Interpolation and decimation using newton polyphase filters

A multistage interpolation filter for interpolating a digital signal, comprising two or more interpolation filters connected in series, the interpolation filters comprising at least:

• a first interpolation filter, which comprises:
• a first cascade of first template filters, each having an identical first stage template transfer function A1(z), which is arranged to receive and filter an input sequence representing the digital signal sampled at an input sampling rate;
• first ancillary circuitry, which is coupled to the first cascade so as to produce first and second phase outputs;
• and
• a first multiplexer, which is arranged to multiplex the first and second phase outputs in order to generate a first output sequence having a first output sampling rate equal to twice the input sampling rate;
• and
• a second interpolation filter, which comprises:
• a second cascade of second template filters, each having an identical second stage template transfer function A2(z), which is arranged to receive and filter the first output sequence at the first output sampling rate;
• second ancillary circuitry, which is coupled to the second cascade so as to produce third and fourth phase outputs;
• and
• a second multiplexer, which is arranged to multiplex the third and fourth phase outputs in order to generate a second output sequence having a second output sampling rate equal to twice the first output sampling rate.

A decimation filter for decimating a digital signal, comprising:

• a demultiplexer, which is arranged to demultiplex an input sequence representing the digital signal sampled at an input sampling rate, so as to produce first and second phase inputs;
• ancillary circuitry, which is coupled to process the first and second phase inputs, so as to produce a set of weighted inputs;
• and
• a cascade of template filters, each having an identical template transfer function A(z), which are arranged to filter the weighted inputs so as to generate an output sequence having an output sampling rate equal to half the input sampling rate.

An analog front-end circuit for converting a digital discrete multi-tone (DMT) signal to an analog signal, comprising:

• one or more interpolation filters, which are arranged to receive and interpolate the digital DMT signal so as to produce an interpolated signal, each interpolation filter comprising:
• a cascade of template filters, each having an identical template transfer function A(z), which is arranged to receive and filter an input sequence representing the digital signal sampled at an input sampling rate;
• ancillary circuitry, which is coupled to the cascade so as to produce first and second phase outputs;
• and
• a multiplexer, which is arranged to multiplex the phase outputs in order to generate an output sequence having an output sampling rate equal to twice the input sampling rate;
• and
• a digital-to-analog converter, which is arranged to convert the interpolated signal to an analog signal.

A method for interpolating a digital signal, comprising:

• receiving an input sequence representing the digital signal sampled at an input sampling rate;
• filtering the input sequence using a cascade of template filters each having an identical template transfer function A(z);
• processing the input sequence and outputs of the template filters so as to produce first and second phase outputs;
• and
• multiplexing the phase outputs in order to generate an output sequence having an output sampling rate equal to twice the input sampling rate.

A method for decimating a digital signal, comprising:

• receiving an input sequence representing the digital signal sampled at an input sampling rate;
• demultiplexing the input sequence, so as to produce first and second phase inputs;
• processing the first and second phase inputs using ancillary circuitry, so as to produce weighted inputs;
• and
• filtering the weighted inputs using a cascade of template filters each having an identical template transfer function A(z), so as to generate an output sequence having an output sampling rate equal to half the input sampling rate.