IIR filter design (butter, cheby1) in SciPy - Mini Project: Build & Apply

IIR Filter Design with Butterworth and Chebyshev Type I Filters

📖 Scenario: You are working on a project to clean noisy sensor data. To do this, you need to design digital filters that remove unwanted frequencies.Two common filters are Butterworth and Chebyshev Type I filters. They help keep the important signals while reducing noise.

🎯 Goal: You will create two digital filters using scipy.signal: a Butterworth filter and a Chebyshev Type I filter. Then, you will print their filter coefficients.

📋 What You'll Learn

Use scipy.signal.butter to create a Butterworth filter

Use scipy.signal.cheby1 to create a Chebyshev Type I filter

Set filter order to 4

Set cutoff frequency to 0.3 (normalized frequency)

Print the filter coefficients for both filters

💡 Why This Matters

🌍 Real World

Digital filters like Butterworth and Chebyshev are used in audio processing, sensor data cleaning, and communication systems to remove noise and unwanted signals.

💼 Career

Understanding how to design and use IIR filters is important for roles in signal processing, data analysis, and embedded systems engineering.

1

Create filter order and cutoff frequency variables

Create a variable called order and set it to 4. Create another variable called cutoff and set it to 0.3.

SciPy

# Create variables order and cutoff
# Your code here

Hint

Use simple assignment like order = 4 and cutoff = 0.3.

2

Import butter and cheby1 functions from scipy.signal

Import butter and cheby1 from scipy.signal.

SciPy

order = 4
cutoff = 0.3
# Import butter and cheby1 from scipy.signal
# Your code here

Hint

Use from scipy.signal import butter, cheby1 to import both functions.

3

Create Butterworth and Chebyshev Type I filters

Use butter with order and cutoff to create a lowpass Butterworth filter. Save the output as b_butter and a_butter. Use cheby1 with order, ripple of 1, and cutoff to create a lowpass Chebyshev Type I filter. Save the output as b_cheby and a_cheby.

SciPy

order = 4
cutoff = 0.3
from scipy.signal import butter, cheby1
# Create Butterworth filter coefficients
# Create Chebyshev Type I filter coefficients
# Your code here

Hint

Use butter(order, cutoff, btype='low') and cheby1(order, 1, cutoff, btype='low').

4

Print the filter coefficients

Print the variables b_butter, a_butter, b_cheby, and a_cheby each on a separate line.

SciPy

order = 4
cutoff = 0.3
from scipy.signal import butter, cheby1
b_butter, a_butter = butter(order, cutoff, btype='low')
b_cheby, a_cheby = cheby1(order, 1, cutoff, btype='low')
# Print the filter coefficients
# Your code here

Hint

Use four print statements, one for each coefficient array.

Practice

1. What is the main difference between a Butterworth and a Chebyshev IIR filter in scipy.signal?

easy

A. Butterworth filters are FIR, Chebyshev filters are IIR.

B. Butterworth filters have ripples, Chebyshev filters have a smooth response.

C. Butterworth filters are only for high-pass, Chebyshev only for low-pass.

D. Butterworth filters have a smooth frequency response, Chebyshev filters have ripples in the passband.

Solution

1. Step 1: Understand Butterworth filter characteristics

   Butterworth filters are designed to have a maximally flat frequency response in the passband, meaning no ripples.

2. Step 2: Understand Chebyshev filter characteristics

   Chebyshev filters allow ripples in the passband to achieve a sharper cutoff compared to Butterworth filters.

3. Final Answer:

   Butterworth filters have a smooth frequency response, Chebyshev filters have ripples in the passband. -> Option D

4. Quick Check:

   Butterworth smooth, Chebyshev ripples = D [OK]

Hint: Butterworth = smooth, Chebyshev = ripples [OK]

Common Mistakes:

• Confusing which filter has ripples
• Thinking Butterworth is FIR
• Assuming filter types are limited to passband types

2. Which of the following is the correct way to design a 4th order Butterworth lowpass filter with cutoff frequency 0.3 (normalized) using scipy.signal.butter?

easy

A. b, a = butter(0.3, 4, btype='low')

B. b, a = butter(4, 0.3, btype='low')

C. b, a = butter(4, 0.3, type='lowpass')

D. b, a = butter(order=4, cutoff=0.3, kind='low')

Solution

1. Step 1: Recall butter function signature

   The function signature is butter(N, Wn, btype='low', analog=False, output='ba'), where N is order and Wn is cutoff frequency.

