FFT of any sinusoidal signal -- how many point fft to take?

1. How many points do you need for FFT?
2. How many samples do I need for FFT?
3. How do I choose a FFT size?
4. What is the minimum digital sampling rate required for this signal?

How many points do you need for FFT?

Because the FFT function uses a base 2 logarithm by definition, it requires that the range or length of the time series to be evaluated contains a total number of data points precisely equal to a 2-to-the-nth-power number (e.g., 512, 1024, 2048, etc.).

How many samples do I need for FFT?

The number of samples (N) in the FFT must be an integer power of 2. Therefore, N = 2^p, where p is a positive integer. This rule minimizes the number of multiplications—and therefore the computation time—needed to compute the coefficients of the Fourier series.

How do I choose a FFT size?

The frequency resolution is equal to the sampling frequency divided by FFT size. For example, an FFT of size 256 of a signal sampled at 8000Hz will have a frequency resolution of 31.25Hz. If the signal is a sine wave of 110 Hz, the ideal FFT would show a sharp peak at 110Hz.

What is the minimum digital sampling rate required for this signal?

The minimum sampling rate is often called the Nyquist rate. For example, the minimum sampling rate for a telephone speech signal (assumed low-pass filtered at 4 kHz) should be 8 KHz (or 8000 samples per second), while the minimum sampling rate for an audio CD signal with frequencies up to 22 KHz should be 44KHz.