Module hbf 

Half-band filters and cascades

Used to perform very efficient high-dynamic range rate changes by powers of two.

Symmetric and anti-symmetric FIR filter prototype.

Generics

• M: number of taps, one-sided. The filter has effectively 2*M DSP taps

Half band decimation/interpolation filters

Half-band filters (rate change of 2) and cascades of HBFs are implemented in HbfDec and HbfInt etc. The half-band filter has unique properties that make it preferable in many cases:

• only needs M multiplications (fused multiply accumulate) for 4*M taps
• HBF decimator stores less state than a generic FIR filter
• as a FIR filter has linear phase/flat group delay
• very small passband ripple and excellent stopband attenuation
• as a cascade of decimation/interpolation filters, the higher-rate filters need successively fewer taps, allowing the filtering to be dominated by only the highest rate filter with the fewest taps
• In a cascade of HBF the overall latency, group delay, and impulse response length are dominated by the lowest-rate filter which, due to its manageable transition band width (compared to single-stage filters) can be smaller, shorter, and faster.
• high dynamic range and inherent stability compared with an IIR filter
• can be combined with a CIC filter for non-power-of-two or even higher rate changes

The implementations here are all no_std and no-alloc. They support (but don’t require) in-place filtering to reduce memory usage. They unroll and optimize extremely well targetting current architectures, e.g. requiring less than 4 instructions per input item for the full HbfDecCascade on Skylake. The filters are optimized for decent block sizes and perform best (i.e. with negligible overhead) for blocks of 32 high-rate items or more, depending very much on architecture.

Structs

EvenAntiSymmetric

Linear phase FIR taps for odd = false and symmetric = false

EvenSymmetric

Linear phase FIR taps for odd = false and symmetric = true

HbfDec

Half band decimator (decimate by two) state

HbfInt

Half band interpolator (interpolation rate 2) state

OddAntiSymmetric

Linear phase FIR taps for odd = true and symmetric = false

OddSymmetric

Linear phase FIR taps for odd = true and symmetric = true

Constants

HBF_CASCADE_BLOCK

Cascade block size

HBF_DEC_CASCADE

HBF decimation cascade

HBF_INT_CASCADE

HBF interpolation cascade

HBF_PASSBAND

Passband width in units of lowest sample rate

HBF_TAPS

Half band filters taps

HBF_TAPS_98

Half band filter cascade taps

Functions

hbf_dec_response_length

Response length, effective number of taps

hbf_int_response_length

Response length, effective number of taps

Type Aliases

HbfDec2

Half-band decimation filter state

HbfDec4

HBF Decimate-by-4 cascade state

HbfDec8

HBF Decimate-by-8 cascade state

HbfDec16

HBF Decimate-by-16 cascade state

HbfDec32

HBF Decimate-by-32 cascade state

HbfInt2

Half-band interpolation filter state

HbfInt4

HBF interpolate-by-4 cascade state

HbfInt8

HBF interpolate-by-8 cascade state

HbfInt16

HBF interpolate-by-16 cascade state

HbfInt32

HBF interpolate-by-32 cascade state