Electrical Engineering Project: FFT, Hanning Window, DFA, and Filters

This project delves into several signal processing techniques, including the Fast Fourier Transform (FFT) with a Hanning window, Detrended Fluctuation Analysis (DFA), and exponential moving averages. The Hanning window's role in minimizing spectral leakage and its impact on frequency resolution is examined. The DFA section describes generating autoregressive series and applying the DFA methodology, including series integration, box division, detrending, and root mean square (RMS) value calculation, culminating in the DFA plot. The use of MATLAB for these analyses is highlighted, with specific results provided. Finally, the exponential moving average filter is discussed, emphasizing its application in filtering dynamic structures and its equivalence to a discrete first-order low-pass filter. The project incorporates references to relevant research papers, providing a comprehensive overview of these signal processing methods.

FFT and Hanning window:
The Hanning window drives the time period’s amplitude to be at 0 in the initial and the
ending position of the sample interval. But through this it shows the distortion occurrence in
the waveform, which is being computed in amplitude modulation formation, For example, the
signal’s amplitude variation over the time record. Amplitude modulation in waveform
outcomes in the spectrum sidebands and in Hanning window utilization, this side lobs
effectively minimizes the analyser’s frequency resolution. (Kataria, & Mehra, 2013)
MATLAB Result:
Power_Y =
1.9661e+05
Power_fftY =
1.9661e+05

Detrended Fluctuation Analysis Technique:
An autoregressive series is generated for several terms with MATLAB coding program. The
DFA methodology includes a series integration which is again divided into n number of equal
sizing boxes. This consolidated sequence is contoured through the multinomial function
utilization in every box. This consolidated sequence is detrended through regional
tendencies’ subtraction for any particular box. The given function is computed in this analysis
and then rms value or the root mean square value of F(n) is determined. And lastly DFA plot
for log F(n) vs. log (n) is determined. This plot’s slope shows α as correlation coefficient. In
this analysis, the standard DFA-1 method is used. Hence the regional tendency is contoured
with first degree multinomial. (Morariu, Iarinca, Vamoş & Şoltuz, n.d.)
MATLAB Result:
n =
Columns 1 through 10
20 24 29 36 44 54 66 81 99 121
Columns 11 through 20
148 181 221 270 330 403 492 601 735 897
Columns 21 through 26
1096 1339 1635 1998 2440 2980

First level exponential moving average:
The Moving average filter with consideration to every data point in the data window are
equivalent essential at the time of average or filtered value calculation in energetic structures.
Nevertheless, nearly all initial values move to consider in the better position of the process. It
can be elaborated as a filter that places more emphasis on the initially filtered data. The filter
constant value reflects the degree of filtering in Exponentially Weighted Moving Average
Filter. This Exponentially Weighted Moving Average Filter is identical to the discrete first-
order low-pass filter. (Shome, Vadali, Datta, Sen, & Mukherjee, 2012)

References
Kataria, P. & Mehra, R. (2013). Comparative Analysis of FFT Algorithm for Different
Window Techniques. International Journal of Science, Engineering and Technology
Research, 2(9), 1691-1695.
Morariu, V., Iarinca, L., Vamoş, C., & Şoltuz, Ş. DETRENDED FLUCTUATION
ANALYSIS OF AUTOREGRESSIVE PROCESSES, 1-7. Retrieved from
https://arxiv.org/ftp/arxiv/papers/0707/0707.1437.pdf
Shome, S. , Vadali, S. , Datta, U. , Sen, S. & Mukherjee, A. (2012). Performance Evaluation
of Different Averaging based Filter Designs Using Digital Signal Processor and its
Synthesis on FPGA. International Journal of Signal Processing, Image Processing
and Pattern Recognition, 5(3), 75-92.