Matlab output is not matching with the mathematics...

S1=cos(2*pi*f1*t);
S2=cos(2*pi*f2*t);
arg1=acos(S1)=2*pi*f1*t;
arg2=acos(S2)=2*pi*f2*t;
cos(arg1-arg2)=cos(2*pi*(f1-f2)*t);

But output is not coming as expected.if you observe the frequency spectrum of both they are not same.

Why it is happening ?

[per isakson]

Which values do you use for f1, f2 and t ? What differences do you see? Are they large compared to the expected floating point error?

[KALYAN ACHARJYA]

arg1=acos(S1)=2*pi*f1*t;

This is not a valid Matlab statement.

Answer 1

[David Goodmanson]

Hi Hari,

the problem is that 2*pi*f*t is a nice linear function of t for all t, but the output of acos is restricted to the range

0<= acos <pi. With

t = 0:.001:5;
f1 =1;
S1 = cos(2*pi*f1*t);
arg1 = acos(S1)
figure(1)
plot(t,2*pi*f1*t,t,arg1) 
grid on

you will see that the two quanities agree at the beginning, but acos gets chopped up as t increases.

If you compare the cosines of (2*pi*f1*t) and arg1, then those agree as they must. But with cos(arg1-arg2) you are taking the cosine of the difference of two chopped up quantities with different periods, and it doesn't work.

[Hari Ijjada]

Hi David Goodmanson

Thank you for your response..

can you please look after my problem...

I have two signals ....1)Signal1=cos(2*pi*fc*t)

2) Signal2=cos(2*pi*(fc+f_delta)*t)

My task is to get the third signal....Signal3=cos(2*pi*f_delta*t). fc=500, f_delta=100,Fs=6000.

i followed this process........x1=acos(Signal1)....acos------>gives inverse of the Signal1.......2*pi*fc*t

x2=acos(Signal2)........which gives 2*pi*(fc+f_delta)*t

y=exp(j*x2).*exp(-1*j*x1);

y=exp(j*(x2-x1))

y=exp(j*2*pi*f_delta*t)

My output...Signal3=real(y)=cos(2*pi*f_delta*t);

But After Obseving the Output in Frequency domain i am not getting the single Frequency spectrum which is f_delta...i am getting multiple frequencies ....

1..what is the reason behind the multiple frequencies ?

2..Is there any wrong in the process i followed ?

3..If possible suggest me another process to get the output Signal3...?

Thanks in advance....

[David Goodmanson]

Hi Hari,

what process are you looking to use to get signal 3 from signal 1 and signal 2? One very common procedure is to multiply signal 1 by signal 2, which produces two new frequencies.

[Hari Ijjada]

i am trying to develop the algorithim to provide the deviation in the phase or frequency b/w two signals.

if you see the above problem,there is a deviation between my two inputs

Signal1=cos(2*pi*fc*t),Signal2=cos(2*pi*(fc+f_delta)*t)

By taking these two signals as inputs i want to find the f_delta value.

This f_delta value is not constant..it varies from time to time.Whatever the value it is i have to track the f_delta.

For this purpose i used complex muliplication process.

exp(1i*(2*pi*(fc+f_del)*t)) , exp(-1j*2*pi*fc*t)

if i multiply these two signals output should be exp(1j*2*pi*f_del*t)

real value of the output is---cos(2*pi*f_del*t)

this is output is i will use for the further blocks.

but I am not getting as expected(expected output is cos(2*pi*f_del*t) ).

How to find the desired output ?

[Walter Roberson]

i followed this process........x1=acos(Signal1)....acos------>gives inverse of the Signal1.......2*pi*fc*t

That process is incorrect. acos(cos(2*pi*fc*t)) does not give 2*pi*fc*t outside of t in [0, 1/(2*fc)]

Answer 2

[Walter Roberson]

arg1=acos(S1)=2*pi*f1*t;
arg2=acos(S2)=2*pi*f2*t;

Not correct. As you increase t past one period, acos(cos(x)) becomes mod(x,period) rather than x. Those mod() of the two components interact with each other.

[Hari Ijjada]

Can you please help me solving this issue ...

i am trying to develop the algorithim to provide the deviation in the phase or frequency b/w two signals.

if you see the above problem,there is a deviation between my two inputs

Signal1=cos(2*pi*fc*t),Signal2=cos(2*pi*(fc+f_delta)*t)

By taking these two signals as inputs i want to find the f_delta value.

This f_delta value is not constant..it varies from time to time.Whatever the value it is i have to track the f_delta.

For this purpose i used complex muliplication process.

exp(1i*(2*pi*(fc+f_del)*t)) , exp(-1j*2*pi*fc*t)

if i multiply these two signals output should be exp(1j*2*pi*f_del*t)

real value of the output is---cos(2*pi*f_del*t)

this is output is i will use for the further blocks.

but I am not getting as expected(expected output is cos(2*pi*f_del*t) ).

How to find the desired output ?