1. A complex exponential vector sequence generator, comprising: a frequency generator stage comprising a multiplier for multiplying first and second programmable input frequency parameters to generate an output frequency value, where the output frequency value has a fixed value for time domain applications and has a changing value for frequency domain applications; a vector phase accumulator stage comprising an accumulator for adding a programmable vector length input parameter to a programmable output from the accumulator to generate an accumulator output that is supplied to a plurality of different vector element paths to generate a plurality of vector phase accumulator values, where each vector phase accumulator value is computed as a first value for time domain applications and is computed as a second value for frequency domain applications; one or more vector element multipliers coupled to receive the output frequency value and the plurality of vector phase accumulator values, and to generate therefrom a complex exponential phase index value for each of the different vector element paths; and a complex exponential generator stage coupled to receive the complex exponential phase index value for each vector element path and to compute therefrom a plurality of complex exponential values.