To find whether x(t) and y(t) signals are same?

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In summary, the question is asking to determine if two signals, x(t) and y(t), are the same given the data ω1=∏/3, ω2=∏/3, τ1=0, τ2=1, δ1=2∏, and δ2=-∏/3. The solution provided concludes that the signals are the same based on the fact that ω1=ω2 and uses the equation ω1τ1+ δ1=ω2τ2+ δ2+2∏k - ∏/2 to justify it, but this is incorrect since one signal is cos and the other is sin.
  • #1
amaresh92
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Homework Statement


let x(t)=cos(ω1(t+τ1) +δ1) and sin (ω2(t+τ2) +δ2)
determine whether both the signal are same for given data
ω1=∏/3 , ω2=∏/3
τ1=0 , τ1=1
δ1=2∏ , δ1=-∏/3

Homework Equations


The Attempt at a Solution


solution is as given-:
as ω1=ω2,
so
ω1τ1+ δ1=ω2τ2+ δ2+2∏k where k is integer
so x(t)=y(t)

i did not understand how they can conclude like that?
 
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  • #2
hi amaresh92! :smile:

i assume you mean …
amaresh92 said:
let x(t)=cos(ω1(t+τ1) +δ1) and sin (ω2(t+τ2) +δ2)
determine whether both the signal are same for given data
ω1=∏/3 , ω2=∏/3
τ1=0 , τ2=1
δ1=2∏ , δ2=-∏/3
as ω1=ω2,
so
ω1τ1+ δ1=ω2τ2+ δ2+2∏k where k is integer
so x(t)=y(t)

i did not understand how they can conclude like that?

(try using the X2 button just above the Reply box :wink:)

if they were both cos, that would be correct, but since one is cos and the other is sin, it would have to be

ω1τ1+ δ12τ2+ δ2+2∏k - ∏/2 :confused:
 
  • #3
:redface:
tiny-tim said:
hi amaresh92! :smile:

if they were both cos, that would be correct, but since one is cos and the other is sin, it would have to be

ω1τ1+ δ12τ2+ δ2+2∏k - ∏/2 :confused:

Oops.
I agree. Now. :redface:
 
Last edited:

What is the process for comparing x(t) and y(t) signals?

The process for comparing x(t) and y(t) signals involves first obtaining the numerical values for each signal at various points in time. This data can then be plotted on a graph to visually compare the two signals. Alternatively, mathematical operations such as calculating the mean, standard deviation, or correlation coefficient can be used to quantitatively compare the signals.

How can I determine if x(t) and y(t) signals are identical?

To determine if x(t) and y(t) signals are identical, you can use the methods mentioned above to compare their numerical values or characteristics. If the two signals have the same values at all points in time, they can be considered identical. However, keep in mind that even small variations in the signals may indicate differences.

What are some factors that can cause differences in x(t) and y(t) signals?

Differences in x(t) and y(t) signals can be caused by a variety of factors, including noise, measurement errors, signal processing techniques, and the underlying physical phenomena being measured. It is important to carefully consider these factors when comparing signals to ensure accurate results.

Can I use statistical tests to determine if x(t) and y(t) signals are the same?

Yes, statistical tests can be used to determine if x(t) and y(t) signals are the same. These tests involve calculating a p-value, which indicates the likelihood that any observed differences between the signals are due to chance. A low p-value indicates a low likelihood of chance and suggests that the signals are significantly different.

How can I interpret the results of comparing x(t) and y(t) signals?

The interpretation of the results of comparing x(t) and y(t) signals will depend on the specific methods used for comparison. Generally, if the signals are found to be identical or highly similar, this suggests that they are measuring the same phenomenon. If the signals are different, further investigation is needed to determine the cause of the differences.

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