# Regarding phase and frequency components in the signal [closed]

As I am not a signal processing student, I have limited understanding of the concepts.

The general formula for sine wave is

$$s(t)= A \sin(\omega t-p)$$

where $A$ is amplitude $\omega$ is frequency and $p$ is phase.

1. Is there any possibility that the phase of the signal remains constant even if the frequency of the signal is changed?

2. If we observe a real-time signal the signal can be a periodic sine wave signal but not smooth curve as it is accompanied by noise. In such cases how the phase of the signal is varied? Can the noise effect the phase of signal?

I find it easier to understand the phase relationships by observing complex tones rather than sines and cosines, which are related using Euler's identity:

$e^{j\theta}= \cos(\theta)+j \sin(\theta)$

$e^{j\theta}$ is simply a phasor with magnitude 1 and angle $\theta$. If that angle is changing with time at a constant rate ($e^{j\omega t})$ the real portion will be a cosine and the imaginary portion will be a sine. If that phasor that is spinning at a constant rate does not start at magnitude = 1 and angle = 0 at time $t = 0$, then we have a phase offset ($e^{j\omega t + \phi})$ where $\phi$ here represents the starting phase at $t = 0$.

Thus a single impulse in the frequency domain is a single spinning phasor in the time domain as shown in the figure below. From that figure the I axis represents the real part of the spinning phasor, which would be a cosine wave, or a sine wave if the starting phase at $t=0$ was $\pi/2$ since $\cos(\theta+\pi/2)= \sin(\theta)$ 