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By C. J. Date

ISBN-10: 020106006X

ISBN-13: 9780201060065

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4. ✠ ☛✏✄ ✆✓✒✍✣ ✞✖☛✏✠ ✂ ✒ ✟ ✒ ✁ ✞ ✣ ✑ ☛ ✣☎✄ ✁ ✡ ✞✡✠ ✛ ✤✥☛✍✞ ✌ ✒✍✌ ✄ ✒✍✣ ✁✍✄✝✆✢✒ ✄☎✕✜✞✡✠☞✎✎☛ ✁ ✣☎✄ ☛ ✌ ❏✁ ❯❣✻ ❍✮❊❇❵✺✻☎❋■✻●✵❆❊ ❍❏✽❑✿✭✳✺❍✮❃✾✽❆✹✭✻❇✷☛❯❏❋■❊❳❞✾✳✺❊●✿❥❭✮▲ ✽❨❍✑❊❇✲❘◗✺❊✾✹✭✹✭❊✐✹ ✵❆❃ ❊❇❉✺❊❇❋❆▲ ❵✺❃✭❍✮❍❏✽✸◗✭✷❨❊ ❵✺❃❳✽✸✿✭✵❛✽❑✿✣✭✾✡ ❯❴❋✮❊❳❞✾✳✺❊❇✿❬❭✮▲ ✹✭❃✾✲❡✻❇✽❑✿✺❁✠✻✬❍❏✽✸✿✭✳✺❍☎❃✾✽❆✹ ❃✾✳✭✷❆✹ ❭❳✻❇❋❏❋❨▲ ❖ ◗✭✽✸✵❨❍ ✍ = log N 2 , N = 512 ✎❴✼✞✚✦❃ ❊❇❉❬❊❇❋■❁✂✻❳❍ 2 ❊★✧✩❵✭✷❆✻●✽✸✿✺❊❳✹✠❵✭❋✮❊❇❉✭✽❆❃✾✳✺❍✫✷▼▲❘✽❑✿✰❍✮❊❳❭❇✵❑✽❆❃✾✿ ✭✭✼✫❖✾✼ ✭✭❁◆❊❇❉✺❊❇❋❆▲✴❯❨❋■❊✾❞✾✳❥❊●✿✺❭■▲❛❭❳❃✾✲✴❵✺❃✾✿✺❊❇✿✭✵✯❭✐✻❇✿✢✿✺❃✾✵❬◗✺❊✱❍✮❊❇✷❨❊❳❭❇✵❨❊❳✹✢✻❳❍❢✻ ❉✺✻❇✷❑✽❆✹ ✻❇✵❨❊❇❋❴✲❛✻❇❋ ✟❣❍✫✽ ❪❫✿✺✻❇✷ ✵✸❚✺❊ ❯❴❋✮❊❳❞✾✳✺❊❇✿❬❭❇✽❆❊✾❍☞✿✺❊❳❊❳✹ ✵❆❃ ◗✺❊ ❍☎❊❇✷❆❊❳❭●✵❆❊❳✹ ❯❨❋■❃✾✲ ✻ ◗✺✻❇✿✺✹ ✷❑✽✸✲✴✽✸✵❆❊✾✹ ❋■❊❳❪ ✽❆❃✾✿✺❁ ❚✭✽❆❭❇❚ ✽❨❍✗✻❇✿ ✻❇✿✭✿✭✳✭✷❑✳✺❍ ◗✺❊☎✵ ❊❳❊❇✿ ❋■✻❳✹✾✽✸✽ ✄✭✼ ✭ ✠ ✻❇✿✺✹ ✄✭✼ ✟ ❭☎▲◆❭☎✷❨❊ ✝✸❵✭✽ ✧❥❊●✷❆✼ ✢◆✳✭❋❴✵❑❚✺❊❇❋❴✲☛❃✾❋■❊❳❁❀❍❏✽❑✿✺❭❳❊ ❵❬❊❳✻✛✟ ❭❇✷❑✽✸✲❘◗✭✽❑✿✺❪✖✿✺❊✐❭❳❊✾❍✮❍❏✽✸✵❨✻❇✵❆❊✾❍❤✹✾✽❆❍❏✵✸✽✸✿✺❭❇✵❈❵✺❊❳✻✛✟✺❍❬✵❨❃ ✹✭❊✾❭❳❃✭✹✩❊❩✻❳✹✭✹✩❊❳✹ ✻❇✵ ❊❇❋❏✲☛✻❇❋✒✟✺❁✩❃✾✿✭✷▼▲ ❃✾✿✺❊❱❯❨❋✮❊❳❞✾✳✺❊❇✿✺❭✮▲ ❭✐✻❇✿❀◗✺❊ ❊❇✲✴◗✺❊❳✹✭✹✭❊❳✹✱✽✸✿ ✻ ✽✸✿✺✹✭❃ ❃✾❯ ❍❏✽❆❄✐❊❙ ✧✩ ✍ ❊❳✼❂❪✝✼ ✩✰✧ ✩ ❃✾❋ ✠✰✧ ✠✠✎❴✼✝✁✛✿ ✵✸❚✭✽❨❍❢❭❳✻❳❍✮❊❳❁✝✵❑❚✺❊❙✳✭❵✭❵✺❊❇❋❤✷✸✽❑✲❘✽❑✵ ❯■❃✾❋❤✵❑❚✺❊ ❭❳✻❇❵✺✻✐❭●✽✸✵▼▲ ✽✸✷❑✷✯◗✺❊ log (αN 2 /V 2 ) ❁ ❚✺❊❇❋■❊ α ❍❏❚✺❃ ❍❩✵✸❚✺❊✱❋■✻❇✵❑✽❆❃✰❃✾❯❢✵✸❚❬❊ ✻❇❋✮❊✐✻ ❃✾❯❢✵❑❚✺❊ ✻❇✿✭✿✭✳✭✷❆✻❇❋ ❋❏✽✸✿✺❪ 2 ❭❳❃✾✿✺❍❏✽❨✹✭❊❇❋✮❊❳✹ ✵❆❃ ✵✸❚✺❊ ✵❨❃✾✵❆✻❇✷✠✻❇❋✮❊❳✻ ✽❑✿✗❯❴❋✮❊❳❞✾✳❬❊❇✿✺❭✮▲ ✹✭❃✾✲❛✻❇✽✸✿❬✼❬✚❘✻❇✲❛❊❇✷▼▲◆❁✺❯■❃❳❋ ✠✺✰❖ ✭✰✧ ✠✺✰❖ ✭ ✽ ✲☛✻✾❪✭❊ ❍❏✽❨❄✐❊❳❁❤✻❇✿✺✹ ✵❆✻ ✟✭✽✸✿✺❪ α ✻❳❍ ✄✭✼ ✩ ❯■❃✾❋ ✵✸❚✺❊ ✻❇✿✭✿✭✳✭✷❆✻●❋ ❋❏✽✸✿✺❪✤◗❬❊❇✵ ❊❳❊❇✿ ❋❲✻❳✹✾✽✸✽ ✄✭✼ ✭ ✠ ✻❇✿✺✹ ✄✭✼ ✟ ❭☎▲◆❭❇✷❨❊ ✝✸❵✭✽ ✧❥❊●✷❆❁✯✵✸❚✭✽❆❍ ✽❑✷❑✷ ❭❳❃✾❋❏❋■❊❳❍❏❵✺❃❫✿✺✹❙✵❆❃ ✰❖ ✭ - ✰❖ ✩❙◗✭✽❑✵❆❍ ✝❆❍❏✽✸✿✭✳✺❍✮❃✾✽❨✹✭✼ 33 3.

