DFT for signals of different length and sampling rate

1. How does sampling rate affect DFT?
2. How does the length of a signal affect the DFT?
3. How does sampling rate affect the signals?
4. What happens when a signal is sampled at less than the Nyquist rate?

How does sampling rate affect DFT?

The amplitude of the DFT (FFT) is proportional to the number of samples. Therefore, if you sample for twice as long at the same sampling frequency, or if you sample for the same duraiton but twice as fast, you will have twice as many data points, and the DFT amplitude will be twice as large.

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.

How does sampling rate affect the signals?

Sampling rate determines the sound frequency range (corresponding to pitch) which can be represented in the digital waveform. The range of frequencies represented in a waveform is often called its bandwidth.

What happens when a signal is sampled at less than the Nyquist rate?

When the sampling frequency drops below the Nyquist rate, the frequencies will crossover and cause aliasing.