How to find frequency of given signal?

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Shanmuka
Shanmuka 2023-1-10
评论： Paul 2023-1-10
fs=2400;
fo=50;
t=0:100;
xp=sin(2*pi*(49.98/fs)*t)+sin(2*pi*(50.01/fs)*t)+sin(2*pi*(49.99/fs)*t)+sin(2*pi*(50.01/fs)*t);
How to find frequency and rate of change of frequency?

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回答（2 个）

Walter Roberson
Walter Roberson 2023-1-10
Ran in:
The frequency is the reciprocal of the time needed for all of the components to first complete an integer number of cycles simultaneously:
format long g
fs = 2400
fs =
2400
time_for_one_cycle = lcm(lcm(lcm(lcm(4998, 5001), 4999), 5001), fs*100)
time_for_one_cycle =
1.66599993336e+15
frequency = 1/time_for_one_cycle
frequency =
6.0024012004802e-16
[49.98/fs, 50.01/fs, 49.99/fs, 50.01/fs] * time_for_one_cycle
ans = 1×4
1.0e+00 * 34694448612222 34715273611389 34701390278611 34715273611389
That last line shows that at that time, the different frequencies have indeed completed an integer number of cycles.
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Walter Roberson
Walter Roberson 2023-1-10
Also note that the units for the xcorr is "lag" (number of signal points) and the units for the other two lines is "seconds".
Paul
Paul 2023-1-10
Ran in:
@Walter Roberson
I got a different answer (Reference)
fs = sym(2400);
syms t real
%fo=50;
%t=0:100;
T = fs./[49.98 50.01 49.99 50.01];
xp(t) = sum(sin(2*pi./T*t));
Ratios of T1/Tj
ratios = simplifyFraction(T(1)./T(2:end))
ratios = 
They are rational, so xp(t) is periodic
Get the LCM of the denominators
[~,den] = numden(ratios);
K = lcm(den);
The fundamental period of xp(t) is (i.e., smallest value of T that satisfies x(t) = x(t + T) )
Txp = K*T(1)
Txp = 
240000
Verify that xp(t) has period Txp
simplify(xp(t) - xp(t + Txp))
ans = 
0
Your solution is a period in that it satisfies the defintion of a periodic signal, but its not the fundamental period
time_for_one_cycle = lcm([4998, 5001, 4999, 5001,fs*100])
time_for_one_cycle = 
1665999933360000
simplify(xp(t) - xp(t + time_for_one_cycle))
ans = 
0

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Image Analyst
Image Analyst 2023-1-10
What do you mean by frequency? That signal has several frequencies in it, not just one. From Fourier theory, any signal can be thought of as a sum of all frequencies. In general you can find out the relative power in all frequencies in a signal by using fft or pwelch
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Walter Roberson
Walter Roberson 2023-1-10
When frequency is considered to be the number of complete cycles per second, then you need to figure out the length of a complete cycle. Which I do in my Answer... it's pretty long. And the answer is different than the average number of pairs of zero crossings per second.

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