#### Two Cosines (``In-Phase'' Case)

Figure 5.7 shows a spectrum analysis of two *cosines*

(6.17) |

where and , and the frequency separation is radians per sample. The zero-padded Fourier analysis uses rectangular windows of lengths , , , and ( , where ). The length FFT output is divided by so that the ideal height of each spectral peak is .

The longest window ( ) resolves the sinusoids very well, while the shortest case ( ) does not resolve them at all (only one ``lump'' appears in the spectrum analysis). In difference-frequency cycles, the analysis windows are two cycles and half a cycle in these cases, respectively. It can be debated whether or not the other two cases are resolved, and we will return to them shortly.

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One Sine and One Cosine ``Phase Quadrature'' Case

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