Low power decimation system and method of deriving same

A decimation system, comprising:

• a plurality of cascaded Finite Impulse Response (FIR) decimation filters, each of the FIR decimation filters having a transfer function H(z)=(1+z−1)N, where N is an integer;
• wherein each of at least two of the plurality of cascaded FIR decimation filters includes a polyphase FIR filter;
• wherein at least one of the polyphase filters comprises:
• an input stage having an input, a first output, and a second output;
• first and second gain stages having their respective inputs coupled to the first output of the input stage;
• third and fourth gain stages having their respective inputs coupled to the second output of the input stage;
• a first combiner having respective inputs coupled to the second output of the input stage sequence generator, and an output of the first gain stage;
• a first unit delay having an input coupled to an output of the first combiner;
• a second combiner having respective inputs coupled to
• an output of the first unit delay,
• an output of the second gain stage,
• an output of the third gain stage,
• an output of the fourth gain stage;
• and
• a second unit delay having an input coupled to an output of the second combiner;
• and
• a third combiner having respective inputs coupled to an output of the second unit delay, and the second output of the input stage.

A method of performing decimation, comprising:

• (a) performing successive stages of Finite Impulse Response (FIR) decimation filtering, each of the stages of FIR decimation filtering using a transfer function H(z)=(1+z−1)N, where N is an integer;
• wherein each of at least two of the successive stages of FIR decimation filtering includes polyphase FIR filtering
• wherein said step of polyphase filtering includes
• generating a plurality of sub-sampled signals from an input signal;
• producing, in parallel, a decimated output signal component from each of the plurality of sub-sampled signals;
• and
• combining the plurality of decimated output signal components, to produce a decimated output signal
• wherein said producing step includes
• separately FIR filtering each of the sub-sampled signals to produce respective FIR filtered signals;
• and
• downsampling each of the FIR filtered signals, to produce the decimated output signal components.

A method of performing decimation, comprising:

• performing successive stages of Finite Impulse Response (FIR) decimation filtering, each of the stages of FIR decimation filtering using a transfer function H(z)=(1+z−1)N, where N is an integer;
• generating, from an input signal, a first sub-sampled signal and a second sub-sampled signal;
• applying first and second weights to the first sub-sampled signal to produce respective first and second weighted signals;
• applying third and fourth weights to the second sub-sampled signal to produce respective third and fourth weighted signals;
• combining
• the second signal, and
• the first weighted signal, to produce a first combined signal;
• producing a delayed first combined signal;
• combining
• the delayed first combined signal,
• the second weighted signal,
• the third weighted signal, and
• the fourth weighted signal, to produce a second combined signal;
• producing a delayed second combined signal;
• and
• combining
• the delayed second combined signal, and
• the second signal, to produce a decimated output signal.