the discrete fourier transform pdf
The Discrete Fourier Transform
Ngày tải lên :
13/09/2012, 09:49
... on the shape of the waveform being decomposed.
Chapter 8- The Discrete Fourier Transform 145
Type of Transform Example Signal
Fourier Transform
Fourier Series
Discrete Time Fourier Transform
Discrete ... another chunk of data. Let's see how this applies to the topic at
hand: the Discrete Fourier transform.
Notation and Format of the Real DFT
As shown in Fig. 8-3, the discrete Fourier 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 the family...
- 28
- 677
- 0
mathematics of the discrete fourier transform
Ngày tải lên :
31/03/2014, 15:21
... INTRODUCTION TO THE DFT Page 5
Having completely understood the DFT and its inverse mathemati-
cally, we go on to proving various Fourier Theorems, such as the “shift
theorem,” the “convolution theorem,” ... values in
the “obvious way” as integers from 0 to 2
N−1
−1, and then the negative
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O.
Smith, CCRMA, Stanford, Winter 2002. The latest ... travel the farthest and resonate near the helicotrema. The
membrane resonance effectively “shorts out” the signal energy at that
frequency, and it travels no further. Along the basilar membrane there
are...
- 247
- 352
- 0
The discrete fourier transform
Ngày tải lên :
08/06/2014, 20:19
... ω
0
=
2π
N
k
0
, then the sinc is sampled only at the peak and the nulls, which gives the Dirac impulse form above.
Otherwise the sinc is sampled at many nonzero values, which gives the messy form ... computer since there is just a finite sum. Fortunately, we can implement
the sums cleverly using the fast -Fourier transform (FFT), as discussed in Ch. 6.
Although the ranges of the indices only ... manually, one can either use the 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...
- 31
- 320
- 0
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
... eigenvectors of the DFT matrix inspired by
the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the
analog s-domain is mapped to the unit ... advantage of
the bilinear transform, which is a good discrete substitute for
the derivative operator.
The algorithm is straightforward; we substitute the
second derivative and the Fourier transform ... functions
of the discrete Fourier transform, ” IEEE Transactions on
Acoustics, Speech, and Signal Processing, vol. 30, no. 1, pp. 25–
31, 1982.
[13] F. A. Gr
¨
unbaum, The eigenvectors of the discrete Fourier
transform: ...
- 7
- 362
- 0
The Fast Fourier Transform
Ngày tải lên :
13/09/2012, 09:50
... an
Chapter 12- The Fast Fourier Transform 235
TABLE 12-4
The Fast Fourier Transform in BASIC.
1000 &apos ;THE FAST FOURIER TRANSFORM
1010 'Upon entry, N% contains the number of points in the DFT, ... is
placed in the real part of the time domain, and the other signal is placed in the
imaginary part. After calculating the complex DFT (via the FFT, of course),
the spectra are separated using the even/odd ... flipped left-for-right (such as in 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...
- 18
- 555
- 1
The Complex Fourier Transform
Ngày tải lên :
13/09/2012, 10:20
... we
restrict the mathematics to be real numbers, problems arise. In other words,
these problems are not solved by the complex Fourier transform, they are
introduced by the real Fourier transform. In the ... 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) ... Fourier Transforms
A time domain signal can be either continuous or discrete, and it can be either
periodic or aperiodic. This defines four types of Fourier transforms: the
Discrete Fourier Transform...
- 14
- 651
- 0
The Race to Transform pdf
Ngày tải lên :
06/03/2014, 03:20
... in the province, and the impact that these
constructs have in the contemporary struggle for control of provincial cricket.
In this context one of the key questions posed is whether the transformation ... www.hsrcpress.ac.za
32 the race to transform: sport in post-apartheid south africa
task ahead. The , whose deep investment in the success of the process
would not allow them to see talks fail, ...
was there in cricket, Patel was there in rugby – so all the other little
ones, like swimming, we would ask among ourselves, who knows
how to tackle these whiteys in swimming…And then, they’d...
- 280
- 302
- 0
Báo cáo hóa học: " Moving Target Indication via Three-Antenna SAR with Simplified Fractional Fourier Transform" pdf
Ngày tải lên :
20/06/2014, 22:20
... Section VI concludes the whole paper.
2 Simplified Fractional Fourier Transform (FrFT)
The FrFT is a generalizatio n of regular Fourier trans-
form in that the Fourier transform transforms a signal
from ... and
F
α
r
is the fractional Fourier transform operator, then the
FrFT possesses the following important properties.
