Signal Processing , Power Spectral Density ( Used MATLAB)

SIGNAL PROCESSING POWER SPECTRAL DENSITY ( PSD ) Fourier Transform The basis of the frequency characteristics of the signal is Fourier transform (Brook and Wynne 1991). Fast Fourier Transform (FFT) is an algorithm for calculating Discrette Fourier Transform (DFT). General function of the Fourier transform is to find the frequency components of the signal that is hidden by a time domain signal filled with noise (Krauss et.al 1995) are: S=fft (y) (1) S=fft(y,n) (2)

(3) (4)

In the equation, t is time and fh is the frequency. x is a signal notation in the space of time and X is a notation for signals in the frequency domain. Equation (1) is called the Fourier transform of x (t), while equation (2) is called the inverse Fourier transform of X (f), namely x (t). Equation (1) can also be written as: Cos(2_ft)+jSin(2_ft)

(5)

Fourier transformation can capture information whether a signal having a specific frequency or not, but can not capture the frequency in which it occurs. Command form (3) and (4) is almost the same, that compute the DFT of vector x, only the command (4) is added with the use of the FFT length parameter (n). Power Spectral Density The frequency of a wave is naturally determined by the frequency source. The rate of the wave through a medium is determined by the properties of the medium. Once the frequency (f) and speed of sound (v) of the wave has been given, then the wavelength () has been set. With the relationship f = 1 / T can be obtained equation (6).





(6) f Because the study used the speed of sound in the liquid medium, ie seawater. Then the speed of sound in air is denoted by (v) can be changed with the speed of sound in water that is denoted by (C), so that equation (7) C  (7) f Power Spectral Density (PSD) is defined as the amount of power per frequency interval, in the form of mate, tinkers (Brook and Wynne 1991): PSD =

……………………….(

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By : MUHAMMAD ZAINUDDIN LUBIS , and PRATIWI DWI WULANDARI

(8)

SIGNAL PROCESSING POWER SPECTRAL DENSITY ( PSD )

PSD calculations in MATLAB using Welch (Krauss et.al 1995), which is looking for a DFT (based on calculations by the FFT algorithm), then squaring the magnitude value. Here are the results of processing which is executed by using the syntax:

In the picture above shows the 10 cycles generated by syntax dijalakan using MATLAB, the cycle is indicated by a blue line drawing. The cycle has the same value up to the value to 0007 with the remaining value on the y-axis is the range of 0 -1, because time is 1 / n / Fs. so that the maximum value is generated by the cycle is 1.

In the picture above is shown the results of Power spectral density at a value of x (t) using frequency is 12.000 Hz, while the value of Fs that is 2-fold greater the frequency in accordance with the calculation in finding Frequency sample amounting to 24,000 Hz has the highest score is at 0.004 with the axis x is worth 2500, and -2500, with its low point in 0002 the value of which is at 500 and -500, negative and positive center has charts the same highs and lows there is no difference between the (+) and (-), with Power_of_x = 0.499995833333333

By : MUHAMMAD ZAINUDDIN LUBIS , and PRATIWI DWI WULANDARI

SIGNAL PROCESSING POWER SPECTRAL DENSITY ( PSD )

In the picture above is the power spectral density of x (t) with units of dB already incorporated into the anti-log function 10 log (n), can be seen in the above picture has the same pattern with the highest value on the y axis which is at -20 dB, with values which are at an interval of 2500 and - 2500, it showed no difference between the peak value axis negative (-) and the axis of the positive (+) with ans = 0.499995833333346, and the frequency used is 12:00 Hz and frequency Sample is 24,000 Hz. Syntax used : clear all close all fs=24000; %Fs merupakan frekuensi sample T=10; % time duration of the waveform, in sech n=T*fs; % time is the vector of the sample time time=(1:n)/fs; % waktu adalah vektor dari sampel waktu f=12000/(2*pi); x=cos(2*pi*f*time); t=find(x