2. Step 2: Check correct parameter usage

   b, a = butter(4, 0.3, btype='low') uses butter(4, 0.3, btype='low'), which matches the signature correctly.

3. Final Answer:

   b, a = butter(4, 0.3, btype='low') -> Option B

4. Quick Check:

   Order first, cutoff second, btype='low' = A [OK]

Hint: Order first, cutoff second, btype='low' in butter() [OK]

Common Mistakes:

• Swapping order and cutoff parameters
• Using wrong keyword names like 'type' or 'kind'
• Passing cutoff frequency as first argument

3. What will be the output shape of the coefficients when running this code?

from scipy.signal import cheby1
b, a = cheby1(3, 1, 0.4, btype='high')

medium

A. (3,), (3,)

B. (3, 3), (3, 3)

C. (4,), (4,)

D. (2,), (2,)

Solution

1. Step 1: Understand cheby1 output

   The function returns numerator (b) and denominator (a) coefficients arrays each of length N+1, where N is filter order.

2. Step 2: Calculate length for order 3

   For order 3, length is 3+1 = 4, so both b and a have shape (4,).

3. Final Answer:

   (4,), (4,) -> Option C

4. Quick Check:

   Length = order + 1 = 4 [OK]

Hint: Coefficients length = order + 1 [OK]

Common Mistakes:

• Assuming length equals order
• Expecting 2D arrays instead of 1D
• Confusing numerator and denominator shapes

4. Identify the error in this code snippet for designing a Chebyshev type I filter:

from scipy.signal import cheby1
b, a = cheby1(5, 0.5, 0.2, btype='bandpass')

medium

A. The cutoff frequency should be a list or tuple for bandpass, not a single float.

B. The ripple parameter is missing and required.

C. The order parameter should be a float, not integer.

D. The btype 'bandpass' is not supported by cheby1.

Solution

1. Step 1: Check bandpass cutoff frequency format

   For bandpass filters, cutoff frequency must be a sequence (list or tuple) of two frequencies, not a single float.

2. Step 2: Verify other parameters

   Order as integer and ripple (second parameter) are correctly provided; btype 'bandpass' is valid.

3. Final Answer:

   The cutoff frequency should be a list or tuple for bandpass, not a single float. -> Option A

4. Quick Check:

   Bandpass cutoff needs two frequencies = C [OK]

Hint: Bandpass cutoff must be two frequencies in a list/tuple [OK]

Common Mistakes:

• Passing single float for bandpass cutoff
• Confusing ripple parameter position
• Using unsupported btype values

5. You want to design a Chebyshev type I lowpass filter with order 6, 0.5 dB ripple, and cutoff frequency 0.25. Which code snippet correctly creates the filter and applies it to a signal x using scipy.signal.lfilter?

hard

A. from scipy.signal import cheby1, lfilter
b, a = cheby1(6, 0.5, 0.25, btype='low')
y = lfilter(b, a, x)

B. from scipy.signal import cheby1, lfilter
b, a = cheby1(6, 0.5, 0.25, btype='high')
y = lfilter(a, b, x)

C. from scipy.signal import butter, lfilter
b, a = butter(6, 0.25, btype='low')
y = lfilter(b, a, x)

D. from scipy.signal import cheby1, lfilter
b, a = cheby1(0.5, 6, 0.25, btype='low')
y = lfilter(b, a, x)

Solution

1. Step 1: Verify cheby1 parameters order

   Order is first parameter (6), ripple second (0.5), cutoff third (0.25), and btype='low' for lowpass.

2. Step 2: Check lfilter usage

   lfilter takes numerator coefficients (b), denominator coefficients (a), and signal (x) in that order.

3. Final Answer:

   from scipy.signal import cheby1, lfilter b, a = cheby1(6, 0.5, 0.25, btype='low') y = lfilter(b, a, x) -> Option A

4. Quick Check:

   Correct order and lfilter usage = A [OK]

Hint: Order, ripple, cutoff in cheby1; lfilter(b, a, x) [OK]

Common Mistakes:

• Swapping order and ripple parameters
• Using butter instead of cheby1
• Swapping b and a in lfilter