Meaning Fourier transform
Why do we use to replace the original sinusoidal curve it? If we also can be square or triangle instead, the method for decomposing a signal is infinite, but the purpose is to decompose signal more easily handling original signal. Is represented by the cosine of the original signal will be more simple, because the nature of the other has a cosine signal do not have: sinusoidal fidelity . After a sinusoidal input signal, the output remains sinusoidal, only the amplitude and phase may vary, but the frequency and wave shape remains the same, and only sinusoidal only have such properties, why we do not have side or triangle to represent.
FFT understand
FFT is a fast algorithm for the discrete Fourier transform (DFT) is here we have to discuss is a discrete signal for a continuous signal that we will not be discussed, because the computer can only handle discrete signal values, our ultimate goal is to use the computer to process the signal. So for converting discrete signals only discrete Fourier transform (DFT) in order to be applicable only for a computer and the data discrete finite length can be processed.
Digital signal obtained by sampling oscilloscope, FFT can do the conversion. N sample points, after FFT, the FFT results can be obtained N points. To facilitate FFT operation, N is typically a power of two. Assumed that the sampling frequency Fs, the frequency of the signal F, the sampling points is N. Then the result is the N after FFT plural points. Each point corresponds to a frequency. The modulus value of a point, is at the frequency amplitude characteristic value.
Before and after the frequency resolution of the FFT
Sampling rate 1024Hz sampling 1024 points, just one second, that is, the signal sampling time of 1 second and do an FFT, the result can be analyzed accurately to 1Hz, two seconds if the sampling signal and to do an FFT, the result can be analyzed accurate to 0.5Hz. If you want to increase the frequency resolution, it must increase the number of samples, ie sampling time. Frequency resolution and sampling time is the inverse relationship.
Before and after the FFT spectral width
The Nyquist sampling theorem, the spectral width (Frequency Span) after FFT is a maximum only 1/2 of the sampling rate of the original signal, the original signal sampling rate if 4GS / s, then the bandwidth of up to only after the FFT 2GHz. The reciprocal of the time-domain signal sample period (Sample Period), i.e., the sampling rate (Sample Rate) multiplied by a constant factor that is a spectrum after transform width, i.e. Frequency Span = K * (1 / ΔT), wherein [Delta] T is sampling period , K value depends on whether we are down-sampling the original signal (snapshot) prior to FFT, as this can reduce the amount of FFT computation.
to sum up
Higher spectral resolution requires a longer sampling time, a wider spectrum distribution need to increase the sampling rate of the original signal, of course, we hope that a wider spectrum, more accurate resolution, the oscilloscope's long memory is necessary! It provides the ability to collect your longer signals at high sampling rates!