Filter recognition from transfer function

1. How do you identify a filter using the transfer function?
2. How do you identify a filter from Z transform?
3. How do you know if a filter is high pass or low pass from transfer function?
4. What is the transfer function of IIR filters?

How do you identify a filter using the transfer function?

At ω = 0 and ω = ∞, the above equation reduces to zero; when ω = a/ω or ω² = a, the H is equal to K/b, which indicates that this equation describes a filter that attenuates low and high frequencies and passes midband frequencies; in other words, the equation describes a bandpass filter.

How do you identify a filter from Z transform?

So, H(z)=1+exp(−2jω) at z=exp(jω). When ω=0;H(z)=2 and w=π gives H(z)=2. Thus, both at high and low frequencies the the system function provides same gain and hence the filter with the given H(z) is a BAND REJECT/ NOTCH FILTER with H(z)=0 at ω=π/2.

How do you know if a filter is high pass or low pass from transfer function?

Yeah, it's easy. A high pass filter will have a transfer function that drops off at low frequencies. A low pass filter's transfer function drops off at high frequencies, and a band pass filter drops off on both sides.

What is the transfer function of IIR filters?

A general IIR transfer function can be written as in equation 2.22. The numerator in this transfer function can be implemented by using an FIR filter. The denominator entails the use of a recursive structure. The cascade of these realizations for the numerator and denominator is shown in Figure 2.11.