DFT on a specified frequency

spectral analysis (amplitude & phase) of recorded time-series data

Compute the discrete Fourier transform at specified frequencies, not using fft.
Why one may need this?

(1) MATLAB fft function computes the amplitude of signals only (no phase).
(2) Once having the recorded time-series data, one often uses fft to do the spectral analysis. However, the frequency set at which you do the fft may not contain the specified frequency of interest. For example, when we use two primary tones (f1, f2) to stimulate the ear, we are interest in comptuting the distortion product at frequency of 2f1-f2. This frequency may not be inculuded in the frequency set for the fft analysis