What is the Step Size in FFT?

 

In FFT (Fast Fourier Transform), the step size refers to the spacing between consecutive points in the input data before performing the transform. It's often determined by the sampling rate of the signal. The step size is crucial for accurate frequency representation, and smaller step sizes provide finer frequency resolution in the resulting frequency domain representation.

 

Step Size of a Signal in the Time Domain

Suppose you have a signal sampled at 1000 Hz (sampling rate) for a duration of 1 second. The step size, or the time difference between consecutive samples, is then given by the inverse of the sampling rate:

$$Step size=1Sampling rate=11000 Hz=0.001 seconds

If you perform an FFT on this signal, the resulting frequency resolution in the frequency domain will be determined in part by this step size. Smaller step sizes provide a finer frequency resolution.

 

Step Size of a Signal in the Frequency / FFT Domain 

The term "step size" can have different meanings in the time domain and the frequency domain.

In the time domain, the step size typically refers to the time difference between consecutive samples in a signal. It is determined by the inverse of the sampling rate, as mentioned in our previous discussion.

In the frequency domain, the term "step size" is often associated with the spacing between discrete frequency bins after performing a Fourier Transform, such as in FFT. The frequency resolution is inversely proportional to the duration of the signal being transformed. Smaller step sizes in the frequency domain result in finer frequency resolution.

In the frequency domain, the step size (also known as frequency bin width) after performing an FFT with N bins is determined by the total bandwidth of the signal divided by the number of bins.

$\text{Frequency Step Size}=\frac{\text{Total Bandwidth}}{N}$

Where N is the number of fft bins or size of FFT​

The total bandwidth is equal to the sampling rate (inverse of the time domain step size) divided by 2 (due to the Nyquist theorem).

$\text{Total Bandwidth}=\frac{\text{Sampling Rate}}{2}$

Substituting this into the first equation, you get:

$\text{Frequency Step Size}=\frac{\frac{\text{Sampling Rate}}{2}}{N}$

So, the frequency step size in the frequency domain after an FFT with N bins is inversely proportional to the number of bins and is influenced by the sampling rate. Smaller step sizes provide finer frequency resolution.