Home | | **Discrete Time Systems and Signal Processing** | Method For Designing Digital Filters Using BZT

Normalized analog transfer function is frequency scaled by replacing s by s/ωp*.

**METHOD FOR DESIGNING DIGITAL
FILTERS USING BZT**

**step 1. Find out the value of ω**c***,.**

**step 2. Find out the value of frequency scaled
analog transfer function**

Normalized
analog transfer function is frequency scaled by replacing s by s/ωp^{*}.

**step 3. Convert into digital filter**

Apply
BZT. i.e Replace s by the ((z-1)/(z+1)). And find out the desired transfer
function of digital function.

**Example:**

Q) Design
first order high pass butterworth filter whose cutoff frequency is 1 kHz at
sampling frequency of 10^{4} sps. Use BZT Method

**Step 1. To find out the cutoff frequency**

ωc = 2∏f

= 2000
rad/sec

**Step 2. To find the prewarp frequency**

ωc* = tan
(ωc Ts/2) = tan(∏/10)

**Step 3. Scaling of the transfer function**

For First
order HPF transfer function H(s) = s/(s+1) Scaled transfer function H*(s) =
H(s) |s=s/ωc*

H^{*}(s)=
s/(s + 0.325)

**Step 4. Find out the digital filter transfer
function. Replace s by (z-1)/(z+1)**

Q) Design
second order low pass butterworth filter whose cutoff frequency is 1 kHz at
sampling frequency of 10^{4} sps.

Q) First
order low pass butterworth filter whose bandwidth is known to be 1 rad/sec .
Use BZT method to design digital filter of 20 Hz bandwidth at sampling
frequency 60 sps.

Q) Second
order low pass butterworth filter whose bandwidth is known to be 1 rad/sec .
Use BZT method to obtain transfer function H(z) of digital filter of 3 DB
cutoff frequency of 150 Hz and sampling frequency 1.28 kHz.

Q) The
transfer function is given as s^{2}+1 / s ^{2}+s+1 The function
is for Notch filter with frequency 1 rad/sec. Design digital Notch filter with
the following specification

(1) Notch
Frequency= 60 Hz

(2) Sampling
frequency = 960 sps.

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