Continuity issue when applying an IIR filter on successive time-frames

Question

I would like to apply a FIR or IIR filter (example: lowpass filter) on successive blocks/time-frames of 1024 samples each.

Possible applications:

• realtime audio processing, such as EQing. At a precise time, we only have the next 1024 samples in a buffer. The next samples to process are not available yet (realtime).

• make a cutoff-time-varying filter by splitting the input signal in blocks, as suggested in this answer.

I tried this here:

import numpy as np
from scipy.io import wavfile
from scipy.signal import butter, lfilter, filtfilt, firwin

sr, x = wavfile.read('input.wav')
x = np.float32(x)
y = np.zeros_like(x)

N  = 1024  # buffer block size = 23ms for a 44.1 Khz audio file
f = 1000  # cutoff
pos = 0  # position

while True:
    b, a = butter(2, 2.0 * f / sr, btype='low')
    y[pos:pos+N] = filtfilt(b, a, x[pos:pos+N])
    pos += N
    f -= 1   # cutoff decreases of 1 hz every 23 ms, but the issue described here also present with constant cutoff!
    print f
    if pos+N > len(x):
        break

y /= max(y)  # normalize

wavfile.write('out_fir.wav', sr, y)

I tried:

• both with a Butterworth filter or a FIR (replace the line before by b, a = firwin(1000, cutoff=f, fs=sr), 1.0)

• both with lfilter and filtfilt (the latter has the advantage to apply the filter forward and backwards, and this solves phase issues),

but here is the problem:

At the boundaries of each time-frames' output, there is a continuity issue, that makes the audio signal heavily distorded.

How to solve this discontinuity problem? I thought about windowing+OverlapAdd method, but there surely must be an easier way.

Answer 1

As mentioned by @sobek in a comment, it's of course needed to specify the initial conditions to allow continuity. This is done with the zi parameter of lfilter.

The problem is solved by changing the main loop by:

while True:
    b, a = butter(2, 2.0 * f / sr, btype='low')
    if pos == 0:
        zi = lfilter_zi(b, a)
    y[pos:pos+N], zi = lfilter(b, a, x[pos:pos+N], zi=zi)
    pos += N
    f -= 1 
    if pos+N > len(x):
        break

This seems to work even if the filter's cutoff (and thus the a and b) is modified at each iteration.