How do I generate a smaller DFT result?

1. How does the length of a signal affect the DFT?
2. What is the output of a DFT?
3. How many samples are needed for DFT?
4. What happens if we apply DFT twice to a signal?

How does the length of a signal affect the DFT?

The length N of the DFT is the number of frequency points that will result in the DFT output. Zero padding will result in more frequency samples, however this does not increase frequency resolution, it just interpolates samples in the DTFT.

What is the output of a DFT?

All DFT outputs for a real N-sample input sequence with even N follow this pattern: 1 real value, N/2-1 complex values, 1 real value, N/2-1 conjugates. A diagram of the 64-point example is shown below, where blue squares indicate non-redundant information.

How many samples are needed for DFT?

So at least 6 samples should be taken to complete one cycle of min frequency. Now the frequency resolution is 100 Hz. Since the sampling frequency is 10 MHz, Maximum frequency can be detected is 5 MHz. So 5MHz/100Hz = 50000 points will be there in first half of FFT.

What happens if we apply DFT twice to a signal?

Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.