4 analog optical fourier transforms
Tài liệu Mathematics - Fourier Transforms and Waves pptx
Ngày tải lên :
17/12/2013, 06:15
... nonrealizable, fold, 20 Fourier downward continuation, 33 Fourier integral, 10 Fourier sum, 7, 10, 17 Fourier transform, Fourier transform quefrency, 14 radian, 7, 10 random, 14 ray, 29, 30 ray parameter, ... digitizing, dip, 32 double-sided exponential, 14 odd function, 14 envelope, 15 evanescent, 32 even function, 14, 22 exponential, 14 exponential double-sided, 14 Pascal’s triangle, phase velocity, 31 ... Z -TRANSFORMS 1.2 FOURIER SUMS 1.3 FOURIER AND Z-TRANSFORM 1 .4 CORRELATION AND SPECTRA 11 Discrete Fourier...
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Tài liệu Mathematics - Fourier Transforms and Waves pdf
Ngày tải lên :
22/12/2013, 21:17
... nonrealizable, fold, 20 Fourier downward continuation, 33 Fourier integral, 10 Fourier sum, 7, 10, 17 Fourier transform, Fourier transform quefrency, 14 radian, 7, 10 random, 14 ray, 29, 30 ray parameter, ... digitizing, dip, 32 double-sided exponential, 14 odd function, 14 envelope, 15 evanescent, 32 even function, 14, 22 exponential, 14 exponential double-sided, 14 Pascal’s triangle, phase velocity, 31 ... Z -TRANSFORMS 1.2 FOURIER SUMS 1.3 FOURIER AND Z-TRANSFORM 1 .4 CORRELATION AND SPECTRA 11 Discrete Fourier...
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Tài liệu Analog Optical Links Theory and Practice ppt
Ngày tải lên :
25/01/2014, 07:20
... photodetection devices 4. 3.1 PIN photodiode 4. 3.2 Diode laser 4. 3.3 Mach–Zehnder modulator 4. 4 Bode–Fano limit 4. 4.1 Lossy impedance matching 4. 4.2 Lossless impedance matching Appendix 4. 1 Small signal ... Frequency response of links 4. 1 Introduction 4. 2 Frequency response of modulation and photodetection devices 4. 2.1 Diode lasers 4. 2.2 External modulators 4. 2.3 Photodetectors 4. 3 Passive impedance ... 12 17 19 19 20 20 20 34 49 54 63 63 69 69 70 72 74 75 viii Contents 3.3.1 Optical power 3.3.2 Wavelength 3.3.3 Modulation slope efficiency and photodetector responsivity 3 .4 Large signal intrinsic...
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Tài liệu 01 Fourier Series, Fourier Transforms, and the DFT doc
Ngày tải lên :
27/01/2014, 03:20
... ω(n) = 0. 54 − 0 .46 cos(2π n/N ), 0≤n≤N −1 ω(n) = 0 .42 − 0.5 cos(2π n/N ) + 0.08 cos (4 n/N ), ≤ n ≤ N − Mainlobe Width Minimum Stopband Attenuation (dB) −13 4 /N −21 −25 8π/N −25 −31 43 43 8π/N ... Discrete Fourier Transform Properties of the Discrete Fourier Series • Fourier Block Processing in Real-Time Filtering Applications • Fast Fourier Transform Algorithms Family Tree of Fourier Transforms ... product nk can be expressed in either of two ways: nk nk = (4k0 )n2 + (4k1 + 2k0 )n1 + (4k2 + 2k1 + k0 )n0 = (4n0 )k2 + (4n1 + 2n0 )k1 + (4n2 + 2n1 + n0 )k0 (1.25a) (1.25b) Substituting (1.25a) into...
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Fourier transforms in spectroscopy kauppinen j
Ngày tải lên :
17/03/2014, 14:45
... Next, we compute N /2 Fourier transforms of four data using the N Fourier transforms of two data, then the N /4 Fourier transforms of eight data, and so on until we have one Fourier transform of ... 229 229 230 232 233 2 34 236 239 240 242 243 248 250 255 258 Answers to problems 261 Bibliography 265 Index 269 Fourier Transforms in Spectroscopy J Kauppinen, J Partanen ... theorem 13 Applying Fourier transforms, compute the following integrals: ∞ sinc4 x dx, (a) −∞ ∞ exp −π x cos(2π ax) dx, where a is a real constant (b) −∞ ∞ 14 Applying Fourier transforms, compute...
