Sometimes the terms 'Fourier domain', 'complex frequency domain', 'Frequency domain' and 's domain' are used interchangeably.
Take those answers here for example: http://answers.yahoo.com/question/index?qid=20090924230321AAxvnJg
Can you really use them interchangeably all the time, without being technically wrong? So, could you describe what would be wrong if I would replace 'complex frequency domain' by 'fourier domain' for example? Or replacing 'complex frequency domain' by 'frequency domain'?
"Fourier domain" and "frequency domain" are sometimes used interchangeably, depending on the field. In engineering and signal processing, one often encounters "frequency domain". However, this is a bit of a blanket term, because this can refer more broadly to a domain encountered through some spectral transform that need not necessarily be a Fourier transform (such as a periodogram, which is essentially, but not quite, a Fourier transform), or which need not go through the complex plane.