. The Bell System technical journal . abstractionwhich cannot be physically realized since it will have phase distortionand infinite transmission delay. It can, however, be approached withsufficiently elaborate phase equalization. For the above type of characteristic, A(oo) — 1 between oj = 0 andcoi, while i/(co) = coTd, where Td is the transmission delay. With thesevalues in (): Pit) = d(x)i sin coi^o TT COi^o () where ^o = ^ — t^ is the time referred to the peak amplitude of thereceived pulse. The resultant pulse transmission characteristic is shown in Fig. 7,with the factor Scoi/x o
. The Bell System technical journal . abstractionwhich cannot be physically realized since it will have phase distortionand infinite transmission delay. It can, however, be approached withsufficiently elaborate phase equalization. For the above type of characteristic, A(oo) — 1 between oj = 0 andcoi, while i/(co) = coTd, where Td is the transmission delay. With thesevalues in (): Pit) = d(x)i sin coi^o TT COi^o () where ^o = ^ — t^ is the time referred to the peak amplitude of thereceived pulse. The resultant pulse transmission characteristic is shown in Fig. 7,with the factor Scoi/x omitted. The peak amplitude is attained after aninfinite time, since the above type of characteristic can be realized onlywith Td —> 00. The impulse characteristic is zero when coiio = ±nT, orto = ±Ti, ± 2ri, • • • ± UTi where 1 ()Impulses can thus be transmitted at the latter intervals Avithout 2f; (a) AMPLITUDE AND PHASECHARACTERISTICS (b)IMPULSE CHARACTERISTIC -to*— 1 —•■to K-PHASE AMPLITUDE SINT^toA. FREQUENCY, CV , , , , - , ; , - , , i i Fig. 7 — Idealized low-pass characteristic with sharp complete cut-off. THEORETICAL FlXDAlVIEXTAES OF PULSE TRANSMISSION 737 mutual interference between the peaks of the received pulses. This is abasic theorem underhing the determination of the transmission capacityof idealized systems. For an idealized bandpass characteristic between wo and wi, it followsfrom () with ^(») = iiTd and ^( — u) = —iiTd that the impulsecharacteristic with respect to the midband frequency w, = co„, is P(t) = 2 cos[co„,^o - M P(t), () where P(t) is given by () and i/o = ^m — (^mTd is the phase interceptat zero frequency. For the transmission characteristic to be ideal in thesense that the peak pulse amplitude occurs when ^o = ^ — r^ = 0, it isnecessary that \{/o = ±nT, where n is an integer. This is not necessaryif the bandwidth is small in relation to the midband frequency. Therewill then be a large num
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
