Effect of Nyquist frequency on Fourier transformed data

1. How does sampling rate affect Fourier Transform?
2. What is the significance of the Nyquist frequency?
3. What happens above Nyquist frequency?
4. What happens when we sample a waveform with frequencies above the Nyquist frequency?

How does sampling rate affect Fourier Transform?

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. See examples below.

What is the significance of the Nyquist frequency?

The Nyquist theorem is important for capturing audio through digital methods. The average human ear is only sensitive to frequencies between 20 Hz and 20 kHz. Therefore, according to the Nyquist theorem, the optimal sample rate for the human ear is 40 kHz.

What happens above Nyquist frequency?

Above Nyquist frequency, seismic signal with higher frequencies are reconstructed in the form of seismic signal with lower frequencies. The highest frequency that can be successfully recovered from sampled seismic data is one half divided by the sample period.

What happens when we sample a waveform with frequencies above the Nyquist frequency?

A problem called aliasing occurs when a signal to be sampled contains energy at frequencies above the sampling Nyquist frequency.