4. 5. 6. 7. ❏✁ ✿ ✵✸❚✭✽❨❍✂❍✮❊✾❭❇✵✸✽❨❃✾✿✺❁ ✵✸❚✺❊✴❊★✧✩✵❆❊❇✿✺❍✫✽❆❃✾✿✤❃✾❯✥✵❑❚✺❊ ❵✩❋■❃✾❵✺❃✭❍☎❊❳✹ ❇✻ ✵ ❊❇❋❏✲☛✻❇❋✒✟✭✽✸✿❬❪❀✲❡❊❇✵✸❚✺❃✭✹ ✵❆❃ ❋❲❊❳❍❴✽❆❍✫✵❙❍✫✷✸✽❆❭●✽✸✿✺❪ ✻❇✵❑✵❆✻❳❭✛✟✢✽❨❍❩✹✭❊❳❍☎❭❇❋❴✽❑◗❥❊✾✹✭✼ ✚✦❊✐❭❳❊✐❍☎❍✮✻❇❋❆▲☛❭✾❃✾✿✺✹✾✽✸✵✸✽❨❃✾✿✺❍❝❯■❃✾❋❩❭❳❃❳❋❴❋❲❊✾❭❇✵ ❇✻ ✵❆❊❇❋❴✲☛✻●❋ ✟✢❋❲❊❳❭✾❃✾❉❥❊●❋❆▲❡✻❇❯❴✵❨❊❇❋❱✵❑❚✭✽❆❍ ✟✭✽❑✿✺✹✢❃✾❯ ✻❇✵❑✵❆✻❳❭✛✟✺❍❱✻❇❋❲❊❩✬❊ ✧❥✻●✲❘✽✸✿✺❊✾✹✭✼ ✌✍❚✺❊❝✲☛✻●❋ ✟✭✽✸✿❬❪✱❍✫✽❆❪❫✿❬✻❇✷❈✲☛❃✭✹✭❊❇✷❈✽✸✿ ✭ -✡ ❭❳✻❇✿❀◗❬❊ ❋❴✽❑✵✸✵❨❊❇✿ ✻✐❍ s(x,y) = N ❚✺❊❇❋■❊ • • ✭✹ ❊❇✿✺❃✾✵❨❊❳❍❬✵✸❚✺❊❙✻❇✲❘❵✭✷❑✽✸✵✸✳✺✹✭❊❙❃✾❯❥✵✸❚✺❊ i✆❆✵✸❚ ❭❳❃✾✲✴❵✺❃✾✿❥❊●✿✭✵ ✌✍❚✺❊❙❯❴❋✮❊❳❞✾✳❬❊❇✿✺❭✮▲❡❃✾❯❤✵✸❚✺❊ i ✵✸❚ ❭❳❃✾✲✴❵✺❃✾✿✺❊❇✿✭✵ ✽❨❍❢✻❙❉✺❊❳❭❇✵❨❃✾❋ Ai ✹✾✽✸❋✮❊❳❭❇✵❑✽❆❃✾✿ ✁ i =1 ✍ ✭✭✼✫❖ ✎ Ai cos ( 2 [Fx ,i x +Fy ,i y]) φ i = arctan( Fy ,i / Fx,i ) ✻❇✿✺✹❙✲❛❃✭✹✾✳✭✷✸✳✺❍ Fi ✵❑❚✺✻❇✵ ❚✺✻❳❍❱✵❑❚✺❊❙❵✭❋■❃✾❵✺✻❳❪✝✻●✵✸✽❆❃✾✿ | Fi |= F = Fx ,i + Fy ,i 2 2 ✼ 27 • ✯✧ ✿★✵✸❚✺❊ ✧ - ✻❇✿✺✹ ▲ -✻✬✧❥❊✾❍ ❃✾✿✺❊ ❃✾◗✺❍✮❊❇❋❏❉✺❊❳❍✏✆ F = F cos φ ✻❇✿✺✹ x ,i i ✚❘❊❇✿✺❭❳❊❝✵❑❚❬❊❩❍❏✽✸✿✭✳✺❍☎❃✾✽❆✹❀❭❳✻❇✿❀◗❬❊ ❋❴✽❑✵✸✵❨❊❇✿❀✽✸✿❀❵✺❃✾✷❨✻❇❋❥✿✺❃✾✵❨✻❇✵✸✽❨❃❳✿ ✻❳❍ Fy ,i = F sin φ i N s ( x, y ) = i =1 ✗ ☛✍✣ ✒✍✣ ✞✖☛✏✠ ☛ ✟ ☎✁ ✄☎✒✍✣✥☛ ✄ ✴❴✥ ✓✖✝ ✠ ✞☎ ✝ ✎☛✝✟✚ ✡ ✑ ✟✫ ✥ ✝ ✲ ✥✮✫ ✢✔❃❳❋ ❍❏✽❑✲❘❵✭✷✸✽❨❭❇✽✸✵✸▲ ✆ ✝✞✟ x ✡✆✜ s (z ) ✁✄✂✆☎✞✝✰☎ z✠ = ☎ ✄ ✚ ❭ ✫ ✘✎ ☎❆✝ ✝ ✥ ✘✎ ✚✞✎ ✠☛✡✩✷ ✎☛✂✆☎ ☛✠ ✲ ✚ ✷ ☎ ✑ ✗ ☎ ✌ ✎☛✝ ✓ ✲ ✕✆☎ ✌✪✥✮✲ ✪☎ ✑ 2D ✍ ✭✭✼✫❖✾€✠✎ ❊ ✹✭❊●✿✺❃✾✵❆❊ ✂ ✥✮✲✬✠ ✎☛✎✍☎ ● ✜ ✫ ✝ ✥✮✲ ✆✡ ✥ ✁ ✥✮✡❁✫✟✥ ✝ ❆✌ ❃ ✞✚ ✝ ✠ ✎ ✯ ✻ S ' (ω ) = Ai cos(2π [ Fi cos φ i x +Fi sin φ i y ]) y ✁ ✁ ✁ ✁ ✁ S (ω ) = s ( x ) exp(− jω T x )dx ✚✪✑ ✎☛✂✆☎ 2D ☞ ✌✍✎ ω x ✡ ✻✒✬ ✑ ☎ ✌ ✎ ✥ ✝ ✡✆✥ ✎✍✚✞✎ ✠✍✥✪✡❉✫✟✥ ✝✔✓❪✚ ✡✆✜ ω ✚✞✝ ☎ ω✏ = ☛ ωy s ' ( z ) → s ( Rz ) s ( Rz ) exp(− jω T z )dz = 1 |R| 2D ✁✄✂✆☎✞✝✟☎✖✕ ✠ ✑ ✑ ✮✥ ✲ ☎ ✝ ✥ ✎✍✚✞✎ ✠✍✥✮✡ ✲ ✚✞✎☛✝ ✠ ★✩❵ ✎✧✂✆☎ s (u ) exp(− jω T R −1u )du ❞ ✹✖✻✼✹ ▲✖❢ or S ' (ω ) = 1 |R| 2D s (u ) exp(− j ( Rω ) T u )du = S ( Rω ) ❞ ✹✖✻✼✹ ❍✮❢ ❭❪✑●✚●✝✟☎✪✑ ✓ ❃ ✎✘❵ ✎✧✂✆☎ ✑ ✗ ☎ ✌ ✎✧✝ ✓ ✲ ✠ ✎✘✑✰☎ ❃☛✫ ✠ ✑❯✝ ✥ ✎✍✚✞✎✸☎ ✜ ✻ ❴✴ ✥ ✝ ✌✮✥✳✲✏✗✖❃ ☎❆★✘✗ ✎ ✥✮✡ ☎✮✑✰❵ ✫✟✥✮❃✧❃✘✥ ✁ ✠☛✡✆✷ ✎✧✝ ✚ ✡ ✑ ✫✰✥ ✝ ✲ ✗ ✚ ✠ ✟✝ ✑ ✌ ✚ ✡ ✕✩☎❱✁☞✝ ✠ ✎✧✎✘☎ ✡ N s( z ) = T i =1 s' ( x) = N i =1 Ai exp( j 2πFi z ) ↔ N i =1 Ai exp( j 2πFi R −1 x) ↔ T Ai δ ( f − Fi ) N i =1 Ai δ ( f − RFi ) ❞✔✹✖✻✼✹✖✹ ❢ ❞✔✹✖✻✼✹✚✙ ❢ ✼ 28 ✞ ❍ ✻●✿✗❊★✧❬✻❇✲✴❵✭✷❆❊❩❯■❃✾❋☞✻ ❏❍ ✽❑✿✺❪❫✷❆❊❩✵❨❃✾✿✺❊ ❚❬❊❇❋■❊ F = ( F ,0) ✻❇✿✺✹ ✻ €☎✄ -✹✭❊✐❪❫❋■❊✐❊❩❋✮❃✾✵❆✻❇✵❑✽❆❃✾✿ ✲☛✻❇✵❑❋❴✽ ✧ ✦ x ✝ ✭✠✎❴❁✾❯✮❃✾✷✸✷❆❃ ✽✸✿❬❪✖✵❑❋■✻❇✿✺❍❴❯✮❃❳❋❴✲ ✺❵ ✻●✽✸❋■❍❱❭❳✻❇✿❀◗❬❊❩❃✾◗✭✵❆✻●✽✸✿✺❊❳✹ R(π s ( x) = A exp( j 2πF T z ) = A exp( j 2πFx x) ↔ Aδ ( f x − Fx , f y ) s ' ( x) = A exp( j 2πuRx) ↔ Aδ ( f x , f y − u ) ✂✁☎✄✆✁✞✝✠✟ ✡✁☎✄✆✁☎☛☎✟ ✂ ✄ ✛ ✤ ✄ ✁ ✟ ☎✁ ✄☎✒✍✣✥☛✏✄ ✌☞✎✍✑✏✓✒✕✔✡✖✠✗✡✍✙✘✞✚✠✏✛✔✢✜✕✣✥✤✦✘✞✧✙✏✕★✥✤✪✩✫✤✪✧✠✜✕✣✬✏✭✗✮✘✞✧✠✏✯✘✞✔✰✩✱✘✞✔✢✏✲✘✴✳✫✣✪✍✠✏✓✵✞✤✥✩✱✏✕✧✠✗✡✤✬✘✞✧✠✗ ✄✷✶ ✏✕✸✑✜✕✩✫✚☎★✦✏✹✤✥✧✺✣✪✍✠✏ ✁✞✻ ✘✞✔ ✒✭✜✭✗✛✏✼✘✭✧✠✏✹✍✠✜✭✗ ✿ 1 0✽ P= ✾ 0 0 ✂✁☎✄✆✁☎❃☎✟ ❀❁❂ ❄ ✳❆❅❇✏❈✒✞✘✞✧✠✗✡✤✦✵☎✏✕✔✑✣✪✍✠✏✼✗❉✤✪✧✑❊❋★✦✏❈✗❉✤✪✧☎✖✠✗●✘✞✤✬✵ [ ] s ( z ) = A exp( j 2π Fx x + Fy y ) ↔ Aδ ( f x − Fx , f y − Fy ) ❍ ✜✕✳✡✣✦✏✕✔✑✚☎✔✢✘❏■❋✏✞✒✕✣✪✤✬✘✞✧ s ' ( z ) = s ( Pz ) = A exp( j 2πF T Pz ) = A exp( j 2πFx x) ✂✁☎✄✆✁☎❑☎✟ ❅❆✍☎✤✪★✦✏▲✣✪✍✠✏✼✗❉✚✠✏✭✒✕✣✪✔✡✖☎✩◆▼✠✏✴✒✭✘✭✩✮✏✭✗●❖ S ' (ω ) = 2D s ( Pz ) exp(− jω T z )dz = s ( x,0) exp(− jω x x − jω y y )dxdy = δ (ω x − Fx )δ (ω y ) = S ( Pω ) δ (( I − P )ω ) = S ( Pω ) δ (ω y ) ✗ ☛✍✣ ✒✍✣ ✞✖☛✏✠❘◗ ✂ ✄ ✛ ✤ ✄❚❙ ✌ ✞✂✁☎✁ ✁ ✟ ✁☎✄☎✒✍✣ ✞✡☛✏✠ ✂✁☎✄✆✁☎€☎✟ ❱❯❆▼☎❲☎✤✦✘✞✖✠✗✡★✪❳ s ' ( z ) = s ( PRz ) ↔ S ' (ω ) = S ( PRω ) ✂✁☎✄✆✁☎❨☎✟ 29 ✌ ✞ ✁ ✞✡✠☞✎ ☛ ✒ ✡ ✞✖✠ ✛ ✤✥☛✍✞ ✌☞✒✍✌ ✆ ✡✌ ✒✏✠☞✁ ✁✫❯ ✽✸✲❛✻❳❪✝❊❳❁❜✻●❯❴✵❨❊❇❋✖✵❑❚✺❊☞❋✮❃✾✵❆✻❇✵❑✽❆❃✾✿✬❃✾❯✙✵✸❚✺❊☞❵✭✷❨✻❇✿✺❊☞◗✩▲ ❊ ✻❳❍✮❍❏✳✭✲❛❊☞✵✸❚✺✻●✵ φp F ✻❇✿✺✹ ✻●❋■❊❘❊●✲❘◗✺❊❳✹✭✹✭❊✐✹ ✵❆❃ ✻☎✿ Rπ / 2 F ✻❇✿✺✹❛❭☎❋❏✳✺❍❏❚✭✽✸✿✺❪ ❃✾✿✺❊❘❃✾❯✙✵✸❚✺❊✴✻★✧❬❊❳❍ ✍ ✷❆❊❇✵ ❍✠❍☎✻■▲ ▲ ✎❜✵✸❚❬❊ ❃✾◗✺❍✮❊❇❋❏❉✺❊❳✹ ❖ -✡✏❯❴❋■❊❳❞✾✳✺❊❇✿✺❭❇✽ ❊✐❍ ✽❑✷✸✷✶◗✺❊✖✆ ✍ ✭✭✼ ✩☎✄✠✎ F ' = Fx cos φ p − Fy sin φ p F ' ' = Fx sin φ p + Fy cos φ p ✒✖❍❏✵✸✽❑✲☛✻●✵✸✽❆❃✾✿ ❃✾❯❬✵✸❚✺❊❝✲❛❃✭✹✾✳✭✷✸✳✪❍ ✆ • ✌✍❚✺❊ ✲☛❃✭✹✾✳✭✷❑✳✺❍ ❃✾❯ ✵❑❚✺❊ ❯✫❋■❊❳❞✾✳✺❊❇✿✺❭✮▲ ❭✐✻❇✿ ◗✺❊ ❋■❊✾❭❳❃❳❉✺❊❇❋■❊✾✹ ✻❳❍ | F |= F ' 2 + F ' ' 2 ( Fx cos φ p − Fy sin φ p ) 2 + ( Fy cos φ p + Fx sin φ p = | F |= Fx + Fy 2 2 ❍❏✽❑✲❘✽✸✷❨✻❇❋❴✷✸▲ ◗✺❊✴✹✩❊❇✵❨❊❇❋❴✲✴✽✸✿✺❊❳✹❘✽❑❯✙✵❑❚✺❊ ✵ ❃ ❍❏✽✸✿✭✳✺❍☎❃✾✽❆✹✭❍☞✻❇❋❲❊❘❊●✲❘◗✺❊❳✹✭✹✭❊✾✹ ✝ ✭✭❁✐❚✺❃ π 2 ❍✫✽✸✿✺❭❳❊ ✼✑✌✍❚❬❊❀✲☛❃✭✹✾✳✭✷✸✳✺❍ ❭❳✻❇✿ ✽✸✵✸❚✤✻❇✿✤✻❇✿❬❪❫✷❆❊ θ ✹✾✽✸❯❏❯■❊☎❋✮❊❇✿✭✵✍✵✸❚✺✻❇✿ ❊❇❉✺❊☎❋❥✵✸❚✺❊❢€☎✄ -✹✭❊✾❪✾❋❲❊❳❊❱❉✺✻❇❋❏✽❆❊❇✵❦▲✂❵ ❋✮❃✾❉✺❊❳❍❥✵❆❃❩◗✺❊❱✵❑❚✺❊❢❊❳✻❳❍❏✽❨❊❳❍❏✵ ✵❨❃❩✵✸❋■✻✾❭✛✟✺✼ ✢✔❃✾❋✥❍❏✽✸✲✴❵✭✷✸✽❨❭❇✽✸✵▼▲ | F |= F ✽❆❍❱✻❳❍✮❍❏✳✭✲❛❊❳✹✭✼ • ✒✖❍❏✵✸✽❑✲☛✻●✵✸✽❆❃✾✿ ❃✾❯❬✵✸❚✺❊❩✹✾✽❑❋■❊❳❭●✵✸✽❆❃✾✿✂✆ ✔✖❃❫✿✺❍❏✽❆✹✭❊❇❋❏✽✸✿✺❪ arctan ✵✸❚✺❊ ✻●❋❲❭❇✵❆✻☎✿✺❪ ❊❇✿✭✵ ❃✾❯ ✵✸❚✺❊ ❋❲✻❇✵❑✽❆❃ Fy cos φ p + Fx sin φ p Fx cos φ p − Fy sin φ p ❁❩✽✸❯ ❃✾❯ ✵✸❚✺❊ ❊❣❊★✧✩❵✭❋■❊✾❍✮❍ ✵✸❚✺❊ ❯❏❋❲❊✐❞✾✳✺❊❇✿✺❭❇✽❨❊❳❍ ❊❳❍❏✵❑✽✸✲☛✻●✵❆❊❳✹ ( Fx , Fy ) ❯❏❋■❊❳❞✾✳✺❊●✿❥❭●✽❆❊❳❍✮❁ ✽✸✿ ✵❆❊❇❋❏✲☛❍✤❃✾❯☛❵✺❃✾✷❨✻❇❋ ❭❳❃✭❃✾❋✮✹✾✽✸✿✺✻❇✵❨❊❳❍ arctan Fy cosψ + Fx sin ψ Fx cosψ − Fy sin ψ = arctan | F | sin φ f cos φ p + | F | cos φ f sin φ p | F | cos φ f cos φ p − | F | sin φ f sin φ p = arctan