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I'm attempting to use a frequency mixer to shift one frequency range to another. Right now, I have a complex sine wave at $43\ \rm kHz$. My imaginary value on the complex object is 0.

If I output a frequency-amplitude spectrum it looks like this:

enter image description here

Now let's say I want to move that frequency to $65\ \rm kHz$. For that I realized that I need to create a new complex sine wave at that frequency and multiply it by my original signal in time.

The problem is, it's not working. I'm getting 2 spikes for some reason. I don't understand why that happens.

enter image description here

Here is my code:

typedef std::complex<float> Complex;

Complex chunk[N];
float Fs = 176400; // How many time points are needed i,e., Sampling Frequency
const double  T = 1 / Fs; // At what intervals time points are sampled
float value;
float value2;
for (int i = 0; i < N; i++)
{
    value2 = (float)(1 * sin(2 * M_PI * 43000 * (i * T))); // Original Signal
    Complex value3 = {(float)(1 * sin(2 * M_PI * 12000 * (i * T))), 0}; // The frequency I want to add
    double multiplier = 0.5 * (1 - cos(2*M_PI*i/256)); // Hamming Window
    chunk[i] = {value2 * multiplier, 0 };// generate (complex) sine waveform
    chunk[i] = chunk[i] * value3; // Frequency Mixer
}
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your original signal is a real-valued sine - so, that's not one spike to begin with, but two.

Nothing in your code actually computes a complex sine, so that's your bug!

You will have to review what a complex sine is (hint: it's not a complex number where the imaginary part is 0!). The rest will clear itself up.

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  • $\begingroup$ This code was just an example, I actually read 1D samples from a wav audio file, I don't have an option but to use real-valued "complex" value where the imaginary part is 0, and it's working fine until now where I came across this issue. $\endgroup$ Sep 1 at 17:13
  • $\begingroup$ your mixer / local oscillator still is not a complex one. So, that's your bug. You introduce that imaginary part for exactly no purpose – it's zero all along. $\endgroup$ Sep 1 at 17:14
  • $\begingroup$ @yarinCohen Write your signals in terms of complex exponentials, and carry out the calculations -- you will see what is happening. $\endgroup$
    – MBaz
    Sep 1 at 17:16
  • $\begingroup$ Thank you, I solved my issue by creating my sine wave this way: Complex value3 = {(float)(1 * cos(2 * M_PI * 22000 * (i * T))),(float)(1 * sin(2 * M_PI * 22000 * (i * T)))}; $\endgroup$ Sep 1 at 17:20

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