Filtering, 3

When a sinusoidal form https://www.w3.org/1998/Math/MathML" display="inline"> A c o s ⁡ 2 π f t - φ o is applied to a LINEAR FILTER, it is remembered that the output is a sinusoidal form of the same frequency but : its AMPLITUDE A is multiplied by a coefficient https://www.w3.org/1998/Math/MathML" display="inline"> G ( f ) which is the gain of the filter. its PHASE https://www.w3.org/1998/Math/MathML" display="inline"> φ 0 is augmented by a value https://www.w3.org/1998/Math/MathML" display="inline"> φ ( f ) which is its phase shift, this is demonstrated below : An equation shows A cosine function with amplitude A, angular frequency 2 pi f, time t, and phase phi subscript 0 is shown as the input to a linear electrical filter. The output is a cosine signal with amplitude A multiplied by gain G of f, angular frequency 2 pi f, and a phase shift = psi subscript 0 plus phi of f, demonstrating frequency-dependent amplitude scaling and phase modification by the filter. https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003761020/e10523ab-dbe3-4c4f-8f3e-863ae3683950/content/pg80_1.tif "/>