Finding attenuation frequency from the roots
Okumaya devam et...
← Previous revision | Revision as of 22:35, 4 May 2024 |
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| # Find <math>P(S) = G_{num}(S)G_{num}(-S) - B^2_{arith}G_{den}(S)G_{den}(-S)</math> | # Find <math>P(S) = G_{num}(S)G_{num}(-S) - B^2_{arith}G_{den}(S)G_{den}(-S)</math> |
| # Find the roots of P(S) using a [[Root-finding algorithms|root finding algorithm.]] | # Find the roots of P(S) using a [[Root-finding algorithms|root finding algorithm.]] |
| # Of the set of roots from above, select the positive imaginary root for off order filters, and positive real root for even order filters. | |
| # Of the set of roots from above, there will be one and only one positive imaginary root for all-pole filters, and others for attenuations that lye between the pass band and stop band attenuation. The imaginary value of this root will be frequency that results in the desired attenuation, <math>\omega_c </math>. Cutoff attenuations that are above the pass band ripple or below the stop band ripple will come back with multiple roots, so the correct root will have to be selected. | |
| ## Cutoff attenuations that are above the pass band ripple or below the stop band ripple will come back with multiple roots, so the correct root will have to be selected. | |
| === Obtaining the reflection coefficient, R(s) === | === Obtaining the reflection coefficient, R(s) === |
Okumaya devam et...