If the multiplier takes two voltages as input and returns a voltage as output, then there is necessarily a constant involved, with units of [1/V]. Take for example, AD633 (which was the first search result). The output is the product of the 2 inputs times a constant: $V_{out} = \frac{V_1 \times V_2}{10V}$ So the output units are Volts.


In addition to Juancho's answer for the general mixer, I would like to give an example for a more simpler frequency mixer most commonly used in communication systems to shift the frequency spectrum of a message signal up or down for transmission or reception etc. The simplest understanding of a physical realisation of a mixer assumes an on-off switching ...


Mathematically speaking $V^2$ is perfectly alright to use. Physically I am not sure you can multiply electrical signals like that.


I can't find anything on the Internet regarding its practical applications. Translation, in general, occurs when a series is multiplied with (or "modulated by") a sinusoid. I write "series" because the translation effect can be applied to both the time domain and the frequency domain. The main thing to keep in mind here is that when you multiply a time ...


You can use a Sinc (or windowed Sinc) kernel for interpolation between FFT/DFT result bins. Note that near DC and Fs/2, the interpolation needs to be circular. After shifting a peak up and determining its phase, you can again use Sinc interpolation to figure out how it should be represented in some number of nearby (non-fractional) bins. Added: Linear ...

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