series fourier transforms and the dft

Tài liệu 01 Fourier Series, Fourier Transforms, and the DFT doc

... Fourier Series, Fourier Transforms, and the DFT 1.1 1.2 Introduction Fourier Series Representation of Continuous Time Periodic Signals Exponential Fourier Series • The Trigonometric Fourier Series ... Trigonometric Fourier Series Although Fourier series expansions exist for complex periodic signals, and Fourier theory can be generalized to the case of complex signals, the theory and results ... discussion with the classical Fourier series representation of a periodic time domain signal, and then derive the Fourier integral from this representation by ﬁnding the limit of the Fourier coefﬁcient...

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Tài liệu Mathematics - Fourier Transforms and Waves pptx

Danh mục: Cơ khí - Chế tạo máy

... on the letter to denote the axis being Fourier transformed So is the angular spatial frequency on the -axis and is its Fourier kernel For each axis and Fourier kernel there is the question of the ... corkscrew, where the real and imaginary parts are plotted on the - and -axes, and time runs down the axis of the screw The complex conjugate of this signal reverses the -axis and gives the screw an ... (counterclockwise), and to rotation in the other direction To see why, suppose and Then The Fourier transform is (1.34) The integrand oscillates and averages out to zero, except for the frequency...

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Tài liệu Mathematics - Fourier Transforms and Waves pdf

Danh mục: Cơ khí - Chế tạo máy

... on the letter to denote the axis being Fourier transformed So is the angular spatial frequency on the -axis and is its Fourier kernel For each axis and Fourier kernel there is the question of the ... corkscrew, where the real and imaginary parts are plotted on the - and -axes, and time runs down the axis of the screw The complex conjugate of this signal reverses the -axis and gives the screw an ... (counterclockwise), and to rotation in the other direction To see why, suppose and Then The Fourier transform is (1.34) The integrand oscillates and averages out to zero, except for the frequency...

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Báo cáo toán học: "On the Generalized Convolution with a Weight - Function for Fourier, Fourier Cosine and Sine Transforms" pot

Danh mục: Báo cáo khoa học

... for the Fourier, Fourier Cosine and Sine Transforms Deﬁnition Genneralized convolution with the weight-function γ(y) = sign y for the Fourier, Fourier cosine and sine transforms of functions f and ... γ(y) = sign y for the Fourier, Fourier cosine and sine transforms of functions f and g has a meaning and belongs to L(R) and the factorization property holds Nguyen Xuan Thao and Nguyen Minh Khoa ... (22) The equalities (21) and (22) yield (20) The proof is complete Theorem In the space of functions belonging to L(R+ ) the generalized convolution (11) is not associative and satisﬁes the following...

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OccasiOnal Pa Per series nO 109 / a Pril 2010: EURO area Fiscal POlicies and The crisis pot

Danh mục: Ngân hàng - Tín dụng

... the stability of the euro area and, therefore, not least for the monetary policy of the European Central Bank Jürgen Stark Member of the Executive Board and the Governing Council of the ECB There ... processes and their economic impact adjusts automatically to the cycle Given the size of the public sector, their stabilising impact on the economy is relatively large in the euro area Girouard and André ... GDP), while the other half represents largely the loosening of the fiscal stance and to a minor extent the increase in interest expenditures The fiscal stance reflects the impact of the fiscal stimulus...

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WORKING PAPER SERIES NO. 518 / SEPTEMBER 2005: TERM STRUCTURE AND THE SLUGGISHNESS OF RETAIL BANK INTEREST RATES IN EURO AREA COUNTRIES docx

Danh mục: Ngân hàng - Tín dụng

... (2005), Heinemann and Schüller (2002), Sander and Kleimeier (2004)) We then test the stability of the baseline linear ECM before and after the introduction of the euro and assess whether more general ... what the latter should be for the different retail markets that we cover.1 We then test the stability of the baseline linear ECM before and after the introduction of the euro and assess whether ... except Luxembourg and Greece, and the euro area, and the associated MRS and MRL One should note that from January 1999, the MRS is the three-month EURIBOR for all countries All series have a monthly...

