IIR filter design (butter, cheby1) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to design a Butterworth lowpass filter with cutoff frequency 0.3.

SciPy

from scipy.signal import [1]

b, a = [1](4, 0.3, btype='low')

Drag options to blanks, or click blank then click option'

Afirwin

Bcheby1

Cbutter

Dlfilter

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'cheby1' instead of 'butter' for Butterworth filter design.

Confusing filter design functions with filtering functions like 'lfilter'.

The butter function designs a Butterworth filter. Here, it creates a 4th order lowpass filter with cutoff 0.3.

2fill in blank

medium

Complete the code to design a Chebyshev type I highpass filter with 3 dB ripple and cutoff frequency 0.4.

SciPy

from scipy.signal import cheby1

b, a = cheby1(5, [1], 0.4, btype='high')

Drag options to blanks, or click blank then click option'

A1

B3

C0.5

D0.1

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing the ripple parameter with cutoff frequency.

Using values less than 1 dB which might be too small for this example.

The second argument to cheby1 is the ripple in the passband in decibels. Here, 3 dB ripple is specified.

3fill in blank

hard

Fix the error in the code to design a Butterworth bandpass filter between 0.2 and 0.5.

SciPy

from scipy.signal import butter

b, a = butter(4, [1], btype='bandpass')

Drag options to blanks, or click blank then click option'

A[0.2, 0.5]

B0.5

C0.35

D0.2, 0.5

Attempts:

3 left

💡 Hint

Common Mistakes

Passing two separate arguments instead of a list for cutoff frequencies.

Using a single float value for bandpass cutoff.

The cutoff frequencies for a bandpass filter must be given as a list or tuple of two values, e.g., [0.2, 0.5].

4fill in blank

hard

Fill both blanks to create a Chebyshev type I bandstop filter with order 3, ripple 2 dB, and cutoff frequencies 0.3 and 0.6.

SciPy

from scipy.signal import cheby1

b, a = cheby1([1], [2], [0.3, 0.6], btype='bandstop')

Drag options to blanks, or click blank then click option'

A3

B2

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping order and ripple values.

Using ripple values too large or too small.

The first argument is the filter order (3), and the second is the passband ripple in dB (2) for the Chebyshev type I filter.

5fill in blank

hard

Fill all three blanks to create a Butterworth lowpass filter of order 6 with cutoff 0.25 and design it using 'butter'.

SciPy

from scipy.signal import [1]

b, a = [1]([2], [3], btype='low')

Drag options to blanks, or click blank then click option'

Abutter

B6

C0.25

Dcheby1

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing 'butter' and 'cheby1' in the same code.

Using incorrect order or cutoff values.

The butter function is imported and called with order 6 and cutoff 0.25 to design a lowpass Butterworth filter.

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