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

Parameters:¶

freqs: int = 1024¶

freqs: float | ndarray[Any, dtype[float64]]

freqs: ndarray[Any, dtype[float64]]

The frequency specification.

• int: The number of frequency points. The endpoint is not included.

• float: A single frequency.

• npt.NDArray[float]: Multiple frequencies.

sample_rate: float = 1.0¶

The sample rate \(f_s\) of the filter in samples/s.

whole: bool = True¶

Only used if freqs is an integer.

• True: The maximum frequency is max_f = sample_rate.

• False: The maximum frequency is max_f = sample_rate / 2.

decades: int | None = None¶

Only used if freqs is an integer.

• None: f = np.linspace(0, max_f, freqs, endpoint=False).

• int: f = np.logspace(np.log10(max_f) - decades), np.log10(max_f), freqs, endpoint=False).

Returns:¶

• The frequency vector \(f\), only if freqs is an integer.

• The frequency response of the IIR filter \(H(\omega)\).

Examples

In [1]: zero = 0.6; \
   ...: pole = 0.8 * np.exp(1j * np.pi / 8); \
   ...: iir = sdr.IIR.ZerosPoles([zero], [pole, pole.conj()])
   ...: 

Compute the frequency response at 1024 evenly spaced frequencies.

In [2]: iir.frequency_response()
Out[2]: 
(array([0.00000000e+00, 9.76562500e-04, 1.95312500e-03, ...,
        9.97070312e-01, 9.98046875e-01, 9.99023438e-01]),
 array([2.4722987 +0.j        , 2.47271105+0.0041658j ,
        2.47394825+0.00830241j, ..., 2.47601067-0.01238051j,
        2.47394825-0.00830241j, 2.47271105-0.0041658j ]))

Compute the frequency response at 0.0 rad/s.

In [3]: iir.frequency_response(0.0)
Out[3]: np.complex128(2.472298696877605+0j)

Compute the frequency response at several frequencies in Hz.

In [4]: iir.frequency_response([100, 200, 300, 400], sample_rate=1000)
Out[4]: 
array([1.36961426-1.9678537j , 0.57338213-0.77694738j,
       0.52496713-0.3885743j , 0.51520024-0.1706839j ])