. The Bell System technical journal . ) = ».S(co) is a real function,as for a symmetrical pulse. In most pulse transmission systems, the applied pulses can be ap-proximated by short rectangular pulses. Rectangular pulses of unitamplitude and duration 8 have a frequency spectrum SM^S-^^. () coo/ Z The same pulse transmission characteristic as when an impulse isapplied is obtained with a rectangular pulse if A(o)) is modified by thefactor (a;5/2)/sin {co8/2). In the following it will be assumed that theapplied pulses are of sufficiently short duration to be regarded as im- 732 THE BELL SYSTE
. The Bell System technical journal . ) = ».S(co) is a real function,as for a symmetrical pulse. In most pulse transmission systems, the applied pulses can be ap-proximated by short rectangular pulses. Rectangular pulses of unitamplitude and duration 8 have a frequency spectrum SM^S-^^. () coo/ Z The same pulse transmission characteristic as when an impulse isapplied is obtained with a rectangular pulse if A(o)) is modified by thefactor (a;5/2)/sin {co8/2). In the following it will be assumed that theapplied pulses are of sufficiently short duration to be regarded as im- 732 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 A(ajr+u) = t¥(u) PHASE AMPLITUDE A(a;r--u) =. 1 1 / 1 / 1 / 1 // \ / /J^r r(-U)^ / / 1 • 1 / 1 ^ 1 • 1 / Cfr 1 y .f \ip{CCr -U) = >ir(- U) + ^r Fig. 5 — Transfer of reference frequencj^ from co = 0 to co = cor . pulses or that otherwise the above modification is applied, in which case P(0 = - [ A(w) cos M - /(w)] d<^. () In the latter equation A(co) can also be regarded as the frequencyspectrum of a pulse applied to a transmission system having a constantamplitude characteristic and a phase characteristic i/(co) over the bandof the pulse spectum. Equation () applies to any type of transmission-frequency char-acteristic and is convenient in this form for low-pass characteristics. Forband-pass characteristics as shoA\ai in Fig. 5 however, it is convenientfrom the standpoint of general analysis as well as for numerical evalua-tion to use a reference frequency cor within the tranmsission band, thatis, to employ the transformation 00 = 0;^+ » db^ = du. With the notation a(w) = yl(co) = A{U + COr), ^(lO = i/(w) - i
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