Apparatus and method for transforming a signal in a frequency domain to a sequence in a time domain

A communication apparatus comprising:

• a receiver which receives signals mapped on a plurality of frequency bands in a frequency domain, each frequency band being located at a position separate from position(s) of other(s) of the plurality of frequency bands, wherein vector lengths corresponding to sizes of the plurality of frequency bands are each a product of two or more powers of prime numbers or a multiple of the product of the two or more powers of prime numbers, the prime numbers being integer numbers that are greater than 1 and are different from each other, exponents for the prime numbers being a set of non-negative integers, wherein the vector length is a number of subcarriers allocated to a corresponding one of the plurality of frequency bands;
• a combiner which combines the received signals into a combined signal;
• and
• a transformer which transforms the combined signal in the frequency domain into a symbol sequence in a time domain with an inverse discrete Fourier transform (IDFT) having a size that is a product of powers of a plurality of values, the plurality of values being integer numbers that are greater than 1 and are different from each other, exponents for the plurality of values being a set of non-negative integers.