The formula to calculate the transfer function H(z) is:
\[ H(z) = \frac{1 - 2r\cos(\omega₀) + r^2}{1 - 2\cos(\omega₀) + 1} \]
Where:
Let's say the radius (\( r \)) is 0.9 and the angular frequency (\( \omega₀ \)) is 1 radian. Using the formula:
\[ H(z) = \frac{1 - 2 \times 0.9 \times \cos(1) + 0.9^2}{1 - 2 \times \cos(1) + 1} \]
We get:
\[ H(z) = \frac{1 - 1.8 \times 0.5403 + 0.81}{1 - 2 \times 0.5403 + 1} \approx 0.91 \]
So, the transfer function \( H(z) \) is approximately 0.91.
A notch filter, also known as a band-stop filter, is a type of filter that attenuates a specific range of frequencies while allowing frequencies outside that range to pass through. It is commonly used in signal processing to remove unwanted frequencies or noise from a signal. The notch filter is characterized by its notch frequency, which is the frequency at which the attenuation is maximum. This type of filter is widely used in audio processing, communication systems, and various electronic applications to eliminate interference and improve signal quality.
