sdr.FIR - sdr

class sdr.FIR

Implements a finite impulse response (FIR) filter.

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

Notes

A FIR filter is defined by its feedforward coefficients \(h[n]\).

\[y[n] = \sum_{i=0}^{N} h[i] \cdot x[n-i] .\]

The transfer function of the filter is

\[H(z) = \sum\limits_{i=0}^{N} h[i] \cdot z^{-i} .\]

FIR Block Diagram¶

          +------+    +------+            +------+    +------+
x[n] --+->| z^-1 |-+->| z^-1 |-+--...--+->| z^-1 |-+->| z^-1 |-+
       |  +------+ |  +------+ |       |  +------+ |  +------+ |
       |           |           |       |           |           |
  h[0] |      h[1] |      h[2] |       |    h[N-1] |      h[N] |
       |           |           |       |           |           |
       +---------->@---------->@--...->@---------->@---------->@---> y[n]

Examples

See the FIR filters example.

Constructors¶

FIR(h: ArrayLike, streaming: bool = False): Creates an 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[ndarray[Any, dtype[float64]], ndarray[Any, dtype[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 \(\tau_{\phi}(\omega)\) of the FIR filter.

noise_bandwidth(sample_rate: float = 1.0) → float: Returns the noise bandwidth \(B_n\) 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.