What Is Frequency Resolution?

Frequency resolutionis the size of the smallest frequency for which details in the frequency response and the spectrum can be resolved by the estimate. A resolution of 0.1 rad/s means that the frequency response variations at frequency intervals at or below 0.1 rad/s are not resolved.

Specifying the frequency resolution foretfeandspais different than forspafdr.

Frequency Resolution for etfe and spa

Foretfeandspa, the frequency resolution is approximately equal to the following value:

Mis a scalar integer that sets the size of the lag window. The value ofMcontrols the trade-off between bias and variance in the spectral estimate.

The default value ofMforspais good for systems without sharp resonances. Foretfe, the default value ofM给出最大分辨率。

A large value ofMgives good resolution, but results in more uncertain estimates. If a true frequency function has sharp peak, you should specify higherMvalues.

Frequency Resolution for spafdr

In case ofetfeandspa，频率响应定义在均匀频率范围内，0-f_s/2radians per second, whereF_sis the sampling frequency—equal to twice the Nyquist frequency. In contrast,spafdrlets you increase the resolution in a specific frequency range, such as near a resonance frequency. Conversely, you can make the frequency grid coarser in the region where the noise dominates—at higher frequencies, for example. Such customizing of the frequency grid assists in the estimation process by achieving high fidelity in the frequency range of interest.

Forspafdr, the frequency resolution around the frequencyk是价值R(k). You can enterR(k)in anyoneof the following ways:

The default value of the resolution forspafdris twice the difference between neighboring frequencies in the frequency vector.

etfe Frequency Resolution for Periodic Input

If the input data is marked as periodic and contains an integer number of periods (data.Periodis an integer),etfecomputes the frequency response at frequencies $$\frac{2\pi k}{T}\left(\frac{\text{k}}{\text{Period}}\right)\text{where}k=1,2,\mathrm{...},\text{Period}$$.

For periodic data, the frequency resolution is ignored.