# Frequency and phase relationship?

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#### neetendra1

##### Junior Member level 1 If i have a signal of certain Frequency then how to calculate its phase in digital world?

#### saif haider

##### Full Member level 1 y(t)=A*sin(2*pi*f*t+phase)
w=1/frequency.

sin(w*t+phase) = sin(w*t)cos(phase)+sin(phase)cos(w*t)
sin(phase) = cos(pi/2 - phase)

Combined gives us:
y1 = amp * sin(phase)
y2 = amp * sin(w*t2 + phase) = amp*sin(w*t2)cos(phase) + y1 cos(w*t2)
y3 = amp * sin(w*t3 + phase) = amp*sin(w*t3)cos(phase) + y1 cos(w*t3)

#### kak111

##### Advanced Member level 4 Digital signals has no certain definition as phase.

Because signal has only two values over time ( 1 and 0 )
(versus: ie sine has limitless different values over cycle ( or 1 phase of sine )

We should talk about timing , times , on-off ratio etc.

Of cause you do calculation with values in degrees ( or rad´s ),
if you think a value 100% pulse ratio as 360 degr´s ( or 2*PI )

or do mathematical analysis with Fourier series

count the 1st, 3rd, 5th, 7th, 9th ...... harmonic voltages
multiplied by 1, 1/3, 1/5, 1/7, etc.

here...........

Square wave signals : MIXED-FREQUENCY AC SIGNALS

Square Wave -- from Wolfram MathWorld

Regards KAK

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#### neetendra1

##### Junior Member level 1 Don't consider it to be a square wave, let it be a sine wave with amplitude varying from 1 to -1 ........
Amplitude is not my concern here..........but how to connect its frequency with the phase.

#### kak111

##### Advanced Member level 4 how to connect its frequency with the phase.
= Hmmmm do not understand your question ?????? If we have a sine wave 1 cycle = 0...2Pi (rad) = 0...360 degr
If frequency is 1000Hz --- Cycle time is 1/1000 s = 1ms

Now 1ms is an analoque to 0...360 degr ( 0...2Pi rad)
So phase 90 degr is 0.25ms and vice versa

When we talk about frequency it is allways 1/ one cycle time
f = 1/T or T = 1/ f

from this picture we can say , that phase difference between cos and sine signal is 90 degr
or Pi/2 rad

when we talk time difference between zero points ( or Umax ) we must know what is
the frequency or cycle time.

KAK

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#### albbg

##### Advanced Member level 4 You cannot know the frequency of a signal if your only knowledge is its frequency. The frequency is defined as the first derivative of the phase with respect to the time, or: f = dphase/dt. Then if you know the frequency you will know the increment of the phase with the time, but not the absolute phase.
To know the absolute phase you must know, or go back, to the origin of the time axis and also you have to refer it to a sin(x) or cos(x).
Another thing you can define is the relative phase between two signals (explained by kak111).

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