series fourier transforms and the dft

... grass The spectrum is positive random numbers smoothed random Smoothed random numbers are much the same as random numbers, but their spectral bandwidth is limited 1.4.4... standard” FT programs dft- even ... 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 ... both and at uniform locations around the unit circle, i.e., compute Fourier sums and from and Then we would form for all , and. .. a triangle dft- box2triangle [NR] Because of the fast

Ngày tải lên: 17/12/2013, 06:15

... grass The spectrum is positive random numbers smoothed random Smoothed random numbers are much the same as random numbers, but their spectral bandwidth is limited 1.4.4... standard” FT programs dft- even ... 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 ... both and at uniform locations around the unit circle, i.e., compute Fourier sums and from and Then we would form for all , and. .. a triangle dft- box2triangle [NR] Because of the fast

Ngày tải lên: 22/12/2013, 21:17

... is the case for the Fourier transform Therefore, if the objects in integral equations are real-valued, then the use of the constructed convolutions and the Hartley transform brings about the ... v + h) − sin x(u − v − h) Then, similarly to the proof of Theorem 2.1, we can prove the following theorem Theorem 2.2 If f, g ∈ L1 (Rd ), then each of the integral transforms (2.5), (2.6), (2.7), ... for Fourier, Fourier cosine and sine transforms Vietnam J Math 33 (2005), No 4, 421-436 [24] N X Thao and N M Khoa, On the generalized convolution with a weight function for the Fourier sine and

Ngày tải lên: 15/12/2017, 12:37

... 0 degrees and similarly on the other side—in other words, the pattern has reflection symmetry about the line of the array. Thus, if a main lobe is produced at angle ␪ 0 degrees, then there will ... appropriate phase slope across the aperture to steer the beam (i.e., offset it in the angle domain). If, on the other hand, we offset the array in the aperture domain, so that the distribution is given ... reflection of the pattern about these directions. If the patterns in u -space and angle space are g u and g ␪ , then the gain in direction ␪ is given by g ␪ ( ␪ ) = g u (sin ␪ ). 166 Fourier Transforms

Ngày tải lên: 18/06/2014, 10:05

... However, there is the complication to be taken into account that the ‘‘angle’’ coordinate in this case is not the physical angle but the direction cosine along the line of the aperture. In the text ... define the limits of performance, and if practical equipment is achieving results close to the limit, it is clear that little improvement is possible and need not be sought; on the other hand, if the ... illustrating the effect of steering. In Figure 7.11(a, b) the 40-degree beam is steered to 10 degrees, and again we see the rapid deterioration of the approximate repetitions in u space of the beam, and

Ngày tải lên: 18/06/2014, 10:05

... nX ), then the transform is V ( y) = ∑ ∞ n =−∞ u(nX ) exp (−2 ␲ inXy) 32 Fourier Transforms in Radar and Signal Processing This is in the form of a Fourier series, with period 1/X = Y, and the ... 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

Ngày tải lên: 18/06/2014, 15:20

... fact, the 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 ... include the spectrum of u , the Hilbert transform of u and in Section... 0 + 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 ... of the smoothed pulse is that of the spectrum of the original pulse multiplied by one of these spectra. Assuming the smoothing impulse response is fairly short compared with the pulse length, the

Ngày tải lên: 18/06/2014, 15:20

... rate and then explore the gains possible with an oversampled waveform In Section 5.3, we find the weights that give the optimum series in the sense of the least 89 90 Fourier Transforms ... (4.22) and the delay (which is close to a quarter cycle of f 0 ) is given in (4.23). The samples are complex, the real parts are the samples of u, and the imaginary parts are the samples of the ... 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 0 = W /2 and the sampling rate F is the minimum

Ngày tải lên: 18/06/2014, 15:20

... 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 ... levels), and because the fractional delays are distributed over the full range, the results are much the same and intermediate between the extreme cases. These are also the same results as for bandwidths ... between the weights and the patterns, as shown in Sections 7.2 and 7.3 In this chapter we consider only the narrowband case, where the bandwidth is small enough... bandwidth increases the

Ngày tải lên: 18/06/2014, 15:20

... 0 degrees and similarly on the other side—in other words, the pattern has reflection symmetry about the line of the array. Thus, if a main lobe is produced at angle ␪ 0 degrees, then there will ... appropriate phase slope across the aperture to steer the beam (i.e., offset it in the angle domain). If, on the other hand, we offset the array in the aperture domain, so that the distribution is given ... reflection of the pattern about these directions. If the patterns in u -space and angle space are g u and g ␪ , then the gain in direction ␪ is given by g ␪ ( ␪ ) = g u (sin ␪ ). 166 Fourier Transforms

Ngày tải lên: 18/06/2014, 15:20

... 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...

Ngày tải lên: 27/01/2014, 03:20

... 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...

Ngày tải lên: 06/08/2014, 05:20

... 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...

Ngày tải lên: 06/03/2014, 09:22

... (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...

Ngày tải lên: 15/03/2014, 14:20

... (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...

Ngày tải lên: 22/03/2014, 23:20

... 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...

Ngày tải lên: 22/03/2014, 23:20

... 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...

Ngày tải lên: 26/03/2014, 00:29

... 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...

Ngày tải lên: 29/03/2014, 13:20

... 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...

Ngày tải lên: 29/03/2014, 13:20

... 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...

Ngày tải lên: 01/06/2014, 12:02