Sinc Filter

Ripple Attenuation

Transfer function magnitude response features periodic transmission zeros located at integer multiples of the fundamental filter frequency. First-order sinc filters exhibit attenuation slopes of twenty decibels per decade beyond the first null point. Higher-order configurations cascade multiple filter stages, multiplying attenuation slopes and deepening spectral nulls.

The fourth-order variant, known as sinc four, suppresses out-of-band noise sufficiently to support twenty-four-bit analog-to-digital converter decimation.

Group Delay

Linear phase response guarantees constant group delay across all input frequencies, preventing temporal waveform distortion. Passband attenuation near the cutoff frequency causes magnitude droop, requiring post-processing equalization filters to restore flat amplitude response. Finite register bit widths cause coefficient truncation errors, altering null locations in fixed-point DSP implementations.

High stopband sidelobes require combining sinc filters with sharp finite impulse response stages to achieve total out-of-band rejection.

Rejection Limit

Required filter order depends directly on the noise shaping order of preceding delta sigma modulators.