sdr.lowpass_fir(order: int, cutoff_freq: float, window: str | float | tuple | None = 'hamming') → NDArray[float64]

Designs a lowpass FIR filter impulse response \(h[n]\) using the window method.

Parameters:
order: int

The filter order \(N\). Must be even.

cutoff_freq: float

The cutoff frequency \(f_c\), normalized to the Nyquist frequency \(f_s / 2\).

window: str | float | tuple | None = 'hamming'

The SciPy window definition. See scipy.signal.windows.get_window() for details. If None, no window is applied.

Returns:

The filter impulse response \(h[n]\) with length \(N + 1\). The center of the passband has 0 dB gain.

References

Examples

Design a length-101 lowpass FIR filter with cutoff frequency \(f_c = 0.2 \cdot f_s / 2\), using a Hamming window.

In [1]: h_hamming = sdr.lowpass_fir(100, 0.2, window="hamming")

In [2]: plt.figure(); \
   ...: sdr.plot.impulse_response(h_hamming);
   ...: 

In [3]: plt.figure(); \
   ...: sdr.plot.magnitude_response(h_hamming);
   ...:
../../_images/sdr_lowpass_fir_1.png ../../_images/sdr_lowpass_fir_2.png

Compare filter designs using different windows.

In [4]: h_hann = sdr.lowpass_fir(100, 0.2, window="hann"); \
   ...: h_blackman = sdr.lowpass_fir(100, 0.2, window="blackman"); \
   ...: h_blackman_harris = sdr.lowpass_fir(100, 0.2, window="blackmanharris"); \
   ...: h_chebyshev = sdr.lowpass_fir(100, 0.2, window=("chebwin", 60)); \
   ...: h_kaiser = sdr.lowpass_fir(100, 0.2, window=("kaiser", 0.5))
   ...: 

In [5]: plt.figure(); \
   ...: sdr.plot.magnitude_response(h_hamming, label="Hamming"); \
   ...: sdr.plot.magnitude_response(h_hann, label="Hann"); \
   ...: sdr.plot.magnitude_response(h_blackman, label="Blackman"); \
   ...: sdr.plot.magnitude_response(h_blackman_harris, label="Blackman-Harris"); \
   ...: sdr.plot.magnitude_response(h_chebyshev, label="Chebyshev"); \
   ...: sdr.plot.magnitude_response(h_kaiser, label="Kaiser"); \
   ...: plt.ylim(-100, 10);
   ...:
../../_images/sdr_lowpass_fir_3.png