sin(φ p + φ f ) cos(φ p + φ f ) = φp +φf ✍ ✭✭✼ ✩✺❖✖✎ 30 ✌✍❚✭✳✺❍✖✵✸❚✺❊❘✹✾✽✸❋■❊✾❭❇✵✸✽❨❃✾✿✬❃✾❯❙❵✭❋■❃✾❵✺✻✾❪✭✻❇✵✸✽❨❃✾✿✬❭❳✻❇✿✬❃✾✿✭✷▼▲ ◗✺❊✦✹✩❊❇✵❆❊●❋❴✲❘✽❑✿✺❊❳✹ ✵✸❚✺❊✂❍❏✷✸✽❨❭❇✽❑✿✺❪☞❵✭✷❆✻●✿❥❊✂✻❇✿❬❪❫✷❆❊ φp ✼ ✁❏✿✢❯✮✻✐❭❇✵ ❊✙❚❬✻❇❉✺❊✥✵✸❚✭❋❲❊✾❊✙✳✭✿ ✟✭✿✺❃ ✿✺❍ ✽✸✵✸❚✭✽❑✿✤✻ ❭❇✽❑❋■❭❇✷❨❊✴❃✾❯✥❋■✻✾✹✾✽✸✳✺❍ ✻❇✿✺✹ φf Fx + F y 2 2 ✻❇✿✺✹ F1' ✽✸✵✸❚✭✽❑✿☛✵✸❚✺❊✂✳✭✿◆❭❳❊❇❋❴✵❨✻❇✽✸✿✭✵❦▲ ❃❳❯ (F ,φ f ,φ p ) ❃✾✿✭✷▼▲ ✵ ❃✴✽❑✿✺✹✭❊❇❵❬❊❇✿✺✹✭❊❇✿✭✵✔✲❡❊❳✻❳❍❏✳✭❋✮❊❇✲❡❊❇✿✭✵❨❍✏✆ ❃✾❋ ◗✭✳✭✵ ( Fx , Fy , φ p ) ✼❈✌✍❚✺❊✂❯❏❋■❊❳❞✾✳✺❊●✿❥❭✮▲ ❭✐✻❇✿❛◗✺❊✴✹ ❊●✵❆❊❇❋❏✲✦✽✸✿✺❊❳✹ ❃✾✿✭✷▼▲ F2' ✼ ✚✦❃ ❊❇❉✺❊❇❋✥✽✸❯ ❊ ✟✭✿✪❊ ✵✸❚✺❊ ❍❏✷✸✽❨❭❇✽✸✿✺❪ ✻❇✿❬❪❫✷❆❊ φp ✵❑❚✺❊❇✿ F ❃✾✳✭✷❆✹❙◗✺❊❙✹✭❊❇✵❆❊☎❋❏✲❘✽✸✿✺❊✐✹ ✽✸✵❑❚✺❃✾✳✭✵❜✻❇✿✩▲✂✳✭✿✺❭✐❊❇❋❴✵❨✻❇✽✸✿✭✵ y.

3. 3. 1. 2. 3. 3. 4. 4. 5. 6. 7. ❏✁ ✿ ✵✸❚✭✽❨❍✂❍✮❊✾❭❇✵✸✽❨❃✾✿✺❁ ✵✸❚✺❊✴❊★✧✩✵❆❊❇✿✺❍✫✽❆❃✾✿✤❃✾❯✥✵❑❚✺❊ ❵✩❋■❃✾❵✺❃✭❍☎❊❳✹ ❇✻ ✵ ❊❇❋❏✲☛✻❇❋✒✟✭✽✸✿❬❪❀✲❡❊❇✵✸❚✺❃✭✹ ✵❆❃ ❋❲❊❳❍❴✽❆❍✫✵❙❍✫✷✸✽❆❭●✽✸✿✺❪ ✻❇✵❑✵❆✻❳❭✛✟✢✽❨❍❩✹✭❊❳❍☎❭❇❋❴✽❑◗❥❊✾✹✭✼ ✚✦❊✐❭❳❊✐❍☎❍✮✻❇❋❆▲☛❭✾❃✾✿✺✹✾✽✸✵✸✽❨❃✾✿✺❍❝❯■❃✾❋❩❭❳❃❳❋❴❋❲❊✾❭❇✵ ❇✻ ✵❆❊❇❋❴✲☛✻●❋ ✟✢❋❲❊❳❭✾❃✾❉❥❊●❋❆▲❡✻❇❯❴✵❨❊❇❋❱✵❑❚✭✽❆❍ ✟✭✽❑✿✺✹✢❃✾❯ ✻❇✵❑✵❆✻❳❭✛✟✺❍❱✻❇❋❲❊❩✬❊ ✧❥✻●✲❘✽✸✿✺❊✾✹✭✼ ✌✍❚✺❊❝✲☛✻●❋ ✟✭✽✸✿❬❪✱❍✫✽❆❪❫✿❬✻❇✷❈✲☛❃✭✹✭❊❇✷❈✽✸✿ ✭ -✡ ❭❳✻❇✿❀◗❬❊ ❋❴✽❑✵✸✵❨❊❇✿ ✻✐❍ s(x,y) = N ❚✺❊❇❋■❊ • • ✭✹ ❊❇✿✺❃✾✵❨❊❳❍❬✵✸❚✺❊❙✻❇✲❘❵✭✷❑✽✸✵✸✳✺✹✭❊❙❃✾❯❥✵✸❚✺❊ i✆❆✵✸❚ ❭❳❃✾✲✴❵✺❃✾✿❥❊●✿✭✵ ✌✍❚✺❊❙❯❴❋✮❊❳❞✾✳❬❊❇✿✺❭✮▲❡❃✾❯❤✵✸❚✺❊ i ✵✸❚ ❭❳❃✾✲✴❵✺❃✾✿✺❊❇✿✭✵ ✽❨❍❢✻❙❉✺❊❳❭❇✵❨❃✾❋ Ai ✹✾✽✸❋✮❊❳❭❇✵❑✽❆❃✾✿ ✁ i =1 ✍ ✭✭✼✫❖ ✎ Ai cos ( 2 [Fx ,i x +Fy ,i y]) φ i = arctan( Fy ,i / Fx,i ) ✻❇✿✺✹❙✲❛❃✭✹✾✳✭✷✸✳✺❍ Fi ✵❑❚✺✻❇✵ ❚✺✻❳❍❱✵❑❚✺❊❙❵✭❋■❃✾❵✺✻❳❪✝✻●✵✸✽❆❃✾✿ | Fi |= F = Fx ,i + Fy ,i 2 2 ✼ 27 • ✯✧ ✿★✵✸❚✺❊ ✧ - ✻❇✿✺✹ ▲ -✻✬✧❥❊✾❍ ❃✾✿✺❊ ❃✾◗✺❍✮❊❇❋❏❉✺❊❳❍✏✆ F = F cos