Implements a fractional delay FIR filter.

Examples¶

Design $\mathrm{\Delta }n=0.21719$ delay filters with various lengths. Examine the width and flatness of the frequency response passband.

In [1]: plt.figure();

In [2]: for length in [4, 8, 16, 32, 64, 128]:
   ...:     fir = sdr.FractionalDelay(length, 0.21719)
   ...:     sdr.plot.magnitude_response(fir, label=f"$L = {length}$")
   ...: 

In [3]: plt.legend(loc="lower left");

Design filters with length $L=8$ and various fractional delays. Examine the effects on the magnitude response outside the passband as a function of the fractional delay. Note the symmetry about $\mathrm{\Delta }n=0.5$ and that the out-of-band magnitude response is worst at $\mathrm{\Delta }n=0.5$.

In [4]: plt.figure();

In [5]: for delay in np.arange(0.1, 1, 0.1):
   ...:     fir = sdr.FractionalDelay(8, delay)
   ...:     sdr.plot.magnitude_response(fir, label=f"$\Delta n = {delay:0.1f}$")
   ...: 

In [6]: plt.ylim(-10, 1); \
   ...: plt.legend(loc="lower left");
   ...: 

Examine the effects on the group delay outside the passband as a function of the fractional delay. Note the symmetry about $\mathrm{\Delta }n=0.5$. The out-of-band group delay is worst around $\mathrm{\Delta }n\approx 0.5$, however the group delay is perfectly flat at exactly $\mathrm{\Delta }n=0.5$.

In [7]: plt.figure();

In [8]: for delay in np.arange(0.1, 1, 0.1):
   ...:     fir = sdr.FractionalDelay(8, delay)
   ...:     sdr.plot.group_delay(fir, label=f"$\Delta n = {delay:0.1f}$")
   ...: 

In [9]: plt.legend(loc="lower left");

Constructors¶

FractionalDelay(length: int, delay: float)

Creates a fractional delay FIR filter.

Special methods¶

__call__(x: ArrayLike, ...) → NDArray

Filters the input signal $x[n]$ with the FIR filter.

__len__() → int

Returns the filter length $N+1$.

Streaming mode only¶

reset()

Resets the filter state. Only useful when using streaming mode.

flush() → NDArray

Flushes the filter state by passing zeros through the filter. Only useful when using streaming mode.

property streaming : bool

Indicates whether the filter is in streaming mode.

property state : NDArray

The filter state consisting of the previous $N$ inputs.

Methods¶

impulse_response(N: int | None = None) → NDArray

Returns the impulse response $h[n]$ of the FIR filter.

step_response(N: int | None = None) → NDArray

Returns the step response $s[n]$ of the FIR filter.

frequency_response(...) → tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.complex128]]]

frequency_response(freqs: float, ...) → complex

frequency_response(freqs, ...) → ndarray[Any, dtype[complex128]]

Returns the frequency response $H(\omega )$ of the FIR filter.

group_delay(...) → tuple[NDArray, NDArray]

Returns the group delay ${\tau }_g(\omega )$ of the FIR filter.

phase_delay(...) → tuple[NDArray, NDArray]

Returns the phase delay ${\tau }_{\varphi }(\omega )$ of the FIR filter.

Properties¶

property taps : NDArray

The feedforward taps $h[n]$ with length $N+1$.

property order : int

The order of the FIR filter $N$.

property delay : int

The delay of the FIR filter $d=\lfloor \frac{N+1}{2}\rfloor$ in samples.