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Rather we are multiplying the two DFT arrays together, element by element. … When we switch back to the time domain via an inverse DFT, we have effectively done a circular convolution in the time domain. …

Based on your description it sounds like the idea is to use the FFT to figure out where your signal energy is in terms of frequencies. Once you know that you know what the passband of your filter sho …

Your sin frequency is 50 Hz, but in your 16 point DFT there is no 50 Hz bin. There is a 0 Hz bin and a 100 Hz bin, and you can see that some of the signal power goes into both of them. … The 8 point DFT has a 50 Hz bin, and you can see that it captures almost all of the signal power. …

You can do a transform that uses triangle waves instead of sine waves, but it is not a good choice because they are not orthogonal. Orthogonality is an important property of transform vectors. Prope …

I think that you could get the best performance in terms of demodulator bit-error rate (BER) with a phase-locked loop. You need it to be fast, though. I think your best bet for a fast algorithm that …

Real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. The Fourier transform is defined as the following- $$H(f) = \int h …

So, if you were doing DFT's that are 512 samples long and you did four DFT's, you would calculate the bins for the average DFT by averaging the bins of the four DFT's. … Once the "length" of the averaged DFT (sample period * number of samples per DFT * number of DFT's) gets to the point where the signal's peak is changing bins the signal will start to get smeared. …

You need to change how you're calculating the phase from "atan" to "atan2". The reason is that atan doesn't work in all quadrants. More on atan2 here.

Since convolution via DFT is circular convolution, it's not so much of a quadrant swap as it is a wrap around. I believe that if you put the non-zero taps in the middle that it will fix the problem. …