# Tag Info

## New answers tagged math

0

How can adding a modulated I and Q result in an SSB signal? Let’s start with an LO at f0. The complex FFT of a cosine has a real spike at f0. The complex FFT of a sine has an imaginary spike at f0. Let’s 100% amplitude modulate (DSB) both at by a sinusoid of frequency f2, where f2 << f0 And look at the FFTs of both, one at a time. The FFT of the ...

1

As to the Hilbert transform for Rx or Tx? If you have a strictly real signal X (you calling CQ into a mic, etc.), it has conjugate symmetric sidebands, which is necessary for all the imaginary stuff to cancel out, which is required if your signal is actually strictly real. If you want to transmit an SSB signal Y from this strictly real input X, you will ...

1

The concept of "negative frequency" deserves more attention. Real-world signals can be described in a number of ways to submit them to mathematical manipulation. This video shows two phasors rotating at the same rate but in opposite directions. (original source) Each phasor represents a signal. Each signal comprises a "real" part mapped ...

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I believe a good point of view is the concept of orthogonality. This is clear under everybody's eyes when seen in physical space, take for instance a 2-dimension space, a plane. In the example above any point on the plane can bear two indipendent informations, its x and y. The keyword here is indipendent, I can freely change one, let's say go from x1 to x2 ...

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First let's look at what happens in the case of a single mixer: simulate this circuit – Schematic created using CircuitLab We know that mixers produce sum and difference frequencies. That is to say, the Fourier transform will contain impulses at $f_1 + f_2$ and also $f_2 - f_1$. Or is it $f_1 - f_2$? It doesn't actually matter, and it's important to ...

-1

Forget sinewaves and complex exponentials. Many, perhaps most QRP SDR IQ modulators actually use square wave modulators (they are implemented as Tayloe quadrature switching mixers). And imaginary components are usually not included in the BOM or on the PCB. So you have a square wave switch turning on at a certain frequency. Call its phase zero. Turn on a ...

9

I think it's more intuitive if you unlearn some things first. Oscillation is not: $$\cos(\omega t)$$ where $\omega$ is the angular frequency in radians per second, and $t$ is time. Rather, oscillation is: $$e^{i \omega t}$$ By Euler's formula this can be expanded to: $$\cos(\omega t) + i \sin(\omega t)$$ If you plot this function on the complex plane, ...

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