Comparing Two Discrete Lowpass Filters with Low Distortion

In signal processing, elegant algorithms exist for digital filters that can pass or block selected ranges of frequencies and respond to other aspects of the signal.

The Parks–McClellan algorithm is often used to design a finite impulse response (FIR) discrete filter that is Chebyshev optimized with linear phase. However, an infinite impulse response (IIR) filter can have a maximum of

|H(iω)-exp(-iωd)|

over the passband for a constant delay

d

that is as small as a linear phase FIR filter but with shorter delay. This Demonstration compares an optimal discrete FIR lowpass filter with an IIR lowpass filter. The passband of each lowpass filter is

[0,

ω

pass

]

, where

ω

pass

=0.5π

. The stopband of each lowpass filter is

[

ω

stop

,π]

, where

ω

stop

=0.6π

with 36 dB attenuation in the stopband. The gain of the IIR filter in the low end of the transition band is higher than the gain of the FIR filter, and that is a tradeoff made to achieve an even lower group delay in the passband than could otherwise be found.