Frequency Transformation
Frequency transformation is needful for converting a frequency-selective filter from single type to different type.
Analog-to-analog transformations Suppose we are provided a continuous-time normalized low pass filter G(s) with a cut-off frequency of 1 rad/sec. Then what is the effect of the transformation s′ = sΩc where s′ shows the transformed frequency variable? In different words, we prepare the substitution s → s′/Ωc in the transfer function. Since s′ = sΩc relates to W′ =ΩΩc, it follows that the frequency range 0 ≤ Ω ≤ 1 is related into the range 0 ≤Ω′ ≤Ωc. Thus G(s′) shows a low pass filter with a cut-off frequency of Ωc. In the last of what shows, rather than use an explicitly different symbol s′ we need instead shows such transformation by s → s/Ωc and the given transfer function by H(s) = G(s)] s → s / Wc .
Digital-to-digital transformations Similarly, a group of transformations may be found that take a low-pass digital filter and convert it into another low-pass or high-pass or band-pass or band stop digital filter.
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