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.