Implements a polyphase finite impulse response (FIR) interpolating filter.

Notes¶

The polyphase interpolating filter is equivalent to first upsampling the input signal \(x[n]\) by \(r\) (by inserting \(r-1\) zeros between each sample) and then filtering the upsampled signal with the prototype FIR filter with feedforward coefficients \(h_{i}\).

Instead, the polyphase interpolating filter first decomposes the prototype FIR filter into \(r\) polyphase filters with feedforward coefficients \(h_{i, j}\). The polyphase filters are then applied to the input signal \(x[n]\) in parallel. The output of the polyphase filters are then commutated to produce the output signal \(y[n]\). This prevents the need to multiply with zeros in the upsampled input, as is needed in the first case.

                       +------------------------+
                   +-->| h[0], h[2], h[4], h[6] |--> ..., y[2], y[0]
                   |   +------------------------+
 ..., x[1], x[0] --+
                   |   +------------------------+
                   +-->| h[1], h[3], h[5], 0    |--> ..., y[3], y[1]
                       +------------------------+

 Input Hold                                          Output Commutator
                                                     (top-to-bottom)

The polyphase feedforward taps \(h_{i, j}\) are related to the prototype feedforward taps \(h_i\) by

Constructors¶

FIRInterpolator(taps: ArrayLike, rate: int, streaming: bool = False)

Creates a polyphase FIR interpolating filter with feedforward coefficients \(h_i\).

Methods¶

filter(x: ArrayLike, ...) → ndarray

Filters and interpolates the input signal \(x[n]\) with the FIR filter.

reset()

Streaming-mode only: Resets the filter state.

Properties¶

property polyphase_taps : ndarray

The polyphase feedforward taps \(h_{i, j}\).

property rate : int

The interpolation rate \(r\).

property streaming : bool

Indicates whether the filter is in streaming mode.

property taps : ndarray

The prototype feedforward taps \(h_i\).