Sine and Cosine waves – Gaussian. Waves (4. 0 votes, average: 4. Loading.. Articles in this series: How to Interpret FFT results – complex DFT, frequency bins and FFTShift. How to Interpret FFT results – obtaining Magnitude and Phase information. FFT and Spectral Leakage. How to plot FFT using Matlab . I intend to show (in a series of articles) how these basic signals can be generated in Matlab and how to. For example, I intend to generate a \(f=1. Now that you have determined the frequency of the sinewave, the next step is to determine the sampling rate. Matlab is a software that processes everything in digital. In order to generate/plot a smooth sine wave, the sampling rate must be far higher that the prescribed minimum required sampling rate which is at least twice the frequency \(f\) – as per Nyquist Shannon Theorem. A oversampling factor. Thus the sampling rate becomes \(f. If a phase shift is desired for the sine wave, specify it too. Usually, power spectrum is desired for analysis in frequency domain. In a power spectrum, power of each frequency component of the given signal is plotted against their respective frequency. The command FFT(x,N) computes the \(N\)- point DFT. The number of points – \(N\) – . It can also be chosen as next power of 2 of the length of the signal. Different representations of FFT: Since FFT is just a numeric computation of \(N\)- point DFT, there are many ways to plot the result. Plotting raw values of DFT: The x- axis runs from \(0\) to \(N- 1\) – representing \(N\) sample values. Since the DFT values are complex, the magnitude of the DFT (\(abs(X)\)) is plotted on the y- axis. From this plot we cannot identify the frequency of the sinusoid that was generated.
A C-language program for the computation of power spectra. A computer program is described which performs power-spectral analyses on time-domain data. The program is written in the C language and incorporates an.Power Spectral Density. The DSA Power Spectral Density (PSD). Performs a variety of computations related to the power spectral density (PSD) and autocorrelation function of a signal x(t). Problem 1 from the Fall 2013 EE504 exam. FFT plot – plotting raw values against Normalized Frequency axis: In the next version of plot, the frequency axis (x- axis) is normalized to unity. Just divide the sample index on the x- axis by the length \(N\) of the FFT. This normalizes the x- axis with respect to the sampling rate \(f. Still, we cannot figure out the frequency of the sinusoid from the plot. FFT plot – plotting raw values against normalized frequency (positive & negative frequencies): As you know, in the frequency domain, the values take up both positive and negative frequency axis. In order to plot the DFT values on a frequency axis with both positive and negative values, the DFT value at sample index \(0\) has to be centered at the middle of the array. This is done by using \(FFTshift\) function in Matlab. The x- axis runs from \(- 0. FFT plot – Absolute frequency on the x- axis Vs Magnitude on Y- axis: Here, the normalized frequency axis is just multiplied by the sampling rate. From the plot below we can ascertain that the absolute value of FFT peaks at \(1. Hz\) and \(- 1. 0Hz\) . Thus the frequency of the generated sinusoid is \(1. Hz\). The small side- lobes next to the peak values at \(1. Hz\) and \(- 1. 0Hz\) are due to spectral leakage. Power Spectrum – Absolute frequency on the x- axis Vs Power on Y- axis: The following is the most important representation of FFT. It plots the power of each frequency component on the y- axis and the frequency on the x- axis. The power can be plotted in linear scale or in log scale. The power of each frequency component is calculated as$$P. In Matlab, the power has to be calculated with proper scaling terms (since the length of the signal and transform length of FFT may differ from case to case). Power Spectrum – One- Sided frequencies. In this type of plot, the negative frequency part of x- axis is omitted. Only the FFT values corresponding to \(0\) to \(N/2)\) sample points of \(N\)- point DFT are plotted. Correspondingly, the normalized frequency axis runs between \(0\) to \(0. The absolute frequency (x- axis) runs from \(0\) to \(f.
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