# plotting the frequency spectrum

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aaa on 24 Apr 2012
Answered: Khathutshelo Mudau on 27 Sep 2020 at 12:19
Hi,
I am having trouble plotting the frequency spectrum of a sine wave. For this code, i expect the main frequency component to be centered around 1/(2*pi), but they are not. Is there something I am missing in my code?
x = [0:0.1:2*pi];
y = sin(x);
z = fft(y);
z = fftshift(z);
N = length(y);
f = [-N/2:N/2-1]/N;
plot(f,abs(z))

Rick Rosson on 24 Apr 2012
%%Time specifications:
Fs = 100; % samples per second
dt = 1/Fs; % seconds per sample
StopTime = 1; % seconds
t = (0:dt:StopTime-dt)';
N = size(t,1);
%%Sine wave:
Fc = 12; % hertz
x = cos(2*pi*Fc*t);
%%Fourier Transform:
X = fftshift(fft(x));
%%Frequency specifications:
dF = Fs/N; % hertz
f = -Fs/2:dF:Fs/2-dF; % hertz
%%Plot the spectrum:
figure;
plot(f,abs(X)/N);
xlabel('Frequency (in hertz)');
title('Magnitude Response');
HTH.
Rick

Mere on 2 Dec 2016
Could someone please explain how you know to set up the frequency vector that way?
shalabh mishra on 5 Nov 2017
%%Fourier Transform:
X = fftshift(fft(x));
@Rick Rosson
In the above command, Why we are not using X=fftshift(x) or X=fft(x)?
Le Dung on 29 Jan 2018
X = fftshift(fft(x)); is first to calculate fft of x, then you will shift the fft value. If you use fftshift(x), mean that you didn't have any fft value of x to shift, or more exactly, you shift values of x but not fft of values of x.

kittipob techawudtipat on 16 Apr 2016
i'm having trouble with this >> n = 1:2:5; >> x = -3.98*(sin((pi*n)/2))/(n*pi)+32*(sin((pi*n)/2))/((n.^3)*(pi.^3)*(10.^6)); >> y = 1.996 + x; >> plot(y(1:50)) Index exceeds matrix dimensions.
how can i solve this problem. the graph i order to plot dont happen thankyou bro

Dr. Seis on 24 Apr 2012
N = length(y);
dt = x(2)-x(1); % Time increment
Nyq = 1/(2*dt); % Nyquist frequency
df = 1/(N*dt); % Frequency increment
if mod(N,2) == 0 % N is even
f = -Nyq : df : Nyq-df;
else % N is odd
f = [sort(-1*(df:df:Nyq)) (0:df:Nyq)];
end

#### 1 Comment

Dr. Seis on 24 Apr 2012
Forgot the "== 0" in the if statement... whoops!

reddy on 21 May 2015
Hi every one
could you please plot spectrum for the variables that are in EXCEL file which is attached.?
thanks.
Phanindra

Deepanshu Gupta on 23 Nov 2017
I am trying to plot spectrum of wave for a string plucked halfway along it's length.I am not seeing any figure when I run it. c = 343; % speed of sound air% L = 1000; % string length% w0 = 200; % Displacement distance % Bn = 0; % string at rest, -ve part is zero% x = (0:L); % distance on L%
n = 2; %no. of modes%
fn = (n*c)/2*L;
omega = 2*pi*fn; %omega%
omegaN = n * omega; %w is displacement%
kn = w0/c; % wave no.%
t = 1/fn; %time%
An = ((8*w0)/n^2*pi^2)*sin((n*pi)/2); %incident wave part +ve%
W = sum((An*cos(omegaN*t) + Bn*sin(omegaN*t))*sin(kn*x)); %Displacement eq. sum n=1:10%
plot(W,t); title('hinged string') xlabel('displacement') ylabel('time')

Khathutshelo Mudau on 27 Sep 2020 at 12:19
Hy, can someone help me with determining or plotting the error spectrum of a sound signal