Python Polyphase API
Kaiser window filter-bank design tools and DPMFS polynomial coefficient
fitting — used to generate the coefficient banks consumed by
doppler.resample.
Source:
python/dsp/doppler/polyphase/
doppler.polyphase
Kaiser window design formulas for polyphase FIR filter banks, and DPMFS polynomial coefficient fitting.
dataclass
DPMFS polynomial coefficient bank.
c has shape (2, M+1, N), float32:
- axis 0: j ∈ {0, 1} — polyphase component (j = ⌊2μ⌋)
- axis 1: m ∈ {0..M} — polynomial order
- axis 2: k ∈ {0..N-1} — tap index (inner, contiguous for C)
At a given fractional delay μ ∈ [0, 1)::
j = int(2 * mu) & 1
mu_J = 2 * mu - j
h[k] = Horner(c[j, :, k], mu_J)
evaluate(mu: float) -> np.ndarray
Return the N-tap coefficient vector for fractional delay μ.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
mu
|
float
|
Fractional delay in [0, 1). |
required |
Returns:
| Type | Description |
|---|---|
ndarray
|
float32 array of shape (N,). |
validate(polyphase: ndarray, verbose: bool = True) -> dict
Compare reconstructed coefficients against a reference bank.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
polyphase
|
ndarray
|
Reference bank of shape (L, N) from |
required |
verbose
|
bool
|
Print a one-line summary when True. |
True
|
Returns:
| Type | Description |
|---|---|
dict
|
|
to_c_header(name: str = 'dpmfs') -> str
Return a C header snippet with the coefficient arrays.
The arrays are named {name}_c{j}_m{m}[N], suitable for
inclusion in a C source file.
kaiser_beta(attenuation_db: float) -> float
Return Kaiser window β for the given stopband attenuation (dB).
kaiser_taps(attenuation: float = 60.0, passband: float = 0.4, stopband: float = 0.6) -> int
Return prototype filter length for the given Kaiser spec.
kaiser_prototype(attenuation: float = 60.0, passband: float = 0.4, stopband: float = 0.6, image_attenuation: float = 80.0, phases: int = None) -> np.ndarray
Return a Kaiser-windowed sinc prototype filter (float32).
fit_dpmfs(polyphase: ndarray, M: int = 3, passband: float = 0.4, stopband: float = 0.6, attenuation: float = 60.0) -> DPMFSCoeffs
Fit DPMFS coefficients to a polyphase bank via least squares.
For each polyphase component j ∈ {0, 1} and each tap k, solves::
V @ c[j, :, k] ≈ polyphase[j*half : (j+1)*half, k]
where V is a Vandermonde matrix in μ_J ∈ [0, 1).
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
polyphase
|
ndarray
|
Float32 array of shape (L, N) — the |
required |
M
|
int
|
Polynomial order (default 3). Order 3 (cubic) gives tight fits for smooth prototype filters with minimal overshoot. |
3
|
passband
|
float
|
Filter specifications stored in the result for reference. These do not affect the fit — they describe the input bank. |
0.4
|
stopband
|
float
|
Filter specifications stored in the result for reference. These do not affect the fit — they describe the input bank. |
0.4
|
attenuation
|
float
|
Filter specifications stored in the result for reference. These do not affect the fit — they describe the input bank. |
0.4
|
Returns:
| Type | Description |
|---|---|
DPMFSCoeffs
|
Polynomial coefficient bank |
optimize_dpmfs(passband: float = 0.4, stopband: float = 0.6, attenuation: float = 60.0, N: int = 6, M: int = 3, a: float = 1.0, b: float = -0.5, num_der: int = -1, K_pass: float = 10.0, K_stop: float = 1.0, n_pass: int = 100, n_stop: int = 500) -> DPMFSCoeffs
Design a DPMFS resampler via LP minimax optimization.
Wraps :func:optimize_pbf and converts the result to a
:class:DPMFSCoeffs object compatible with the C runtime.
The polyphase decomposition uses J=2 (DPMFS): c[j, m, k] = C[2k + j, m]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
passband
|
float
|
Normalised band edges (fraction of 2π, i.e. fraction of Fin). |
0.4
|
stopband
|
float
|
Normalised band edges (fraction of 2π, i.e. fraction of Fin). |
0.4
|
attenuation
|
float
|
Target stopband attenuation in dB (stored for reference only; the LP optimizer minimises the Chebyshev error directly). |
60.0
|
N
|
int
|
Number of polynomial pieces (even). Default 6. |
6
|
M
|
int
|
Polynomial order. Default 3 (cubic DPMFS). |
3
|
a
|
float
|
Basis function constants. Default a=1, b=-0.5. |
1.0
|
b
|
float
|
Basis function constants. Default a=1, b=-0.5. |
1.0
|
num_der
|
int
|
Continuity order (-1 = unconstrained). |
-1
|
K_pass
|
float
|
Passband / stopband LP weights. |
10.0
|
K_stop
|
float
|
Passband / stopband LP weights. |
10.0
|
n_pass
|
int
|
Frequency grid density. |
100
|
n_stop
|
int
|
Frequency grid density. |
100
|
Returns:
| Type | Description |
|---|---|
DPMFSCoeffs
|
Fitted coefficient bank, shape c[2, M+1, N//2], float32. |
optimize_pbf(N: int, M: int, passband: float = 0.2, stopband: float = 0.8, a: float = 1.0, b: float = -0.5, K_pass: float = 10.0, K_stop: float = 1.0, n_pass: int = 100, n_stop: int = 500, num_der: int = -1) -> tuple[np.ndarray, float]
Minimax PBF optimization via linear programming.
Minimizes the weighted Chebyshev error between the PBF frequency response and the ideal lowpass response, subject to optional time-domain continuity constraints.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
N
|
int
|
Number of polynomial pieces (must be even for symmetry). |
required |
M
|
int
|
Polynomial order (e.g. 3 for cubic). |
required |
passband
|
float
|
Normalised passband edge (fraction of 2π). |
0.2
|
stopband
|
float
|
Normalised stopband edge. |
0.8
|
a
|
float
|
Basis function constants. DPMFS default: a=1, b=-0.5. |
1.0
|
b
|
float
|
Basis function constants. DPMFS default: a=1, b=-0.5. |
1.0
|
K_pass
|
float
|
Passband / stopband weights. |
10.0
|
K_stop
|
float
|
Passband / stopband weights. |
10.0
|
n_pass
|
int
|
Number of frequency grid points in each band. |
100
|
n_stop
|
int
|
Number of frequency grid points in each band. |
100
|
num_der
|
int
|
Continuity order (-1 = none, 0 = continuous, k = k derivatives continuous). |
-1
|
Returns:
| Name | Type | Description |
|---|---|---|
C |
ndarray
|
Coefficient matrix, shape (N, M+1). |
delta |
float
|
Minimised maximum weighted error. |