A method and apparatus may be used to generate complex exponentials for either frequency domain or time domain applications by programming input parameter values into a complex exponential vector generator (260) having a frequency generator stage (281) and a vector phase accumulator stage (282) arranged with a vector element multiplier stage (283) to generate complex exponential phase index values (α0, α1, . . . αv−1) that are processed by a complex exponential generator stage (284) to output a plurality of complex exponential values (e.g., ej2πα0, ej2πα1, . . . ej2παv−1) that may be rearranged by a permutation unit (286) for use by vector data path.