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Chương 4: Biến đổi Fourier cho th liên tục pdf
Ngày tải lên :
01/04/2014, 09:21
... Chương 4: Biến đổi Fourier cho th liên tục Biến đổi Fourier cho th liên tục Những tính chất biến đổi Fourier cho tín hiệu liên tục Hệ thống đặc trưng ptvp hệ số Biến đổi Fourier cho ... đổi Fourier cho th liên tục Co giãn thời gian tần số Những tính chất biến đổi Fourier cho th liên tục Duality Những tính chất biến đổi Fourier cho th liên tục Ví dụ: tìm khai triển fourier ... Khả tích Những tính chất biến đổi Fourier cho th liên tục Tuyến tính Những tính chất biến đổi Fourier cho th liên tục Dịch thời gian Những tính chất biến đổi Fourier cho th liên tục Ví dụ:...
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Fourier Transforms in Radar And Signal Processing_2 pdf
Ngày tải lên :
18/06/2014, 10:05
... indicates complex conjugate (2. 14) , (2.13), Y = 1/X , constant Prime indicates differentiation ͬ 22 Fourier Transforms in Radar and Signal Processing Table 2.2 Fourier Transforms Pairs Pair Function ... relating to Fourier transforms and a set of Fourier transform pairs We then include three illustrations as examples before the main applications in the following chapters 2.2 Notation 2.2.1 Fourier ... p is greater than the repetition interval T Any Figure 2 .4 Step functions: (a) the unit step; (b) a scaled and shifted step 18 Fourier Transforms in Radar and Signal Processing Figure 2.5 The...
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Fourier Transforms in Radar And Signal Processing_3 pot
Ngày tải lên :
18/06/2014, 10:05
... (Figure 3 .4) It is the limiting version of the trapezoidal pulse and is given by u (t ) = (1/ ) rect (t /T ) ⊗ A rect (t /T ) Figure 3.2 Product of sinc functions (3 .4) 42 Fourier Transforms ... 2 iy ͪ |ͬ ∞ iy The Fourier transform of h (x ) is now found to be, using P1b, ͫ 1 ␦( y) + iy ͬ 36 Fourier Transforms in Radar and Signal Processing P2b: From P2a and R4, the transform of ͫ ... ∞ u ′(x ) = ͵ 2 iyU ( y ) exp (2 ixy ) dy −∞ so u ′(x ) is the inverse Fourier transform of 2 iyU ( y ) 34 Fourier Transforms in Radar and Signal Processing R9b: ∞ U( y) = ͵ u (x ) exp (−2...
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Fourier Transforms in Radar And Signal Processing_4 ppt
Ngày tải lên :
18/06/2014, 10:05
... in Section 4. 6 (quadrature sampling) we include a quarter wave delayed form of u The sampling techniques of Sections 4. 4 and 4. 6 are for narrowband waveforms—signals on a carrier 4. 3 Wideband ... equivalent form of (4. 4) is u (t ) = ⌺u (nT ) sinc (t − nT ) (4. 7) and the equivalence of the waveform to its interpolated sampled form is illustrated in Figure 4. 2 It is clear (from Figure 4. 1, for example) ... sampling rates 2W ′ is given by Figure 4. 5 rep2w U ( f ) near +f Figure 4. 6 Selecting U ( f ) 72 Fourier Transforms in Radar and Signal Processing Figure 4. 7 Maximum sampling rate 2f u /k = 2(k...
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Fourier Transforms in Radar And Signal Processing_5 doc
Ngày tải lên :
18/06/2014, 10:05
... + (4. 18) U ( f − 2f ) [1 + exp (4 if )] ( f − W /2 < f < f + W /2) Figure 4. 10 Basic quadrature sampling Sampling Theory 77 This is simply U ( f ), as required, if we choose such that 4f ... sinc (Wt ) cos (2 f t ) (4. 21) This interpolating function also appears in the uniform sampling case [see (4. 9)] and the Hilbert sampling case [see (4. 16)] Equation (4. 19) states that the real ... define the boundaries, and the central values rc are shown as dashed lines in Figure 4. 14 We note from Figure 4. 14 that there are no unallowed sampling rates above 2W This is because when the interval...
