How to smooth a Fourier transform plot?

Hey everyone!

Actually, I have plotted FFT of a system in some range of frequencies. However, the plot isn't smooth at all, which I can't use for my project, but the results almost right.

I tried to use smooth function in matlab, but it doesn't work as I want. Furthermore, I tried to use moving average filter with different weights, and was the same thing!

The following is the output of the system without and with a moving average filter filter

[Luna]

Please share your code, so we can see what you have done so far.

How you did the smoothness or moving average and plot, etc..?

[Hussam Eldin Rabah]

clear all; close all; clc;

Meq = 0.0282354; %%The Equivalent Mass

Keq = 269.5; %%The Equivalent Stiffness

Ceq = 0.05517; %%The Equivalent Damping

Wn = 97.6973; %%Natural Frequency

Rload = 105522.6537;

EMCC = 1.71e-4;

M = 1.0154;

Cs = 97e-9;

Fs = 1000; % Sampling frequency

T = 1/Fs; % Sampling period

L = 5000; % Length of signal

t = (0:L-1)*T; % Time vector

A = [0 1 0 ; -Keq/Meq -Ceq/Meq -EMCC/Meq ; 0 EMCC/Cs -1/(Cs*Rload)];

B = [0 ; 1 ; 0];

C = [1 0 0];

D = [0];

freq1 = 11;

freq2 = 11.5;

freq3 = 12;

freq4 = 12.5;

freq5 = 13;

freq6 = 13.5;

freq7 = 14;

freq8 = 14.5;

freq9 = 15;

freq10 = 15.5;

freq11 = 16;

freq12 = 16.5;

freq13 = 17;

freq14 = 17.5;

freq15 = 18;

freq16 = 18.5;

freq17 = 19;

freq18 = 19.5;

freq19 = 20;

freq20 = 20.5;

freq21 = 21;

s = sin(2*pi*freq1*t) + sin(2*pi*freq2*t) + sin(2*pi*freq3*t) + sin(2*pi*freq4*t) + sin(2*pi*freq5*t) + sin(2*pi*freq6*t) + sin(2*pi*freq7*t) + sin(2*pi*freq8*t) + sin(2*pi*freq9*t) + sin(2*pi*freq10*t) + sin(2*pi*freq11*t) + sin(2*pi*freq12*t) + sin(2*pi*freq13*t) + sin(2*pi*freq14*t) + sin(2*pi*freq15*t) + sin(2*pi*freq16*t) + sin(2*pi*freq17*t) + sin(2*pi*freq18*t) + sin(2*pi*freq19*t) + sin(2*pi*freq20*t) + sin(2*pi*freq21*t) + 2*rand(size(t));

system = ss(A , B , C , D);

y = lsim(system,s,t);

Y = fft(y);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

%Moving Average Filter

Width = 2;

FR = ones(1,Width) / Width;

FR1 = filter(FR, 1, P1);

%Savitzky-Golay Filters

%a = sgolayfilt(P1, 3, 5);

f = Fs*(0:(L/2))/L;

plot(f,P1)

hold on

plot(f,FR1)

hold on

legend("No filters","Moving Average Filter","Savitzky-Golay Filters")

grid on

xlim([12 20])

title('Spectrum of System')

xlabel('Frequency (Hz)')

ylabel('Magnitude')

hold on

[Hussam Eldin Rabah]

You can use random function or multi tune function as a summation of multi sin waves of multi frequencies instead of makin a loop.