Fundamentals of Time-Frequency Analyses in Matlab/Octave by Mike X Cohen

By Mike X Cohen

Time-frequency analyses are serious for characterizing and knowing platforms in lots of components of technological know-how and engineering. This reasonably cheap booklet specializes in sensible implementations of the analyses in Matlab/Octave. The publication explains time-frequency analyses via written causes and lots of figures, instead of via opaque mathematical equations. each one of one hundred twenty figures within the e-book corresponds to Matlab code that's to be had within the publication and on-line (, and will be run, inspected, and changed on any computing device. via studying this e-book and dealing in the course of the workouts, the reader will achieve the information and abilities to use frequency and time-frequency analyses to simulated and to actual info. The booklet additionally comprises introductions to non-frequency-dependent time sequence analyses together with stationarity and de-noising.

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This means the time series has a sampling rate of 1000 Hz, or 1 kHz. The resulting time series may be difficult to interpret in the time domain, but the individual waves can easily be isolated in the frequency domain, as will be demonstrated in the next chapter. 4 | Several summed sines Noise can be added to sine waves. swave = swave + mean(a)*randn(size(t)); plot(t,swave) In addition to containing sine waves of multiple frequencies simultaneously, sine waves can also contain sudden changes in frequency and in amplitude.

Consider measuring a sine wave: The resolution is determined by the sampling rate, while the precision is related both to the sampling rate and to the frequency of the sine wave. However, because the sampling rate is much faster than the sine wave, the precision remains roughly the same, which is to say, a data point in the 100-Hz signal and its corresponding point in the 1000-Hz signal contains a similar amount of information about the 1 Hz sine wave. In this case, it seems that both sampling rates have similar precisions, even though their resolutions differ by an order of magnitude.

For example, the 10 Hz component from the above signal cannot be extracted by typing swaveX(10). 8 Hz (to obtain this result, type hz(10)). This can be achieved in one of two ways. [junk,tenHzidx] = min(abs(hz-10)); tenHzidx = dsearchn(hz',10); Both approaches return the number 51, meaning that the 51st element in the hz (and, thus, in swaveX) vector corresponds to 10 Hz. Now the results can be extracted from specific frequencies for further analysis. frex_idx = sort(dsearchn(hz',f')); requested_frequences = 2*abs(swaveX(frex_idx)); bar(requested_frequences) xlabel('Frequencies (Hz)'), ylabel('Amplitude') set(gca,'xtick',1:length(frex_idx),...

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