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Fourier Transforms in Radar And Signal Processing_6 ppt
Ngày tải lên :
18/06/2014, 10:05
... ( − k )/2q ] sinc [(1 + a ) ( − k )/2q ] (5 .46 a) and b hk = sinc [(1 − a ) (k − h )/2q ] sinc [(1 + a ) (k − h )/2q ] (5 .46 b) 1 14 Fourier Transforms in Radar and Signal Processing 5.3.3 Error ... (1 + a ) F 2 /4, so we have to divide by this factor to give the normalized spectrum: | X ( f ) | = [4/ (1 + a ) (1 − a ) F ] rect [2 f /(1 − a ) F ] ⊗ rect [2 f /(1 + a ) F ] (5 .44 ) The transform ... exp (−2 ) (5 .42 ) Expressing the variance in terms of the spectral limit level, A , we obtain a k = exp [−2 ( − k )2/1.84A q ] and (5 .43 ) b hk = exp [−2 (h − k )2/1.84A q ] Trapezoidal...
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Fourier Transforms in Radar And Signal Processing_7 docx
Ngày tải lên :
18/06/2014, 10:05
... (forward) transforms to i sncr , so, from Rule 4, we have i snc (x ) ⇔ ramp (−y ) = −ramp ( y ) (as ramp is odd)—that is, ramp ( f ) inverse transforms to −i snc (t ) (However, as ramp2 is even, it transforms ... single element or, 136 Fourier Transforms in Radar and Signal Processing Figure 6 .4 Equalization of linear amplitude distortion: (a) m = 7, q = 1; (b) m = 7, q = 1.5; (c) m = 47 , q = 1; (d) m = 7, ... a and B are given more specifically by (5 .46 a, b) The result of implementing this delay equalization is shown in Figure 6.7 The receiver 140 Fourier Transforms in Radar and Signal Processing...
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Fourier Transforms in Radar And Signal Processing_8 pdf
Ngày tải lên :
18/06/2014, 10:05
... (6 .40 ) 150 Fourier Transforms in Radar and Signal Processing b r = a [(r − s )T ] + b [(r −  )T ] + ( 2 /4) c [(r − s )T ] (6 .41 ) Now, for the trapezoidal spectrum we have [as in (5 .44 )] ... 1+a 2 snc2 ͬ ͫ (1 + a ) Ft (1 − a ) Ft sinc 2 ͬ (6 .47 ) Using (6 .43 ), (6 .46 ), and (6 .47 ) to substitute for a , b , and c in (6 .40 ) and (6 .41 ), and also putting FT = 1/q , as the sampling interval ... 142 Fourier Transforms in Radar and Signal Processing Figure 6.8 Sum beam frequency response; effect of bandwidth: (a) 10% bandwidth; and (b) 200% bandwidth Equalization 143 equalization,...
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Fourier Transforms in Radar And Signal Processing_9 doc
Ngày tải lên :
18/06/2014, 10:05
... 1 64 Fourier Transforms in Radar and Signal Processing a sampled aperture; we can still use the Fourier transform, but the aperture distribution ... lobes nominally at −55 dB 1 74 Fourier Transforms in Radar and Signal Processing lobes are seen to be very close to this level—the pattern levels at ±2.5, ±3.5, and 4. 5 are precisely −50 dB by ... ͮ + 0.0267 [exp (2 i 2.362y ) + exp (−2 i 2.362y )] = rect ( y ) [1 + cos (2 y ) + 0.05 34 cos (4. 7 24 y )] (7.15) As we started with the normalized variable v = u /U, this distribution is in...
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Fourier Transforms in Radar And Signal Processing_10 pot
Ngày tải lên :
18/06/2014, 10:05
... pulse, 41 44 defined, 41 illustrated, 43 spectrum, 43 44 See also Pulses; Pulse spectra Transforms diagrams, 11 Hilbert, 7, 74, 75, 85, 86–88 inverse, 87 of ramp functions, 158 See also Fourier transforms ... linear, 1 64 80 Asymmetrical trapezoidal pulse, 44 47 illustrated, 45 rising edge, 44 spectra illustrations, 46 spectrum examples, 45 47 See also Pulses; Pulse spectra Aliasing defined, 94 no, 95 ... 59, 1 14 Pulses asymmetrical trapezoidal, 44 47 general rounded trapezoidal, 53–58 raised cosine, 47 49 rectangular, 49 regular RF train, 58–59 rounded, 49 –53 symmetrical trapezoidal, 40 41 symmetrical...
