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 plurality of first template filters, which have respective first inputs and first outputs and an identical first stage template transfer function A1(z), which are connected in a first cascade such that a first input of a given first template filter is connected to a first output of another first template filter that precedes the given first template filter in the first cascade, and which are 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 receive and process a first subset of the first inputs and the first outputs to produce a first phase output, and to receive and process a second subset of the first inputs and the first outputs, different from the first subset, to produce a second phase output;
• 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 plurality of second template filters, which have respective second inputs and second outputs and an identical second stage template transfer function A2(z), which are connected in a second cascade such that a second input of a given second template filter is connected to a second output of another second template filter that precedes the given second template filter in the second cascade, and which are arranged to receive and filter the first output sequence at the first output sampling rate;
• second ancillary circuitry, which is coupled to receive and process a third subset of the second inputs and the second outputs to produce a third phase output, and to receive and process a fourth subset of the second inputs and the second outputs, different from the third subset, to produce a fourth phase output;
• 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
• wherein at least the first and second stage template transfer functions are different from one other.

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:
• multiple template filters, which have respective inputs and outputs and an identical template transfer function A(z), which are connected in a cascade such that an input of a given template filter is connected to an output of another template filter that precedes the given template filter in the cascade, and which are arranged to receive and filter an input sequence representing the digital signal sampled at an input sampling rate;
• ancillary circuitry, which is coupled to receive and process a first subset of the inputs and the outputs of the template filters to produce a first phase output, and to receive and process a second subset of the inputs and the outputs of the template filters, different from the first subset, to produce a second phase output;
• 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,
• wherein the ancillary circuitry in each interpolation filter is coupled to delay, scale and combine the inputs and outputs in the respective first and second subsets in order to produce the first and second phase outputs.

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 multiple template filters, which are implemented in an Application Specific Integrated Circuit (ASIC) and have respective inputs and outputs and an identical template transfer function A(z), and which are connected in a cascade such that an input of a given template filter is connected to an output of another template filter that precedes the given template filter in the cascade;
• processing a first subset of the inputs and the outputs of the template filters to produce a first phase output, and processing a second subset of the inputs and the outputs of the template filters, different from the first subset, to produce a second phase output;
• and
• multiplexing the phase outputs in order to generate an output sequence having an output sampling rate equal to twice the input sampling rates,
• wherein processing the inputs and outputs in the respective first and second subsets comprises delaying, scaling and combining the inputs and outputs in the respective first and second subsets in order to produce the first and second phase outputs.