### 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

*any*input signal.

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