Phase Response
Now we may isolate the filter phase response by taking a ratio of the and in Eq.(1.5):
Substituting the expansions of and yields
Thus, the phase response of the simple lowpass filter is
We have completely solved for the frequency response of the simplest low-pass filter given in Eq.(1.1) using only trigonometric identities. We found that an input sinusoid of the form
Next Section:
Complex Sinusoids
Previous Section:
Amplitude Response