FIR filter design (firwin) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of FIR filter coefficients using firwin

What is the output array of FIR filter coefficients generated by the following code?

SciPy

from scipy.signal import firwin
coeffs = firwin(numtaps=5, cutoff=0.3)
print(coeffs)

A [0.0375 0.2491 0.4270 0.2491 0.0375]

B [0.1 0.2 0.4 0.2 0.1]

C [0.2 0.2 0.2 0.2 0.2]

D [0.05 0.15 0.5 0.15 0.05]

💡 Hint

The firwin function creates a lowpass filter with symmetric coefficients.

The firwin function with numtaps=5 and cutoff=0.3 generates a symmetric lowpass FIR filter. The coefficients sum to 1 and have a shape similar to option A.

❓ data_output

intermediate

Length of FIR filter coefficients array

What is the length of the FIR filter coefficients array generated by this code?

SciPy

from scipy.signal import firwin
coeffs = firwin(numtaps=11, cutoff=0.5)
print(len(coeffs))

A 10

B 9

C 12

D 11

💡 Hint

The numtaps parameter defines the number of filter coefficients.

The length of the coefficients array equals the numtaps parameter, which is 11 here.

🔧 Debug

advanced

Error raised by incorrect firwin usage

What error does this code raise?

SciPy

from scipy.signal import firwin
coeffs = firwin(numtaps=4, cutoff=[0.2, 0.5], pass_zero=False)

A ValueError: numtaps must be odd for bandpass filters

B TypeError: cutoff must be a float for lowpass filters

C RuntimeWarning: Filter coefficients may be unstable

D No error, runs successfully

💡 Hint

Bandpass filters require an odd number of taps.

When designing a bandpass filter with firwin, numtaps must be odd. Here numtaps=4 is even, so ValueError is raised.

🚀 Application

advanced

Choosing cutoff frequencies for a bandstop FIR filter

You want to design a bandstop FIR filter using firwin to remove frequencies between 0.3 and 0.5 (normalized). Which cutoff parameter should you use?

A [0.0, 0.3]

B [0.3, 0.5]

C [0.0, 0.3, 0.5, 1.0]

D [0.3, 0.5, 1.0]

💡 Hint

For bandstop filters, cutoff is a list of two frequencies defining the stop band.

The cutoff parameter for bandstop filters is a list with two values marking the stop band edges, e.g., [0.3, 0.5].

🧠 Conceptual

expert

Effect of increasing numtaps on FIR filter characteristics

What is the main effect of increasing the numtaps parameter in firwin when designing an FIR filter?

A The filter becomes unstable and may cause runtime errors

B The filter's cutoff frequency shifts to a higher value

C The filter's transition band becomes narrower, improving frequency selectivity

D The filter coefficients become non-symmetric

💡 Hint

More taps mean more coefficients to shape the filter response.

Increasing numtaps increases filter length, which narrows the transition band and improves frequency selectivity.

Practice

1. What is the primary purpose of the firwin function in signal processing?

easy

A. To perform Fourier transform on signals

B. To design FIR filter coefficients based on cutoff frequencies

C. To generate random noise signals

D. To calculate the power spectrum of a signal

Solution

1. Step 1: Understand the role of FIR filters

   FIR filters are used to remove unwanted parts of signals by filtering specific frequency ranges.

2. Step 2: Identify what firwin does

   firwin generates the coefficients needed to build these FIR filters by specifying cutoff frequencies.

3. Final Answer:

   To design FIR filter coefficients based on cutoff frequencies -> Option B

4. Quick Check:

   firwin creates filter coefficients [OK]

Hint: Remember firwin creates filter coefficients from cutoff frequencies [OK]

Common Mistakes:

• Confusing firwin with Fourier transform functions
• Thinking firwin generates signals instead of filters
• Assuming firwin calculates signal power

2. Which of the following is the correct way to import the firwin function from SciPy?

easy

A. import firwin from scipy.signal

B. from scipy import firwin

C. from scipy.signal import firwin

D. import firwin.signal

Solution

1. Step 1: Recall Python import syntax

   To import a specific function from a module, use from module import function.

2. Step 2: Apply to firwin in scipy.signal

   The correct import is from scipy.signal import firwin.

3. Final Answer:

   from scipy.signal import firwin -> Option C

4. Quick Check:

   Correct Python import syntax for firwin [OK]

Hint: Use 'from scipy.signal import firwin' to import correctly [OK]

Common Mistakes:

• Using incorrect import syntax like 'import firwin from ...'
• Importing firwin directly from scipy instead of scipy.signal
• Trying to import firwin as a submodule

3. What will be the length of the filter coefficients array generated by firwin(numtaps=5, cutoff=0.3)?

medium

A. 5

B. 4

C. 3

D. 6

Solution

1. Step 1: Understand the numtaps parameter

   The numtaps parameter specifies the number of filter coefficients (taps) to generate.

2. Step 2: Check the given numtaps value

   Here, numtaps=5 means the output array will have 5 coefficients.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   numtaps = output length = 5 [OK]

Hint: numtaps equals the length of the filter coefficients array [OK]

Common Mistakes:

• Confusing cutoff frequency with output length
• Assuming output length is cutoff * numtaps
• Thinking output length is numtaps - 1

4. Identify the error in this code snippet intended to create a bandpass filter:

from scipy.signal import firwin
coeffs = firwin(cutoff=0.4, numtaps=7, pass_zero=False)

medium

A. numtaps must be even

B. The order of arguments is incorrect

C. pass_zero cannot be False

D. The cutoff frequency must be a list for bandpass filters

Solution

1. Step 1: Understand pass_zero=False meaning

   Setting pass_zero=False designs a highpass or bandpass filter.

2. Step 2: Check cutoff parameter type

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

3. Final Answer:

   The cutoff frequency must be a list for bandpass filters -> Option D

4. Quick Check:

   Bandpass cutoff needs list [OK]

Hint: Use list for cutoff when pass_zero=False for bandpass [OK]

Common Mistakes:

• Passing single float cutoff for bandpass filter
• Assuming pass_zero=False only means highpass
• Believing numtaps must be even

5. You want to design a bandstop FIR filter with cutoff frequencies at 0.2 and 0.5 (normalized). Which firwin call correctly creates this filter?

hard

A. firwin(numtaps=51, cutoff=[0.2, 0.5], pass_zero=True)

B. firwin(numtaps=51, cutoff=[0.2, 0.5], pass_zero=False)

C. firwin(numtaps=51, cutoff=0.35, pass_zero=True)

D. firwin(numtaps=51, cutoff=0.35, pass_zero=False)

Solution

1. Step 1: Understand bandstop filter parameters

   A bandstop filter blocks frequencies between two cutoff points and passes others. For firwin, pass_zero=True with a list cutoff designs a bandstop filter.

2. Step 2: Match parameters to bandstop design

   Using cutoff=[0.2, 0.5] and pass_zero=True correctly creates a bandstop filter with those cutoff frequencies.

3. Final Answer:

   firwin(numtaps=51, cutoff=[0.2, 0.5], pass_zero=True) -> Option A

4. Quick Check:

   Bandstop needs cutoff list and pass_zero=True [OK]

Hint: Bandstop filter: cutoff list + pass_zero=True [OK]

Common Mistakes:

• Using pass_zero=False for bandstop filters
• Passing single cutoff frequency for bandstop
• Confusing bandpass and bandstop parameters