Frequency Transformation

FREQUENCY TRANSFORMATION

When the cutoff frequency Ωc of the low pass filter is equal to 1 then it is called normalized filter. Frequency transformation techniques are used to generate High pass filter, Bandpass and bandstop filter from the lowpass filter system function.

FREQUENCY TRANSFORMATION (ANALOG FILTER)

FREQUENCY TRANSFORMATION ((DIGITAL FILTER)

Example:

Q) Design high pass butterworth filter whose cutoff frequency is 30 Hz at sampling frequency of 150 Hz. Use BZT and Frequency transformation.

Step 1. To find the prewarp cutoff frequency

ωc* = tan (ωcTs/2) = 0.7265

Step 2. LPF to HPF transformation

For First order LPF transfer function H(s) = 1/(s+1) Scaled

transfer function H*(s) = H(s) |s=ωc*/s H*(s)= s/(s + 0.7265)

Step 3. Find out the digital filter transfer function. Replace s by (z-1)/(z+1)

Q) Design second order band pass butterworth filter whose passband of 200 Hz and 300 Hz and sampling frequency is 2000 Hz. Use BZT and Frequency transformation.

Q) Design second order band pass butterworth filter which meet following specification Lower cutoff frequency = 210 Hz

Upper cutoff frequency = 330 Hz Sampling Frequency = 960 sps

Use BZT and Frequency transformation.