φ ✻❇✿✺✹ x ,i i ✚❘❊❇✿✺❭❳❊❝✵❑❚❬❊❩❍❏✽✸✿✭✳✺❍☎❃✾✽❆✹❀❭❳✻❇✿❀◗❬❊ ❋❴✽❑✵✸✵❨❊❇✿❀✽✸✿❀❵✺❃✾✷❨✻❇❋❥✿✺❃✾✵❨✻❇✵✸✽❨❃❳✿ ✻❳❍ Fy ,i = F sin φ i N s ( x, y ) = i =1 ✗ ☛✍✣ ✒✍✣ ✞✖☛✏✠ ☛ ✟ ☎✁ ✄☎✒✍✣✥☛ ✄ ✴❴✥ ✓✖✝ ✠ ✞☎ ✝ ✎☛✝✟✚ ✡ ✑ ✟✫ ✥ ✝ ✲ ✥✮✫ ✢✔❃❳❋ ❍❏✽❑✲❘❵✭✷✸✽❨❭❇✽✸✵✸▲ ✆ ✝✞✟ x ✡✆✜ s (z ) ✁✄✂✆☎✞✝✰☎ z✠ = ☎ ✄ ✚ ❭ ✫ ✘✎ ☎❆✝ ✝ ✥ ✘✎ ✚✞✎ ✠☛✡✩✷ ✎☛✂✆☎ ☛✠ ✲ ✚ ✷ ☎ ✑ ✗ ☎ ✌ ✎☛✝ ✓ ✲ ✕✆☎ ✌✪✥✮✲ ✪☎ ✑ 2D ✍ ✭✭✼✫❖✾€✠✎ ❊ ✹✭❊●✿✺❃✾✵❆❊ ✂ ✥✮✲✬✠ ✎☛✎✍☎ ● ✜ ✫ ✝ ✥✮✲ ✆✡ ✥ ✁ ✥✮✡❁✫✟✥ ✝ ❆✌ ❃ ✞✚ ✝ ✠ ✎ ✯ ✻ S ' (ω ) = Ai cos(2π [ Fi cos φ i x +Fi sin φ i y ]) y ✁ ✁ ✁ ✁ ✁ S (ω ) = s ( x ) exp(− jω T x )dx ✚✪✑ ✎☛✂✆☎ 2D ☞ ✌✍✎ ω x ✡ ✻✒✬ ✑ ☎ ✌ ✎ ✥ ✝ ✡✆✥ ✎✍✚✞✎ ✠✍✥✪✡❉✫✟✥ ✝✔✓❪✚ ✡✆✜ ω ✚✞✝ ☎ ω✏ = ☛ ωy s ' ( z ) → s ( Rz ) s ( Rz ) exp(− jω T z )dz = 1 |R| 2D ✁✄✂✆☎✞✝✟☎✖✕ ✠ ✑ ✑ ✮✥ ✲ ☎ ✝ ✥ ✎✍✚✞✎ ✠✍✥✮✡ ✲ ✚✞✎☛✝ ✠ ★✩❵ ✎✧✂✆☎ s (u ) exp(− jω T R −1u )du ❞ ✹✖✻✼✹ ▲✖❢ or S ' (ω ) = 1 |R| 2D s (u ) exp(− j ( Rω ) T u )du = S ( Rω ) ❞ ✹✖✻✼✹ ❍✮❢ ❭❪✑●✚●✝✟☎✪✑ ✓ ❃ ✎✘❵ ✎✧✂✆☎ ✑ ✗ ☎ ✌ ✎✧✝ ✓ ✲ ✠ ✎✘✑✰☎ ❃☛✫ ✠ ✑❯✝ ✥ ✎✍✚✞✎✸☎ ✜ ✻ ❴✴ ✥ ✝ ✌✮✥✳✲✏✗✖❃ ☎❆★✘✗ ✎ ✥✮✡ ☎✮✑✰❵ ✫✟✥✮❃✧❃✘✥ ✁ ✠☛✡✆✷ ✎✧✝ ✚ ✡ ✑ ✫✰✥ ✝ ✲ ✗ ✚ ✠ ✟✝ ✑ ✌ ✚ ✡ ✕✩☎❱✁☞✝ ✠ ✎✧✎✘☎ ✡ N s( z ) = T i =1 s' ( x) = N i =1 Ai exp( j 2πFi z ) ↔ N i =1 Ai exp( j 2πFi R −1 x) ↔ T Ai δ ( f − Fi ) N i =1 Ai δ ( f − RFi ) ❞✔✹✖✻✼✹✖✹ ❢ ❞✔✹✖✻✼✹✚✙ ❢ ✼ 28 ✞ ❍ ✻●✿✗❊★✧❬✻❇✲✴❵✭✷❆❊❩❯■❃✾❋☞✻ ❏❍ ✽❑✿✺❪❫✷❆❊❩✵❨❃✾✿✺❊ ❚❬❊❇❋■❊ F = ( F ,0) ✻❇✿✺✹ ✻ €☎✄ -✹✭❊✐❪❫❋■❊✐❊❩❋✮❃✾✵❆✻❇✵❑✽❆❃✾✿ ✲☛✻❇✵❑❋❴✽ ✧ ✦ x ✝ ✭✠✎❴❁✾❯✮❃✾✷✸✷❆❃ ✽✸✿❬❪✖✵❑❋■✻❇✿✺❍❴❯✮❃❳❋❴✲ ✺❵ ✻●✽✸❋■❍❱❭❳✻❇✿❀◗❬❊❩❃✾◗✭✵❆✻●✽✸✿✺❊❳✹ R(π s ( x) = A exp( j 2πF T z ) = A exp( j 2πFx x) ↔ Aδ ( f x − Fx , f y ) s ' ( x) = A exp( j 2πuRx) ↔ Aδ ( f x , f y − u ) ✂✁☎✄✆✁✞✝✠✟ ✡✁☎✄✆✁☎☛☎✟ ✂ ✄ ✛ ✤ ✄ ✁ ✟ ☎✁ ✄☎✒✍✣✥☛✏✄ ✌☞✎✍✑✏✓✒✕✔✡✖✠✗✡✍✙✘✞✚✠✏✛✔✢✜✕✣✥✤✦✘✞✧✙✏✕★✥✤✪✩✫✤✪✧✠✜✕✣✬✏✭✗✮✘✞✧✠✏✯✘✞✔✰✩✱✘✞✔✢✏✲✘✴✳✫✣✪✍✠✏✓✵✞✤✥✩✱✏✕✧✠✗✡✤✬✘✞✧✠✗ ✄✷✶ ✏✕✸✑✜✕✩✫✚☎★✦✏✹✤✥✧✺✣✪✍✠✏ ✁✞✻ ✘✞✔ ✒✭✜✭✗✛✏✼✘✭✧✠✏✹✍✠✜✭✗ ✿ 1 0✽ P= ✾ 0 0 ✂✁☎✄✆✁☎❃☎✟ ❀❁❂ ❄ ✳❆❅❇✏❈✒✞✘✞✧✠✗✡✤✦✵☎✏✕✔✑✣✪✍✠✏✼✗❉✤✪✧✑❊❋★✦✏❈✗❉✤✪✧☎✖✠✗●✘✞✤✬✵ [ ] s ( z ) = A exp( j 2π Fx x + Fy y ) ↔ Aδ ( f x − Fx , f y − Fy ) ❍ ✜✕✳✡✣✦✏✕✔✑✚☎✔✢✘❏■❋✏✞✒✕✣✪✤✬✘✞✧ s ' ( z ) = s ( Pz ) = A exp( j 2πF T Pz ) = A exp( j 2πFx x) ✂✁☎✄✆✁☎❑☎✟ ❅❆✍☎✤✪★✦✏▲✣✪✍✠✏✼✗❉✚✠✏✭✒✕✣✪✔✡✖☎✩◆▼✠✏✴✒✭✘✭✩✮✏✭✗●❖ S ' (ω ) = 2D s ( Pz ) exp(− jω T z )dz = s ( x,0) exp(− jω x x − jω y y )dxdy = δ (ω x − Fx )δ (ω y ) = S ( Pω ) δ (( I − P )ω ) = S ( Pω ) δ (ω y ) ✗ ☛✍✣ ✒✍✣ ✞✖☛✏✠❘◗ ✂ ✄ ✛ ✤ ✄❚❙ ✌ ✞✂✁☎✁ ✁ ✟ ✁☎✄☎✒✍✣ ✞✡☛✏✠ ✂✁☎✄✆✁☎€☎✟ ❱❯❆▼☎❲☎✤✦✘✞✖✠✗✡★✪❳ s ' ( z ) = s ( PRz ) ↔ S ' (ω ) = S ( PRω ) ✂✁☎✄✆✁☎❨☎✟ 29 ✌ ✞ ✁ ✞✡✠☞✎ ☛ ✒ ✡ ✞✖✠ ✛ ✤✥☛✍✞ ✌☞✒✍✌ ✆ ✡✌ ✒✏✠☞✁ ✁✫❯ ✽✸✲❛✻❳❪✝❊❳❁❜✻●❯❴✵❨❊❇❋✖✵❑❚✺❊☞❋✮❃✾✵❆✻❇✵❑✽❆❃✾✿✬❃✾❯✙✵✸❚✺❊☞❵✭✷❨✻❇✿✺❊☞◗✩▲ ❊ ✻❳❍✮❍❏✳✭✲❛❊☞✵✸❚✺✻●✵ φp F ✻❇✿✺✹ ✻●❋■❊❘❊●✲❘◗✺❊❳✹✭✹✭❊✐✹ ✵❆❃ ✻☎✿ Rπ / 2 F ✻❇✿✺✹❛❭☎❋❏✳✺❍❏❚✭✽✸✿✺❪ ❃✾✿✺❊❘❃✾❯✙✵✸❚✺❊✴✻★✧❬❊❳❍ ✍ ✷❆❊❇✵ ❍✠❍☎✻■▲ ▲ ✎❜✵✸❚❬❊ ❃✾◗✺❍✮❊❇❋❏❉✺❊❳✹ ❖ -✡✏❯❴❋■❊❳❞✾✳✺❊❇✿✺❭❇✽ ❊✐❍ ✽❑✷✸✷✶◗✺❊✖✆ ✍ ✭✭✼ ✩☎✄✠✎ F ' = Fx cos φ p − Fy sin φ p F ' ' = Fx sin φ p + Fy cos φ p ✒✖❍❏✵✸✽❑✲☛✻●✵✸✽❆❃✾✿ ❃✾❯❬✵✸❚✺❊❝✲❛❃✭✹✾✳✭✷✸✳✪❍ ✆ • ✌✍❚✺❊ ✲☛❃✭✹✾✳✭✷❑✳✺❍ ❃✾❯ ✵❑❚✺❊ ❯✫❋■❊❳❞✾✳✺❊❇✿✺❭✮▲ ❭✐✻❇✿ ◗✺❊ ❋■❊✾❭❳❃❳❉✺❊❇❋■❊✾✹ ✻❳❍ | F |= F ' 2 + F ' ' 2 ( Fx cos φ p − Fy sin φ p ) 2 + ( Fy cos φ p + Fx sin φ p = | F |= Fx + Fy 2 2 ❍❏✽❑✲❘✽✸✷❨✻❇❋❴✷✸▲ ◗✺❊✴✹✩❊❇✵❨❊❇❋❴✲✴✽✸✿✺❊❳✹❘✽❑❯✙✵❑❚✺❊ ✵ ❃ ❍❏✽✸✿✭✳✺❍☎❃✾✽❆✹✭❍☞✻❇❋❲❊❘❊●✲❘◗✺❊❳✹✭✹✭❊✾✹ ✝ ✭✭❁✐❚✺❃ π 2 ❍✫✽✸✿✺❭❳❊ ✼✑✌✍❚❬❊❀✲☛❃✭✹✾✳✭✷✸✳✺❍ ❭❳✻❇✿ ✽✸✵✸❚✤✻❇✿✤✻❇✿❬❪❫✷❆❊ θ ✹✾✽✸❯❏❯■❊☎❋✮❊❇✿✭✵✍✵✸❚✺✻❇✿ ❊❇❉✺❊☎❋❥✵✸❚✺❊❢€☎✄ -✹✭❊✾❪✾❋❲❊❳❊❱❉✺✻❇❋❏✽❆❊❇✵❦▲✂❵ ❋✮❃✾❉✺❊❳❍❥✵❆❃❩◗✺❊❱✵❑❚✺❊❢❊❳✻❳❍❏✽❨❊❳❍❏✵ ✵❨❃❩✵✸❋■✻✾❭✛✟✺✼ ✢✔❃✾❋✥❍❏✽✸✲✴❵✭✷✸✽❨❭❇✽✸✵▼▲ | F |= F ✽❆❍❱✻❳❍✮❍❏✳✭✲❛❊❳✹✭✼ • ✒✖❍❏✵✸✽❑✲☛✻●✵✸✽❆❃✾✿ ❃✾❯❬✵✸❚✺❊❩✹✾✽❑❋■❊❳❭●✵✸✽❆❃✾✿✂✆ ✔✖❃❫✿✺❍❏✽❆✹✭❊❇❋❏✽✸✿✺❪ arctan ✵✸❚✺❊ ✻●❋❲❭❇✵❆✻☎✿✺❪ ❊❇✿✭✵ ❃✾❯ ✵✸❚✺❊ ❋❲✻❇✵❑✽❆❃ Fy cos φ p + Fx sin φ p Fx cos φ p − Fy sin φ p ❁❩✽✸❯ ❃✾❯ ✵✸❚✺❊ ❊❣❊★✧✩❵✭❋■❊✾❍✮❍ ✵✸❚✺❊ ❯❏❋❲❊✐❞✾✳✺❊❇✿✺❭❇✽❨❊❳❍ ❊❳❍❏✵❑✽✸✲☛✻●✵❆❊❳✹ ( Fx , Fy ) ❯❏❋■❊❳❞✾✳✺❊●✿❥❭●✽❆❊❳❍✮❁ ✽✸✿ ✵❆❊❇❋❏✲☛❍✤❃✾❯☛❵✺❃✾✷❨✻❇❋ ❭❳❃✭❃✾❋✮✹✾✽✸✿✺✻❇✵❨❊❳❍ arctan Fy cosψ + Fx sin ψ Fx cosψ − Fy sin ψ = arctan | F | sin φ f cos φ p + | F | cos φ f sin φ p | F | cos φ f cos φ p − | F | sin φ f sin φ p = arctan sin(φ p + φ f ) cos(φ p + φ f ) = φp +φf ✍ ✭✭✼ ✩✺❖✖✎ 30 ✌✍❚✭✳✺❍✖✵✸❚✺❊❘✹✾✽✸❋■❊✾❭❇✵✸✽❨❃✾✿✬❃✾❯❙❵✭❋■❃✾❵✺✻✾❪✭✻❇✵✸✽❨❃✾✿✬❭❳✻❇✿✬❃✾✿✭✷▼▲ ◗✺❊✦✹✩❊❇✵❆❊●❋❴✲❘✽❑✿✺❊❳✹ ✵✸❚✺❊✂❍❏✷✸✽❨❭❇✽❑✿✺❪☞❵✭✷❆✻●✿❥❊✂✻❇✿❬❪❫✷❆❊ φp ✼ ✁❏✿✢❯✮✻✐❭❇✵ ❊✙❚❬✻❇❉✺❊✥✵✸❚✭❋❲❊✾❊✙✳✭✿ ✟✭✿✺❃ ✿✺❍ ✽✸✵✸❚✭✽❑✿✤✻ ❭❇✽❑❋■❭❇✷❨❊✴❃✾❯✥❋■✻✾✹✾✽✸✳✺❍ ✻❇✿✺✹ φf Fx + F y 2 2 ✻❇✿✺✹ F1' ✽✸✵✸❚✭✽❑✿☛✵✸❚✺❊✂✳✭✿◆❭❳❊❇❋❴✵❨✻❇✽✸✿✭✵❦▲ ❃❳❯ (F ,φ f ,φ p ) ❃✾✿✭✷▼▲ ✵ ❃✴✽❑✿✺✹✭❊❇❵❬❊❇✿✺✹✭❊❇✿✭✵✔✲❡❊❳✻❳❍❏✳✭❋✮❊❇✲❡❊❇✿✭✵❨❍✏✆ ❃✾❋ ◗✭✳✭✵ ( Fx , Fy , φ p ) ✼❈✌✍❚✺❊✂❯❏❋■❊❳❞✾✳✺❊●✿❥❭✮▲ ❭✐✻❇✿❛◗✺❊✴✹ ❊●✵❆❊❇❋❏✲✦✽✸✿✺❊❳✹ ❃✾✿✭✷▼▲ F2' ✼ ✚✦❃ ❊❇❉✺❊❇❋✥✽✸❯ ❊ ✟✭✿✪❊ ✵✸❚✺❊ ❍❏✷✸✽❨❭❇✽✸✿✺❪ ✻❇✿❬❪❫✷❆❊ φp ✵❑❚✺❊❇✿ F ❃✾✳✭✷❆✹❙◗✺❊❙✹✭❊❇✵❆❊☎❋❏✲❘✽✸✿✺❊✐✹ ✽✸✵❑❚✺❃✾✳✭✵❜✻❇✿✩▲✂✳✭✿✺❭✐❊❇❋❴✵❨✻❇✽✸✿✭✵ y.

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A Guide to Ingres: A User's Guide to the Ingres Product by C. J. Date


by Donald
4.0

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