the discrete fourier transform pdf

... have been introduced, such as the wavelet transform, the Wigner-Ville distribution, the Radon-Wigner transform, and the Fractional Fourier transform Fractional Fourier transform, as a new time-frequency ... features as the baseline The features based on the FrFT are computed with the same processing used for the MFCCs, but substituting the Fourier transform by the FrFT (we will refer to them as FrFT-MFCC) ... which is called the order of the FrFT, α = pπ/2 is the transform angle, F p [·] denotes the FrFT operator, and Kα (t, u) is the kernel of the FrFT: 4.1 Multiple of Pitch Rate Since the chirp rates

Ngày tải lên: 21/06/2014, 20:20

... Approach to Linear Transform Approximations with Applications to the Discrete Cosine Transform Yinpeng Chen and Hari Sundaram The Katherine K Herberger College of the Arts and the Ira A Fulton ... compared to the baseline, exact DCT transform The speedup is just the ratio of the number of operations needed for the exact 2D DCT (544 operations) to the number of operations needed for the approximation ... approximate transform for input set (e.g., DCT approximation for entire image) The computational complexity of the exact transform set T and the computation complexity of the approximate transform

Ngày tải lên: 21/06/2014, 22:20

... The accuracy of the DRT is determined by Θ (the number of angles), β (the number of beams per angle), and the accuracy of the interpolation method Note that the continuous form of the Radon transform ... implemented In the first stage, the classifier combines the decision results of the neural networks and the Euclidean distance obtained using the three feature sets The results of the first stage ... to the other nonzero components before the decimated vector is shrunk or expanded Since the dimension of the feature vectors are high compared to the number of these additional components, the

Ngày tải lên: 23/06/2014, 01:20

... as the number of users increases The effect of receive diversity is shown in Fig 5.5 As the number of receive antennas increases in the base station, there exist more independent replicas of the ... no error floor exist for the proposed MMSE scheme (in contrast to the MRRC solution) The error floor is caused by the presence MAI in the system and it increases as the number users increases ... where x By defining the transformation matrix B = [INr c jINr c ] ∈ CNr c×2Nr c , where j = √ −1 and simplifying the expression of [Re(¯ xm )T Im(¯ xm )T ]T as shown in (5.19) then the received signal

Ngày tải lên: 10/11/2015, 11:00

... frequency In the classical sense, if we consider a signal to be represented along the time axis and its ordinary Fourier transform to be represented along the frequency axis, then the Fourier transform ... applicable to both theoretical and practical problems as they may be viewed as extensions of the convolution theorem of the Fourier transform Namely, a convolution transform, mathematically, is ... for the Fractional Fourier Transform À Á F a f L1 ðRÞ, we deduce that F a f =A L1 ðRÞ We can now apply the inverse transform of F a to (4.2) to obtain the solution as stated in the theorem The

Ngày tải lên: 12/12/2017, 06:52

... flexibility The thesis provides VLSI architechtures for Discrete Wavelet transform (DWT) These architechtures represente Mallat’s pyramid algorithm for the Wavelet Haar By implementing of the wavelet ... VLSI ARCHITECTURES FOR THE DISCRETE WAVELET TRANSFORM GVHD : TS LÊ TIẾN THƯỜNG HVTH : TRƯƠNG QUANG VINH TP HCM Tháng 07 năm 2002 Lời Cảm Ơn Luận án tốt nghiệp bước ngoăïc then chốt quan trọng học ... based structures with Field Programmable Gate Arrays (FPGA) using Hardware Describe Language (HDL), the report will show a powerful tool to develop hardware for digital signal processings (DSPs) TÓM

Ngày tải lên: 16/04/2021, 04:24

... Regarding the 3D wavelet transform, Kutil and Uhl have conducted a study of the software and hardware needs of the 3D wavelet transform [14]. They have centered their study on the classic wavelet transform ... They have not, however, considered the use of the GOF concept in order to minimize the memory requirements when computing the 3D-WT. In a recent study they have focused on the time taken by the ... N ×N gives the size of the frames in pixels while the third parameter indicates the step number for the different levels of decomposition for the 3D- WT. For the sake of clarity, in the figures,

Ngày tải lên: 22/06/2014, 19:20

... part calculates the Fourier transform of the odd index numbers and then finally merges them to get the Fourier transform for the whole sequence This will reduce the overall time ... N/2 The DFT is defined by the formula [21] Radix-2 divides the DFT into two equal parts The first part calculates the Fourier transform of the even index numbers The other ... DCT, FFT and the MPI library It also talks about the implementation... 10240 2.1 Fastest Fourier Transform in the West (FFTW) The Fastest Fourier Transform in the West package

