Bilinear transformation

Butterworth design

1. Find values of epsilon and lambda, as usual
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   2. 
2. Find actual frequencies using the tan formula
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3. Find the order N
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4. Find Cutoff frequency
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5. Find H(s)
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6. Denormalize using substitution of S (this is analog transfer function)
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7. Find Digital Transfer function with this formula
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8. SIMPLIFY LIKE A CHAD

Chebyshev filter design

1. Find values of epsilon and lambda, as usual
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   2. 
2. Find actual frequencies using the tan formula
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3. Find order of the filter using new formulaa (basically replace butterworths log with cosh inv)
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4. Round upward!
5. Find mu value with this formula
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6. Find A axis:
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7. Find B axis:
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8. Find phik
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9. Find the poles
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10. Denominator polynomial (real part + s whole squared + imaginary part squared) (The denominator polynomial is literally nothing but the equation formed from treating the pole values sk as roots)
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11. Numerator polynomial
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12. Put the transfer function together (numerator and denominator)
13. Find digital version of this analog transfer function by substituting s with this thingamajig
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14. SIMPLIFY SIMPLIFY SIMPLIFY