[resending, I think I accidentally replied off-list] On 1/11/2018 5:00 AM, gm wrote: > My question rephrased:

`> Lets assume a spectrum of size N, can you create a meaningfull`

`spectrum of size N/2`

> by simply adding every other bin together? >

`> Neglecting the artefacts of the forward transform, lets say an`

`artificial spectrum`

`> (or a spectrum after peak picking that discards the region around the`

`peaks)`

>

`> Lets say two sinusoids in two adjacent bins, will summing them into a`

`single bin of a half sized spectrum`

> make sense and represent them adequately?

`> In my limited understanding, yes, but I am not sure, and would like`

`to know why not`

> if that is not the case.

`You can analyze this by looking at the definition of the short-time`

`discrete Fourier transform. (Or the corresponding C code for a DFT).`

`Each spectral bin is the sum of samples in the windowed signal`

`multiplied by a complex exponential.`

`Off the top of my head, assuming a rectangular window, I think you'll`

`find that dropping every second bin in the length N spectrum gives you`

`the equivalent of the bin-wise sum of two length N/2 DFTs computed with`

`hop size N/2.`

`Summing adjacent bins would do something different. You could work it`

`out by taking the definition of the DFT and doing some algebra. I think`

`you'd get a spectrum with double the amplitude, frequency shifted by`

`half the bin-spacing. (i.e. the average of the two bin's center`

`frequencies).`

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