Ngày tải lên: 30/10/2014, 20:11

... operator T as the usual convolution has for T the Fourier transform (T f )(T g) = T (f ∗ g) On Integral Operators Generated by the Fourier Transform and a Reflection 29 Theorem 3.12 For the operator ... Generated by the Fourier Transform and a Reflection Introduction In several types of mathematical applications it is useful to apply more than once the Fourier transformation (or its inverse) to the same ... is not under the conditions we have here imposed to this operator Figure The spectrum of the operator T for different values of the parameters a and b Theorem 3.3 The spectrum of the operator

Ngày tải lên: 16/12/2017, 01:03

... theorem which states that: If f (x) and g (x) are two functions with Fourier transforms F (u) and G (u), then the Fourier transform of the convolution f (x) ∗ g (x) is simply the product of the ... filter G=H.*F; Where F was the Fourier transform of the image, H the filter CM3106 Chapter Filtering in the Frequency Domain 102 Computing Convolutions with the Fourier Transform Example Applications: ... image, Take the Fourier transform of the function describing the effect of the system, Multiply by the effect to apply effect to audio data To remove/compensate for effect: Divide by the effect

Ngày tải lên: 12/02/2020, 14:09

... window, the smaller the width of the time domain window, the better the performance of the parent wavelet in time domain analysis Similarly, the smaller the width of the frequency domain window, the ... analysis The wavelet transform obtains the time information of the signal by translating the parent wavelet The frequency characteristics of the signal are obtained by scaling the width of the parent ... transformation than the discrete counterpart [52, 53] The major reason is that the Discrete Wavelet Transform (DWT) has a downsampling step which discards information in the process Because the

Ngày tải lên: 25/11/2020, 15:44

... DISSERTATION ON A PALEY-WIENER THEOREM FOR THE ZS-AKNS SCATTERING TRANSFORM In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on the set of real potentials ... by the end of this r− (z) ∈ K chapter we will also have established the main result of this thesis, the Nonlinear Paley-Wiener Theorem 1.1.1 for the ZS-AKNS scattering transforms Our proof of Theorem ... Scattering and the Nonlinear Paley-Wiener theorem 3.1 Overview In this chapter, we prove the inverse part of Theorem 1.2.1: cα then w ∈ Kα Theorem 3.1.1 If r− = DP− w ∈ K We will again appeal to the symmetry

Ngày tải lên: 24/07/2023, 00:55

... 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, that is, it possesses the properties ... Fourier Transform The Discrete Time Fourier Transform (DTFT) is the member of the Fourier transform family that operates on aperiodic, discrete signals The best way to understand the DTFT is how ... compression of the signal in one domain results in an expansion in the other, and vice versa For continuous signals, if X (f ) is the Fourier Transform of x( t) , then 1/k × X( f/ k) is the Fourier Transform

Ngày tải lên: 13/09/2012, 09:49

... at the discontinuity the value of the reconstructed signal converges to the midpoint of the step As shown by Gibbs, the summation converges to the signal in the sense that the error between the ... making one-half of the pulse on the right of the graph and the other one-half on the left This appears to the DFT as a single pulse because of the time domain periodicity The DFT of this signal ... is the same as multiplying the longer signal by a rectangular pulse The ones in the rectangular pulse retain the corresponding samples, while the zeros eliminate them How does this affect the

Ngày tải lên: 13/09/2012, 09:49

... sequence into the frequency-domain representation using the z-transform, the discrete-time Fourier transform (DTFT), or the discrete Fourier transform (DFT) The widespread application of the DFT to ... identical to the DFT with the exception of the normalizing factor 1/N and the sign of the exponent of the twiddle factors The IDFT shows that there is no loss of information by transforming the spectrum ... TRANSFORM AND ITS APPLICATIONS The inverse discrete Fourier transform (IDFT) is used to transform the X(k) back into the original sequence x(n) Given the frequency samples X(k), the IDFT is defined as

Ngày tải lên: 28/10/2013, 05:15

... fish and shrimp in the brackish waters of the Mekong Delta The development of aquaculture in the Mekong Basin has been uneven though Most aquaculture production takes place in the Mekong Delta ... www.mrcmekong.org Acknowledgements The material presented here was initially gathered for the MRC Fisheries Sector Review, and subsequently edited into this MRC Technical Paper The paper is based on contributions ... working in the Mekong basin A meeting of some of these experts, hosted by NACA in Bangkok in May 2001, prepared a first draft that was developed through further consultation, including during the NACA/ACIAR

Ngày tải lên: 10/12/2013, 03:15

... 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...

Ngày tải lên: 13/09/2012, 09:49

... 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...

Ngày tải lên: 31/03/2014, 15:21

... 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...

Ngày tải lên: 08/06/2014, 20:19