bw_iir2
Lightweight and fast second-order IIR filter (biquad) in TDF-II form.
This is not a regular DSP module, as it exposes state and coefficients, and it's not appropriate for time-varying operation. If you need that, check out bw_ap2, bw_hs2, bw_ls2, bw_mm2, bw_notch, bw_peak, and bw_svf.
Version: 1.0.0
License:
- GPLv3 for free software/open source projects, or
- proprietary license for all other products.
Included in Brickworks, which is:
- FREE for free software/open source projects (GPLv3), or
- 3,000 € for all other products (proprietary license).
Examples
Here you can download one or more example VST3 plugins for Windows, macOS and Linux. Source code of the audio engine(s) is included in the archive(s).
| Description | Link |
|---|---|
| Second-order recursive filter | Download |
API
Module type: Utility
bw_iir2_reset()
static inline void bw_iir2_reset(
float x_0,
float * BW_RESTRICT y_0,
float * BW_RESTRICT s1_0,
float * BW_RESTRICT s2_0,
float b0,
float b1,
float b2,
float a1,
float a2);
Computes and puts the initial output in y_0 and the initial states in s1_0 and s2_0, given the initial input x_0 and coefficients b0, b1, b2, a1, and a2.
The given coefficients must describe a stable filter.
bw_iir2_reset_multi()
static inline void bw_iir2_reset_multi(
const float * x_0,
float * y_0,
float * BW_RESTRICT s1_0,
float * s2_0,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels);
Computes and puts each of the n_channels initial outputs in y_0 and initial states in s1_0 and s2_0, given the corresponding initial inputs x_0 and coefficients b0, b1, b2, a1, and a2.
y_0 and/or s_0 may be BW_NULL, in which case the corresponding values are not written anywhere.
The given coefficients must describe a stable filter.
bw_iir2_process1()
static inline void bw_iir2_process1(
float x,
float * BW_RESTRICT y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2);
Processes one input sample x using coefficients b0, b1, b2, a1, and a2. The output sample and next states value are put in y and s1/s2 respectively.
The given coefficients must describe a stable filter.
bw_iir2_process()
static inline void bw_iir2_process(
const float * x,
float * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_samples);
Processes the first n_samples of the input buffer x and fills the first n_samples of the output buffer y, while using coefficients b0, b1, b2, a1, and a2. The next state values are put in s1 and s2.
The given coefficients must describe a stable filter.
bw_iir2_process_multi()
static inline void bw_iir2_process_multi(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels,
size_t n_samples);
Processes the first n_samples of the n_channels input buffers x and fills the first n_samples of the n_channels output buffers y, while using coefficients b0, b1, b2, a1, and a2. The next n_channels state values are put in s1 and s2.
The given coefficients must describe a stable filter.
bw_iir2_coeffs_ap2()
static inline void bw_iir2_coeffs_ap2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order allpass filter (180° shift at cutoff, approaching 360° shift at high frequencies) with unitary gain, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the quality factor Q (in [1e-6f, 1e6f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_bp2()
static inline void bw_iir2_coeffs_bp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order bandpass filter (6 dB/oct) with peak gain Q (linear gain), using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the quality factor Q (in [1e-6f, 1e6f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_hp2()
static inline void bw_iir2_coeffs_hp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order highpass filter (12 dB/oct) with gain asymptotically approaching unity as frequency increases, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the quality factor Q (in [1e-6f, 1e6f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_hs2()
static inline void bw_iir2_coeffs_hs2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char high_gain_dB,
float high_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order high shelf filter (12 dB/oct) with unitary DC gain, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, must be finite and positive), the quality factor Q (in [1e-6f, 1e6f]), and the high-frequency gain high_gain, either as linear gain (in [1e-30f, 1e30f]) if high_gain_dB is 0, or otherwise in dB (in [-600.f, 600.f]). If prewarp_freq is 0, then the prewarpingfrequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
cutoff * bw_sqrtf(bw_sqrtf(high_gain)) must be in [1e-6f, 1e12f], where high_gain is expressed as linear gain.
