Pole locations and transfer function The poles of the Chebyshev I filter are laid to those of the Butterworth filter of the similar order and are shown on an ellipse in the s-plane. If N is odd there shall be a pole on the negative real axis. In order to search the pole locations and hence the transfer function we start the parameter β

The poles of H(s), s_k = ζk  + jΩ_k, k = 0, 1, ... , (N-1), are provided by

Note that if the sinh β and cosh β  terms were not shown we could have the pole situation of the normalized Butterworth filter (on the unit circle), that is,

with σ²_k  + Ω²_k = 1 which is the unit circle. Thus, the hyperbolic sine and cosine terms are scale factors which, when applied to the Butterworth pole coordinates, provide the pole coordinates of a Chebyshev I filter of the similar order. The Chebyshev poles are situated on an ellipse in the s- plane defined by

The major axis of the ellipse is on the imaginary (jΩ) axis and the minor axis is on the real axis and the foci are at Ω = ±1. The 3 dB cut-off frequency happens at the point where the ellipse collides the jΩ axis, that is, at Ω = cosh β. In taking together the transfer function, H(s), we laid on the symmetry of pole positions and create use of the left half plane poles only. Finally, the pole positions are measure by the actual "cut-off frequency" Ω₁. That last step amounts to s→ s/Ω₁ (in the case of the Butterworth design this was s→ s/Ω_c).

Email based Pole locations and transfer function of the Chebyshev assignment help - Pole locations and transfer function of the Chebyshev homework help at Expertsmind

Are you finding answers for Pole locations and transfer function of the Chebyshev based questions? Ask Pole locations and transfer function of the Chebyshev questions and get answers from qualified and experienced  Digital signal processing tutors anytime from anywhere 24x7. We at www.expertsmind.com offer Pole locations and transfer function of the Chebyshev assignment help -Pole locations and transfer function of the Chebyshev homework help and  Digital signal processing  problem's solution with step by step procedure.

Why Expertsmind for Digital signal processing assignment help service

1.     higher degree holder and experienced tutors

2.     Punctuality and responsibility of work

3.     Quality solution with 100% plagiarism free answers

4.     On Time Delivery

5.     Privacy of information and details

6.     Excellence in solving Digital signal processing queries in excels and word format.

7.     Best tutoring assistance 24x7 hours