Applications of the Fourier Integral in the Analysis of Color Television Systems

It is shown that a linear-phase network has a better transient response than one having a minimum net phase shift, since it will have a symmetrical transient response to a unit-impulse or unit-step driving force. In the case of an RC low-pass filter characteristic, one having a linear phase shift will have a faster rise time than one having minimum net phase shift. For best response there should be regions of controlled gain, with linear phase shift well beyond the cutoff frequency of the filter. The first region beyond cutoff should be carefully designed for the best transient rise time. In the case of a video amplifier in a color television receiver with a trap at 3.58 megahertz and high attenuation beyond 4.5 megahertz, the gain of the system halfway between these two frequencies should be approximately 6 db less than the gain at low frequencies to best utilize the available bandwidth. The response of an idealized bandpass filter with a linear phase shift to a ramp change of the carrier-wave phase is worked out. Such a network can follow the ramp phase change quite well over most of the range, but it has a phase overshoot and some coincidental amplitude modulation.