FFT and number of samples relations

1. How many samples does FFT need?
2. How does sample rate affect FFT?
3. What is the relationship between sampling frequency number of samples and time?
4. What is the relationship between sampling rate and frequency?

How many samples does FFT need?

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 does sample rate affect FFT?

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 relationship between sampling frequency number of samples and time?

The sampling frequency or sampling rate, f_s, is the average number of samples obtained in one second, thus f_s = 1/T. Its unit is sample per second or hertz e.g. 48 kHz is 48,000 samples per second. Reconstructing a continuous function from samples is done by interpolation algorithms.

What is the relationship between sampling rate and frequency?

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.