More frequencies in FFT

Hi Transmogrifox, thank you very much for your help. We have this blog to interact and to help ourselves.

The Transmogrifox's code is given following:


//Frequency components of a signal
//----------------------------------
// build a noides signal sampled at 1000hz containing to pure frequencies
// at 50 and 70 Hz
sample_rate=1000;
t = 0:1/sample_rate:0.6;
N=size(t,'*'); //number of samples
s=sin(2*%pi*50*t)+ 0.3*sin(2*%pi*70*t+%pi/4)+ 0.2*grand(1,N,'nor',0,1);

y=fft(s);
//the fft response is symetric we retain only the first N/2 points
f=sample_rate*(0:(N/2))/N; //associated frequency vector
n=size(f,'*')
yy = y*2/N;
clf()
plot2d(f,abs(yy(1:n)))


And the following picture is the result.



So, if anyone has any question, I think I and Transmogrifox are ready for help.

Response in frequency

Hi Cek, I saw your comment (here), and I'd like to say that I never worked with these functions before. But we can learn about the functions.

Let's start with the freq(.) function.

This code is the example in Scilab's help.


s = poly(0, 's');
sys = (s+1)/(s^3-5*s+4);
rep = freq(sys("num"), sys("den"), [0,0.9,1.1,2,3,10,20]);
[horner(sys, 0), horner(sys, 20)]
//
Sys = tf2ss(sys);
[A, B, C, D] = abcd(Sys);
freq(A, B, C, [0, 0.9, 1.1, 2, 3, 10, 20])


In the code, we see the function freq(.) is used with polynomials (in the Space of Laplace). The last argument (the vector [0, 0.9, 1.1, 2, 3, 10, 20]) represents the calculated frequencies for the polynomial sys.

The function tf2ss(.) means time/frequency to state-space.

The function refreq(.) does the same things of the function freq(.), but it uses other arguments.

Look the function's description, in Scilab's help.

[ [frq,] repf] = repfreq(sys, fmin, fmax [, step])
[ [frq,] repf] = repfreq(sys [, frq])
[ frq, repf, splitf] = repfreq(sys, fmin, fmax [, step])
[ frq, repf, splitf] = repfreq(sys [, frq])

Parameters

sys: syslin list : SIMO linear system
fmin, fmax: two real numbers (lower and upper frequency bounds)
frq: real vector of frequencies (Hz)
step: logarithmic discretization step
splitf: vector of indexes of critical frequencies.
repf: vector of the complex frequency response



The function horner(.) evaluates a polynomial in a specific point, for example:

s = poly(0,'s');
M = [s, 1/s]; // M is the polynomial in analysis
x1 = horner(M,1)
x1
x1 =

1. 1.

x2 = horner(M,%i)
x2 =

i - i

x3 = horner(M,1/s)
x3 =

1 s
- -
s 1



If you want, then we can try to learn anything about the others functions: bode, syslin and csim.

Operations element by element, again

Hi Jackmatze, how are you? I think you are just as old as me, but it's other thing.
About your question, I made a post that answers you: it's here.

So, let me show an example:

-->matrix1 = [1 2 1;
-->2 1 2;
-->1 2 3]
matrix1 =

1. 2. 1.
2. 1. 2.
1. 2. 3.

-->matrix2 = [1 1 2;
-->0 2 1;
-->1 3 1]
matrix2 =

1. 1. 2.
0. 2. 1.
1. 3. 1.

-->matrix_t = matrix1*matrix2
matrix_t =

2. 8. 5.
4. 10. 7.
4. 14. 7.

-->matrix_dott = matrix1.*matrix2
matrix_dott =

1. 2. 2.
0. 2. 2.
1. 6. 3.


Now, what's the difference of matrix1^2 and matrix1.^2?

matrix1^2 = matrix1*matrix1

matrix1.^2 = matrix1.*matrix1


Ok, Jack? Anything more, I'll try to help you.