EE5410 Signal processing
The magnitude-phase representation of the frequency response of LTI systems
The effect that an LTI system has on the input is to CHANGE the complex amplitude of EACH of the frequency components of the signal.
Y(jw) = H(jw)X(jw) -- continuous-time
1. the effect of an LTI system has on the magnitude of the Fourier transform of the Fourier transform of the signal is to SCALE it by magnitude of the frequency response. For this reason, | H(jw) | is commonly referred to as the GAIN of the system.
2. The phase of the input is modified by the LTI system by adding the phase to it, and is typically referred to as the PHASE SHIFT of the system.
3. The phase shift of the system can change the relative phase relationship among the components of the input, possibly resulting in significant modification to the time domain characteristics of the input even when the GAIN of the system is constant for all frequencies.