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WORKING PAPER SERIES NO. 518 / SEPTEMBER 2005: TERM STRUCTURE AND THE SLUGGISHNESS OF RETAIL BANK INTEREST RATES IN EURO AREA COUNTRIES pptx

Danh mục: Ngân hàng - Tín dụng

... (2005), Heinemann and Schüller (2002), Sander and Kleimeier (2004)) We then test the stability of the baseline linear ECM before and after the introduction of the euro and assess whether more general ... what the latter should be for the different retail markets that we cover.1 We then test the stability of the baseline linear ECM before and after the introduction of the euro and assess whether ... except Luxembourg and Greece, and the euro area, and the associated MRS and MRL One should note that from January 1999, the MRS is the three-month EURIBOR for all countries All series have a monthly...

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WORKING PAPER SERIES NO. 546 / NOVEMBER 2005: THE NATURAL REAL INTEREST RATE AND THE OUTPUT GAP IN THE EURO AREA A JOINT ESTIMATION doc

Danh mục: Ngân hàng - Tín dụng

... stronger in the euro area compared to the US and Germany The null hypothesis that the coecients of the ination terms, b (L), sum to one in the Phillips curve is not rejected by the data 12 The BFGS ... output yt , the output gap yt , the actual and the natural real rate and the real rate gap (rt , rt and rt ) and ination t A notable feature of the reported statistics is that the correlation ... interest rate gap on the output gap, ar , seems to be somewhat weeker in the euro area than in the US and Germany The eect of a change in the output gap on ination, on the other hand, seems to be...

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Comparison between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation

Danh mục: Điện - Điện tử

... because the Standard window reduces the 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 ... Comparison between the inverse of the variance and the CRB for the ﬁrst DOA estimate f2 f1 Å 0.090 Hz and SNR Å 17 dB The TFBMPM reaches the CRB for all u1 u2 because the SNR is above the threshold ... below 10 dB the FTE with the Standard window offers less bias than the TFBMPM Nevertheless, the rmse obtained with the TFBMPM is less than the one computed using the Standard window as seen in...

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Working PaPer SerieS no 967 / november 2008: Central bank miSPerCePtions and the role of money in interest rate rules pptx

Danh mục: Ngân hàng - Tín dụng

... inflation and inflation target Standard deviation of cost-push, demand and money demand shocks Standard deviation of noise of aggregate demand and cost-push shocks Standard deviation of money demand ... rate, π, and the filtered measure of adjusted money growth, μf , for the case that the central bank sticks to the original estimate of the intercept, γ0 , in the money demand equation and never ... never considers the possibility of a structural shift The lower three panels plot the same series for the case that the central bank recursively estimates money demand and considers the possibility...

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Fiscal Dominance and the Long-Term Interest Rate: FINANCIAL MARKETS GROUP SPECIAL PAPER SERIES doc

Danh mục: Ngân hàng - Tín dụng

... rose This rise in the volatility of interest rates served to further reduce the demand for bonds and thus magnify the rise in the interest rate Because the banks were all using the same historical ... statements in The General Theory and other works by Keynes in which he criticised an exclusive focus on the short-term rate in the money market and urged the much greater importance of the long-term ... buy and sell is controversial and has in practice changed radically over time (i) Separate mandates for the central bank and the DMO There are problems with giving central banks the dual mandate...

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tcl and the tk toolkit (addison-wesley professional computing series)

Danh mục: Đại cương

... If the command is deﬁned then the Tcl interpreter invokes its command procedure, passing all of the words of the command to the command procedure The command procedure is free to interpret the ... computing the sizes and locations of widgets and making them appear on the screen The pack command in the example asks a geometry manager called the packer to manage b The command asks that b ﬁll the ... command will delete the existing button and the second command will recreate the button with the new -command option Now when you click on the button the puts command will print a message on standard...

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qos in packet networks the springer international series in engineering and computer science

Danh mục: Đại cương

... are the normal or Gaussian distribution and the Poisson distribution The normal random variable x is a continuous random variable with the following pdf: where is the mean of x and is the standard ... shift the original n random variable to the left in time by the same amount and consider the resulting n random variables: Figure 2-5 shows the original n RV’s and the n shifted RV’s To satisfy the ... pairs of time points and the random variables defined for those four time points: The distances between and and between and are and respectively If the pdf’s of the two pairs of random variables are...