1) Zero rotation:
F
0
r
= I
rotation:
F
2π
r
= I
.
2) Consistency with Fourier transform:
F
π/2
r
= ... SFrFT.
Therefore, after canceling the stationary clutter, the
identification of moving targets can be implemented
with SFrFT in the following steps:
Step 1. Apply one SFrFT to the data in which the...
- 10
- 380
- 0
báo cáo hóa học:" Discrete fourier transform-based TOA estimation in UWB systems" potx
Ngày tải lên :
21/06/2014, 17:20
... based on the phase difference
between the discrete Fourier transforms (DFT) of the transmitted and received signals. The first estimator is based
on the slope of the unwrapped phase and the second ... are
using the discrete Fourier transform (DFT) of the
received signal [11-17].
In this paper, we propose two es timators for the TOA
based on the phase of the DFT of the received signal.
The first ... based on the slope of the phase
and the second one, on the absolute phase. For both
estimators, we first compute local estimates at the dif-
ferent frequency componen ts, and then we combine
them...
- 9
- 355
- 0
Tài liệu Multimedia Applications of the Wavelet Transform pdf
Ngày tải lên :
19/01/2014, 19:20
... is
nonexistent for the Fourier transform. This is why comparisons between the wavelet transform and
the Fourier transform are usually restricted to the special case of the STFT.
The calculation of the Heisenberg ... fundamentals of the wavelet theory: We discuss the time–frequency resolution
of the wavelet transform and compare it to the common short–time Fourier transform. The multiscale
property of the dyadic ... compression, such as the short–
time Fourier and cosine transforms, the wavelet transform offers the convenience of less complexity.
Furthermore, rather than denoting a specific function, the term wavelet...
- 240
- 472
- 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 imaginary ... equations is that the
derivative of the function is zero at the boundary. In this case the natural transform
is the cosine transform. There are several possible ways of defining the transform.
Each ... real, 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...
- 12
- 414
- 0
Tài liệu Fast Fourier Transform part 6 pdf
Ngày tải lên :
21/01/2014, 18:20
... find the real and imaginary components of the transform at
some particular frequency!)
We will implement the multidimensional real Fourier transform for the three
dimensional case L =3, with the ... returns only the positive half of the frequency
spectrum. Figure 12.5.1 shows the logical storage scheme. The returned portion of
the complex output spectrum is shown as the unshaded part of the lower ... E.O. 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...
- 8
- 260
- 0
Comparison between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation
Ngày tải lên :
26/03/2014, 00:29
... bias but at the
same time increases the variance. On the other
hand, the use of the Rectangular window makes a
FTE biased even for high SNR.
In Fig. 21 the behavior of the estimator as the
number ... than the
TFBMPM. Nevertheless, the rmse obtained with the
TFBMPM is less than the one computed using the
Standard window as seen in Fig. 19. This is because
the Standard window reduces the bias ... the value in
work is based on the classic periodogram. The esti-
Fig. 15.
mates of the frequencies, f
ˆ
m
(m Å 1, , K), will
In Fig. 14 the CRB is reached for all
u
1
0
u
2
be the values of the...
- 18
- 415
- 0
báo cáo hóa học:" Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy" pdf
Ngày tải lên :
20/06/2014, 07:20
... which are the spectr oscopic fingerprints of the tissues, provided
the important differentiating information about the malignant and normal tissues. The findings of this study
demonstrate the possible ... the tumor) samples were collected. All the
samples were of stage II and III. For each case two sam-
ples were cut, one was put on the glass sli de and was
used for histological review. The other ... each spec-
trum and the spectra were ratioed against the back-
ground spectrum. The spectra were normalized after the
baseline correction. Second order derivative of all the
spectra were calculated...
- 6
- 324
- 0
Báo cáo hóa học: " Research Article Multicarrier Communications Based on the Affine Fourier Transform in Doubly-Dispersive Channels" pot
Ngày tải lên :
21/06/2014, 07:20
... without the GI, the AFT-MC
system is significantly better in suppressing the interference
in comparison to the OFDM with the GI. In the AFT-MC
system, the ICI is significantly reduced by the properties
of ... arrive
directly in front of the aircraft and the beamwidth of the
scattered components from the obstacles in the airport is
180
◦
. The maximal speed of the aircraft is 150 m/s, and the
Rician factor K
= ... models the
arrival of the aircraft to the terminal or parking. The LOS
path is blocked, resulting in Rayleigh fading. The maximal
speed of the aircraft is 5.5 m/s, and the DPP can be modeled
as the...
- 10
- 379
- 0