Spectrum analysis errors mainly manifest themselves in three aspects:

Spectrum analyzer is an instrument for studying the spectrum structure of electrical signals. It is used to measure signal parameters such as signal distortion, modulation degree, spectral purity, frequency stability and intermodulation distortion. It can be used to measure certain circuit systems such as amplifiers and filters. Parameter is a multi-purpose electronic measuring instrument. It can also be called a frequency domain oscilloscope, tracking oscilloscope, analysis oscilloscope, harmonic analyzer, frequency characteristic analyzer or Fourier analyzer, etc. Modern spectrum analyzers can display analysis results in analog or digital form, and can analyze electrical signals in all radio frequency bands from very low frequencies below 1 Hz to sub-millimeter bands. If digital circuits and microprocessors are used inside the instrument to have storage and computing functions, and standard interfaces are configured, it is easy to form an automatic test system.

The errors in spectrum analysis of signals using DFT/FFT are mainly manifested in three aspects:

Right now:

1. Spectrum aliasing phenomenon;

2. Fence effect;

3. Truncation effect, which also includes spectrum leakage and inter-spectral interference.

FSL Spectrum Analyzer

1. Spectrum aliasing:

The Nyquist theorem is well known, so almost everyone knows that in order to prevent spectrum aliasing, the theoretical sampling spectrum should be greater than or equal to the highest frequency of the signal. So what is the relationship with the time domain?

The reciprocal of the sampling period is the spectral resolution, and the reciprocal of the highest frequency is the sampling period.

Set the number of sampling points to N, the sampling frequency fs, and the maximum frequency fh, so the spectrum resolution f=fs/N, and fs>=2fh, so it can be seen that the maximum frequency and spectrum resolution are contradictory to each other. Improve the spectrum resolution. At the same time as f, when N is determined, it will definitely lead to a decrease in the highest frequency fh; similarly, increasing the highest frequency fh will definitely cause an increase in f, that is, the resolution will become larger.

2. Fence effect:

Since dft only takes k=0,1,2,...N-1, it can only take discrete values. If the intervals between spectra are large, some intermediate information may be lost, and using fft to calculate dft is Inevitably, the solution is to increase the number of sampling points N. In this way, the spectrum interval becomes smaller and the probability of losing information decreases.

In addition, adding 0 allows for more detailed observation of the signal in the frequency domain, but does not increase the spectral resolution.

Here is the impact of zero padding on resolution.

R&S FSH8 handheld spectrum analyzer

3. Truncation effect

Truncation effects include spectrum leakage and interspectral interference.

Spectrum leakage: It is caused by windowing functions. It is also a matter of calculation amount (windowing functions must be added when using fft and dft). Multiplication in the time domain and convolution in the frequency domain cause spectrum distortion of the signal. Only when In rare cases, spectrum leakage will not occur, and in most cases it will cause leakage. For example, x(n)=cos(2π/N), (n=0,1,2,3…..N-1,) fft at point N will not leak, but 2N, or N+1, N +2, etc. will cause distortion, and the distortion can be seen from the expression. , which is equivalent to sampling another value between each value of the N-point dft result, and 2π/(N+2)k is completely different from the N-point fft.

Solution: You can use a longer truncation length T0, that is, expand the width of the window function (wider in the time domain, narrower in the frequency domain, T0=N/fs (time domain and frequency domain are relative), that is, leakage The energy will be smaller), or instead of adding a rectangular window function, you can add a slowly changing window function, which can also make the leakage energy smaller. For example, the Hamming window can make the side lobes of the window smaller. The amplitude of the first side lobe of the Hamming window is 32dB smaller than the first side lobe of the rectangular window. In this way, the inter-spectral crosstalk will be greatly reduced, but the width of the first main lobe is It becomes 8pi/N, which doubles the frequency resolution and reduces the frequency resolution.

Because leakage will cause spectrum expansion, it may also cause spectrum aliasing, and the consequence of leakage is reduced spectrum resolution.

4. Interspectral interference

Spectrum leakage will cause many side lobes next to the main spectral line, which will cause interference between spectral lines. What is more serious is that the energy of the side lobes is so strong that it is difficult to distinguish whether it is a side lobe or the signal itself. This is the so-called inter-spectral interference. .