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Fourier Transforms in Radar And Signal Processing_2 pdf

Danh mục: Kỹ thuật lập trình

... equal to half the width at the first zeros [ ±1 in the basic function and ± F in the scaled version of Figure 2.2(b)], the 3-dB width is 0.886, and the first side-lobe peak is at the rather high ... −∞ and ∞ U( y) = ͵ −∞ U is the Fourier transform of u , and u is the inverse Fourier transform of U We have used a general pair of variables, x and y , for the two transform domains, but in the ... being the operation in the transform domain corresponding to multiplication in the original domain (and vice versa) This is followed by the rules relating to Fourier transforms and a set of Fourier...

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Fourier Transforms in Radar And Signal Processing_3 pot

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... relative levels of the waveforms and spectra The rise and fall times of the edges are ␶ and the pulse is of width T at the half amplitude points The spectrum (from R7b, P3a, and R5) is U ( f ) ... exercise in the use of the rules -and- pairs method, showing that the method gives a solution for the spectrum quite 39 40 Fourier Transforms in Radar and Signal Processing easily and concisely ... Lighthill [2], particularly for the derivations of the transform of the ␦ -function, P1a, the transform of the signum function used in obtaining P2a, and the comb and rep transforms Figure 2B.1 Contour...

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Fourier Transforms in Radar And Signal Processing_4 ppt

Danh mục: Kỹ thuật lập trình

... wideband (or baseband) sampling theorem and the Hilbert sampling theorem for narrowband (or RF and IF) waveforms are obtained here following the derivations of Woodward [1] Two other narrowband ... W /2 = kW for k integral The lower edge of the band is then at (k − 1)W The spectrum can now be 70 Fourier Transforms in Radar and Signal Processing Figure 4.3 Narrowband spectrum repeated at ... twice the maximum frequency (i.e., at 2f + W here), as in the case of a wideband waveform, but at approximately twice the bandwidth We initially restrict W so that the upper edge of the signal band...

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Fourier Transforms in Radar And Signal Processing_5 doc

Danh mục: Kỹ thuật lập trình

... find the weights that give the optimum series in the sense of the least 89 90 Fourier Transforms in Radar and Signal Processing mean square error (or error in power) between the interpolated series ... all the weights were zero except the first, w −n , then the relative delay of the output series would be −nT.) We take the time series to be that of a complex baseband waveform of finite bandwidth ... − nT ) (4.25) and we see that we multiply the samples of u by the sampled form of the complex exponential In the case where the IF carrier is f = W /2 and the sampling rate F is the minimum 2W,...

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Fourier Transforms in Radar And Signal Processing_6 ppt

Danh mục: Kỹ thuật lập trình

... 5.17 for two of these spectral shapes, the rectangular, using (5.37), and the raised cosine, using (5.40) These give the powers as a function of both the number of taps used and the oversampling ... this is the filter impulse response.) If F is the bandwidth of the spectrum, then we know, from Chapter 4, that the sampling rate must be F or greater, and so the delays between taps in the FIR ... obtain values for the weights and the residues quite easily In the next section, we use the rules -and- pairs technique to find the autocorrelation function for six spectral shapes, and in Section...

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Fourier Transforms in Radar And Signal Processing_7 docx

Danh mục: Kỹ thuật lập trình

... the subject of the second approach, which is to define the filter that will minimize the power in the error signal, the difference between the interpolated series and the exact series, for a given ... across the band (rampr ) and the derivatives of the corresponding order of the sinc function (sncr ) The sinc and rect functions are seen to be the first (or zeroth order) members of these sets ... response, and then we perform the Fourier transforms defined in (6.6) and (6.7) to give the components of a and B, followed by some simple matrix processing The derivation of a and B in the case of...

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Fourier Transforms in Radar And Signal Processing_8 pdf

Danh mục: Kỹ thuật lập trình

... filters, the ripple in the center of the band is quite small (up to 0.25 dB above the fully equalized level), but there is a rather rapid fall in gain at the edges of the band, starting well within the ... aperture in the general array case, the transform is still required in determining the components of the matrix and vector used to obtain the weights The Fourier transform is 161 162 Fourier Transforms ... 1), the results for a fractional bandwidth F /f of r and − r will give the same result The effect of varying the equalization parameters is shown in Figure 6.10 for the 50% bandwidth case and...

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