Applying filters (lfilter, sosfilt) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of lfilter with simple coefficients

What is the output array after applying lfilter with given coefficients on the input signal?

SciPy

from scipy.signal import lfilter
import numpy as np

b = [0.5, 0.5]
a = [1]
x = np.array([1, 2, 3, 4, 5])
y = lfilter(b, a, x)
print(y)

A [0.5 1.5 2.5 3.5 4.5]

B [0.5 1. 1.5 2. 2.5]

C [1. 1.5 2.5 3.5 4.5]

D [0.5 1. 2. 3. 4. ]

💡 Hint

Remember that lfilter applies the filter coefficients as a convolution-like operation starting from the first element.

The filter coefficients b = [0.5, 0.5] average the current and previous input values. The output at each step is 0.5 * x[n] + 0.5 * x[n-1], with x[-1] assumed zero at start.

❓ data_output

intermediate

Number of output samples from sosfilt

Given a second-order sections filter and an input signal of length 8, how many samples does sosfilt return?

SciPy

from scipy.signal import sosfilt
import numpy as np

sos = np.array([[1, 0, -1, 1, -1, 0]])
x = np.arange(8)
y = sosfilt(sos, x)
print(len(y))

A 7

B 8

C 9

D 6

💡 Hint

The output length of sosfilt matches the input length.

sosfilt applies the filter to the input signal and returns an output array of the same length as the input.

🔧 Debug

advanced

Identify the error in lfilter usage

What error will this code raise when run?

SciPy

from scipy.signal import lfilter
b = [1, -1]
a = [1, -0.9]
x = [1, 2, 3]
y = lfilter(b, a)
print(y)

A TypeError: lfilter() missing 1 required positional argument: 'x'

B ValueError: Input arrays must have the same length

C IndexError: list index out of range

D No error, prints filtered output

💡 Hint

Check the function call arguments carefully.

The lfilter function requires three arguments: b, a, and the input signal x. Omitting x causes a TypeError.

🧠 Conceptual

advanced

Effect of filter coefficients on output shape

Which statement about the output length of lfilter and sosfilt is correct?

A <code>lfilter</code> output length is always shorter than input length; <code>sosfilt</code> output length equals input length

B <code>lfilter</code> output length is always longer than input length; <code>sosfilt</code> output length equals input length

C <code>lfilter</code> output length equals input length; <code>sosfilt</code> output length is always longer

D Both <code>lfilter</code> and <code>sosfilt</code> output lengths equal input length

💡 Hint

Think about how these filters process signals sample by sample.

Both lfilter and sosfilt produce output arrays with the same length as the input signal.

🚀 Application

expert

Filter a noisy signal and identify the filtered output mean

Given a noisy signal x and a low-pass filter defined by second-order sections sos, what is the mean of the filtered output y?

SciPy

import numpy as np
from scipy.signal import sosfilt

np.random.seed(0)
x = np.sin(np.linspace(0, 2*np.pi, 100)) + 0.5 * np.random.randn(100)
sos = np.array([[0.2929, 0.5858, 0.2929, 1.0000, -0.0000, 0.1716]])
y = sosfilt(sos, x)
print(round(np.mean(y), 3))

A -0.005

B -0.050

C 0.002

D 0.050

💡 Hint

The filter smooths the signal, so the mean should be close to zero.

The filtered signal mean is close to zero because the low-pass filter removes noise but preserves the sine wave's zero-centered nature.