Apparatus and method for Fast Hadamard Transforms

An apparatus for serially calculating a Fast Hadamard Transform of a sampled signal from a first channel, comprising:

• a first shift register for serially receiving samples of the signal;
• a first two's complement generator for producing a two's complement of a first sample of the signal;
• a first multiplexer for selecting between a first sample of the signal and the two's complement of the signal to produce a multiplexer output;
• and
• a first adder for generating a sum of a second sample of the signal and the multiplexer output.

A method for serially calculating a Fast Hadamard Transform of a sampled signal from a first channel, comprising the steps of:

• serially storing samples of the signal;
• computing a first sum of a first sample of the signal and a last sample of the signal;
• storing the first sum;
• computing a second sum of a first sample of the signal and a two's complement of the last sample of the signal;
• and
• storing the second sum.

An apparatus for serially calculating a Fast Hadamard Transform of order 2N of a sampled signal from a first channel, comprising:

• a first shift register for serially receiving Hadamard Transforms of order 2N−1;
• a first two's complement generator for producing a two's complement of a first Hadamard Transform of order 2N−1 that is stored in the first shift register;
• and;
• a first adder for generating a sum of a second Hadamard Transform of order 2N−1, and the first Hadamard Transform of the order 2N, the first adder also generating a sum of the second Hadamard Transform of order 2N−1 and a two's complements of the first Hadamard Transform of order 2N−1.

An method for serially calculating a Fast Hadamard Transform of a sampled signal from a first channel, comprising the steps of:

• serially storing samples of the signal;
• computing a first sum of a second sample of the signal and a first sample of the signal;
• storing the first sum;
• computing a second sum of the second sample of the signal and a two's complement of the first sample of the signal;
• and
• storing the second sum.