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Fourier Transforms in Radar And Signal Processing_1 ppt
Ngày tải lên :
18/06/2014, 15:20
... (Figure 3 .4) It is the limiting version of the trapezoidal pulse and is given by u (t ) = (1/ ) rect (t /T ) ⊗ A rect (t /T ) Figure 3.2 Product of sinc functions (3 .4) 42 Fourier Transforms ... 2 iy ͪ |ͬ ∞ iy The Fourier transform of h (x ) is now found to be, using P1b, ͫ 1 ␦( y) + iy ͬ 36 Fourier Transforms in Radar and Signal Processing P2b: From P2a and R4, the transform of ͫ ... ∞ u ′(x ) = ͵ 2 iyU ( y ) exp (2 ixy ) dy −∞ so u ′(x ) is the inverse Fourier transform of 2 iyU ( y ) 34 Fourier Transforms in Radar and Signal Processing R9b: ∞ U( y) = ͵ u (x ) exp (−2...
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Fourier Transforms in Radar And Signal Processing_2 docx
Ngày tải lên :
18/06/2014, 15:20
... in Section 4. 6 (quadrature sampling) we include a quarter wave delayed form of u The sampling techniques of Sections 4. 4 and 4. 6 are for narrowband waveforms—signals on a carrier 4. 3 Wideband ... equivalent form of (4. 4) is u (t ) = ⌺u (nT ) sinc (t − nT ) (4. 7) and the equivalence of the waveform to its interpolated sampled form is illustrated in Figure 4. 2 It is clear (from Figure 4. 1, for example) ... sampling rates 2W ′ is given by Figure 4. 5 rep2w U ( f ) near +f Figure 4. 6 Selecting U ( f ) 72 Fourier Transforms in Radar and Signal Processing Figure 4. 7 Maximum sampling rate 2f u /k = 2(k...
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Fourier Transforms in Radar And Signal Processing_3 doc
Ngày tải lên :
18/06/2014, 15:20
... + (4. 18) U ( f − 2f ) [1 + exp (4 if )] ( f − W /2 < f < f + W /2) Figure 4. 10 Basic quadrature sampling Sampling Theory 77 This is simply U ( f ), as required, if we choose such that 4f ... sinc (Wt ) cos (2 f t ) (4. 21) This interpolating function also appears in the uniform sampling case [see (4. 9)] and the Hilbert sampling case [see (4. 16)] Equation (4. 19) states that the real ... define the boundaries, and the central values rc are shown as dashed lines in Figure 4. 14 We note from Figure 4. 14 that there are no unallowed sampling rates above 2W This is because when the interval...
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Fourier Transforms in Radar And Signal Processing_6 doc
Ngày tải lên :
18/06/2014, 15:20
... (6 .40 ) 150 Fourier Transforms in Radar and Signal Processing b r = a [(r − s )T ] + b [(r −  )T ] + ( 2 /4) c [(r − s )T ] (6 .41 ) Now, for the trapezoidal spectrum we have [as in (5 .44 )] ... 1+a 2 snc2 ͬ ͫ (1 + a ) Ft (1 − a ) Ft sinc 2 ͬ (6 .47 ) Using (6 .43 ), (6 .46 ), and (6 .47 ) to substitute for a , b , and c in (6 .40 ) and (6 .41 ), and also putting FT = 1/q , as the sampling interval ... 142 Fourier Transforms in Radar and Signal Processing Figure 6.8 Sum beam frequency response; effect of bandwidth: (a) 10% bandwidth; and (b) 200% bandwidth Equalization 143 equalization,...
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Fourier Transforms in Radar And Signal Processing_7 doc
Ngày tải lên :
18/06/2014, 15:20
... 1 64 Fourier Transforms in Radar and Signal Processing a sampled aperture; we can still use the Fourier transform, but the aperture distribution ... lobes nominally at −55 dB 1 74 Fourier Transforms in Radar and Signal Processing lobes are seen to be very close to this level—the pattern levels at ±2.5, ±3.5, and 4. 5 are precisely −50 dB by ... ͮ + 0.0267 [exp (2 i 2.362y ) + exp (−2 i 2.362y )] = rect ( y ) [1 + cos (2 y ) + 0.05 34 cos (4. 7 24 y )] (7.15) As we started with the normalized variable v = u /U, this distribution is in...
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