?
8. What about (have – to have – having – had) fruits?
9. You ought (wash – to wash – washing – washed) your hands ... Complete the form of the verbs in parentheses:
1. They want (buy) some meat.
2. You must (wash) your hands before meals.
3. I am used to (stay) up late.
4. It takes him 2 hours (finish) this exercise.
5. ... used
4. Peter is too young to see the horror film.
→ Peter is not
5. I do this exercise in three and a half hours.
→ It takes
6. To see that film is interesting.
→ It’s interesting.
7. The...
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