bw_iir2_coeffs_lp2()
static inline void bw_iir2_coeffs_lp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order lowpass filter (12 dB/oct) with unitary DC gain, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the quality factor Q (in [1e-6f, 1e6f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_ls2()
static inline void bw_iir2_coeffs_ls2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char dc_gain_dB,
float dc_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order low shelf filter (12 dB/oct) with gain asymptotically approaching unity as frequency increases, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, must be finite and positive), the quality factor Q (in [1e-6f, 1e6f]), and the dc_gain, either as linear gain (in [1e-30f, 1e30f]) if high_gain_dB is 0, or otherwise in dB (in [-600.f, 600.f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
cutoff * bw_rpcf(bw_sqrtf(bw_sqrtf(dc_gain))) must be in [1e-6f, 1e12f], where dc_gain is expressed as linear gain.
bw_iir2_coeffs_mm2()
static inline void bw_iir2_coeffs_mm2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float coeff_x,
float coeff_lp,
float coeff_bp,
float coeff_hp,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order filter implementing an approximation of the Laplace-domain transfer function
H(s) = coeff_x + (coeff_hp s^2 + 2 pi fc s coeff_bp + (2 pi fc)^2 coeff_lp) / (s^2 + 2 pi fc / Q s + (2 pi fc)^2)
where fc is the cutoff frequency and Q is the quality factor, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), the quality factor Q (in [1e-6f, 1e6f]), and output coefficients coeff_x, coeff_lp, coeff_bp, coeff_hp (all must be finite). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_notch()
static inline void bw_iir2_coeffs_notch(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, b2, a1, and a2 resulting in a second-order notch filter with unitary gain at DC and asymptotically as frequency increases, and null gain at cutoff frequency, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the quality factor Q (in [1e-6f, 1e6f]). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
bw_iir2_coeffs_peak()
static inline void bw_iir2_coeffs_peak(
float sample_rate,
float cutoff,
char use_bandwidth,
float Q_bandwidth,
char prewarp_at_cutoff,
float prewarp_freq,
char peak_gain_dB,
float peak_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
Computes and puts coefficient values in b0, b1, and a1 resulting in a second-order peak filter with unitary gain at DC and asymptotically as frequency increases, using the bilinear transform with prewarping.
It takes the sample_rate (Hz, must be finite and positive), the cutoff frequency (Hz, in [1e-6f, 1e12f]), and the peak_gain, either as linear gain (in [1e-30f, 1e30f]) if peak_gain_dB is 0, or otherwise in dB (in [-600.f, 600.f]). Q_bandwidth indicates either the quality factor (in [1e-6f, 1e6f]) if use_bandwidth is 0, or otherwise the bandwidth (octaves, in [1e-6f, 90.f]), designating the distance between midpoint gain frequencies (i.e., frequencies with gain = peak gain / 2 in dB terms). If prewarp_freq is 0, then the prewarping frequency matches cutoff, otherwise the value specified by prewarp_freq (Hz, in [1e-6f, 1e12f], however interally limited to avoid instability) is used.
If use_bandwidth is non-0, then bw_sqrtf(bw_pow2f(Q_bandwidth) * peak_gain) * bw_rcpf(bw_pow2f(Q_bandwidth) - 1.f) must be in [1e-6f, 1e6f], where peak_gain is expressed as linear gain.
C++ wrapper
Brickworks::iir2Reset
template<size_t N_CHANNELS>
void iir2Reset(
const float * x0,
float * y0,
float * BW_RESTRICT s10,
float * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2);
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
void iir2Reset(
std::array<float, N_CHANNELS> x0,
std::array<float, N_CHANNELS> * BW_RESTRICT y0,
std::array<float, N_CHANNELS> * BW_RESTRICT s10,
std::array<float, N_CHANNELS> * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2);
# endif
template<size_t N_CHANNELS>
void iir2Process(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples);
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
void iir2Process(
std::array<const float *, N_CHANNELS> x,
std::array<float *, N_CHANNELS> y,
std::array<float, N_CHANNELS> * BW_RESTRICT s1,
std::array<float, N_CHANNELS> * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples);
# endif
Changelog
- Version 1.0.0:
- First release.