Basic concepts of Signal Processing-spectrum vs Power Spectrum

Spectrum:

The dynamic signal is analyzed in the frequency domain. The analysis result is the spectrum lines and curves of various physical quantities coordinate by frequency, and the spectrum function f (ω) with various amplitude as the variable can be obtained ). The spectrum is a very rigid thing. It often refers to the Fourier transformation of the signal. In the spectrum analysis, the amplitude spectrum, phase spectrum, power spectrum, and various density spectrum can be obtained. The spectrum analysis process is complex. It is based on Fourier series and Fourier analysis.

 

The signal spectrum is divided into the amplitude spectrum and phase spectrum. The amplitude spectrum corresponds to the first-order analysis. The amplitude distribution of the Signal Fourier transformation in the frequency domain is called the amplitude spectrum, and the phase distribution is called the phase spectrum.

 

Power Spectrum:

The concept of power spectrum isLimited power signalIn the unit band, the signal power changes with the frequency. The power spectrum has an average power dimension per unit frequency, so the standard name is the power spectrum density (that is,Power Spectrum and power spectrum density are a concept).

The power spectrum can be defined in two ways. One is the Fourier transformation of the Self-correlation function, and the other is the Fourier transformation modulus square of the time domain signal, which is divided by the time length.The first definition is often referred to as the inner theory, while the second is actually from the energy spectrum density. According to the parseval theorem, the wavelet transform modulus square is defined as the energy spectrum, and the energy spectrum density obtains the power spectrum on average time.

The power spectrum retains the amplitude information of the spectrum, but the phase information is lost. Therefore, the power spectrum of different spectrum signals may be the same. The power spectrum corresponds to the distribution of the signal power in the frequency domain, corresponding to the second-order Moment Analysis of the signal. The simplest method to calculate the power spectrum is the cycle graph method, that is, the modulus square of the Signal Fourier transformation, the power in the time domain and the power in the frequency domain can be matched by the passal theorem.

Pay attention to the following two points for comparison of power spectrum and amplitude spectrum:

1. the power spectrum is the statistical mean concept of a random process. The power spectrum of a stable random process is a definite function, while the spectrum is the Fourier transformation of samples in a random process. For a random process, the spectrum is also a "random process ". (Random frequency series)

2. Differences between power concepts and amplitude concepts. In addition, only the power spectrum can be discussed for the second-order moment process of the wide and steady state. The existence of the power spectrum depends on whether the second-order moment exists and the Fourier transformation of the second-order moment converges; the existence of the spectrum only depends on whether the Fourier transformation of the sample in the random process converges.

 

Energy Spectrum:

Deterministic signals, especially non-cyclic deterministic signals, are often described by energy spectrum.

However, for random signals, due to the infinite duration, they do not meet the conditions of absolute product and energy product. Therefore, there is no Fourier transformation, so the power spectrum is usually used to describe them. Periodic Signals also do not meet the conditions of Fourier transformation and are often described by power spectrum.

 

In practice, frequency Spectrum--Direct signal operationFFT; Power Spectrum--Signal self-correlation before makingFFT(Or time domain signalFFTAfter the modulus square is divided by the time length); Energy Spectrum--Or time domain signalFFTReturn the square of the modulus.

 

From: http://blog.sina.com.cn/s/blog_6fb8aa0d0102v2vx.html

 

Related Concepts:

Periodic Chart Method: A method for estimating the power spectral density of signals. In order to obtain the power spectrum valuation, the system first obtains the Discrete Fourier transformation of the signal sequence, then obtains the square of its amplitude-frequency characteristic and divides it by the sequence length N.

First-order moment, second-order moment: first-order moment is the expectation of random variables, second-order moment is the expectation of random variable square, and so on. In addition, there is a first-order center moment, second-order center moment, slightly different

Parseval theorem: the time-domain Energy equals the frequency-domain energy and will not change because of the transformation.

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Basic concepts of Signal Processing-spectrum vs Power Spectrum