sdr.IIR - sdr

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sdr.IIR

class sdr.IIR

Implements an infinite impulse response (IIR) filter.

This class is a wrapper for the scipy.signal.lfilter() function. It supports one-time filtering and streamed filtering.

Notes¶

An IIR filter is defined by its feedforward coefficients \(b_i\) and feedback coefficients \(a_j\). These coefficients define the difference equation

\[y[n] = \frac{1}{a_0} \left( \sum_{i=0}^{M} b_i x[n-i] - \sum_{j=1}^{N} a_j y[n-j] \right) .\]

The transfer function of the filter is

\[H(z) = \frac{\sum_{i=0}^{M} b_i z^{-i}}{\sum_{j=0}^{N} a_j z^{-j}} .\]

Examples¶

See the IIR filters example.

Constructors¶

IIR(b: ndarray, a: ndarray, streaming: bool = False): Creates an IIR filter with feedforward coefficients \(b_i\) and feedback coefficients \(a_j\).

classmethod ZerosPoles(zeros: ndarray, poles: ndarray, ...) → Self: Creates an IIR filter from its zeros, poles, and gain.

Methods¶

filter(x: ndarray) → ndarray: Filters the input signal \(x[n]\) with the IIR filter.

frequency_response(...) → tuple[ndarray, ndarray]: Returns the frequency response \(H(e^{j2 \pi f})\) of the IIR filter.

frequency_response_log(...) → tuple[ndarray, ndarray]: Returns the frequency response \(H(e^{j2 \pi f})\) of the IIR filter on a logarithmic frequency axis

impulse_response(N: int = 100) → ndarray: Returns the impulse response \(h[n]\) of the IIR filter.

reset(): Streaming-mode only: Resets the filter state.

step_response(N: int = 100) → ndarray: Returns the step response \(s[n]\) of the IIR filter.

Plotting¶

plot_all(sample_rate: float = 1.0, N_time: int = 100, ...): Plots the zeros and poles, impulse response, step response, and frequency response of the IIR filter in a single figure.

plot_frequency_response(sample_rate: float = 1.0, ...): Plots the frequency response \(H(\omega)\) of the IIR filter.

plot_frequency_response_log(sample_rate: float = 1.0, ...): Plots the frequency response \(H(\omega)\) of the IIR filter on a logarithmic frequency axis.

plot_group_delay(sample_rate: float = 1.0, N: int = 1024): Plots the group delay \(\tau_g(\omega)\) of the IIR filter.

plot_impulse_response(N: int = 100): Plots the impulse response \(h[n]\) of the IIR filter.

plot_step_response(N: int = 100): Plots the step response \(s[n]\) of the IIR filter.

plot_zeros_poles(): Plots the zeros and poles of the IIR filter.

Properties¶

property a_taps : ndarray: Returns the feedback filter taps, \(a_j\).

property b_taps : ndarray: Returns the feedforward filter taps, \(b_i\).

property gain : float: Returns the gain of the IIR filter.

property order : int: Returns the order of the IIR filter, \(N - 1\).

property poles : ndarray: Returns the poles of the IIR filter.

property streaming : bool: Returns whether the filter is in streaming mode.

property zeros : ndarray: Returns the zeros of the IIR filter.