How to Analyze and Synthesize Complex Waveforms in Signal Processing?

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#1 21664570 31 Oct 2012 12:30

Steve Lawson Steve Lawson

Anonymous

Post #1
21664570 31 Oct 2012 12:30

Well, wt stands for "omega * time" where "Omega" is the "angular frequency" usually in radians/second. So, you will, probably, need to convert those to degrees before adding/subtracting from the constant angles (i.e. 40° and -15°).

Not sure what Vol is ("open loop voltage"?) Strange, though, that the term is already being multiplied by 47, which would make this sine wave 47 times the open loop voltage?!?
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#2 21664571 31 Oct 2012 12:33

Steve Lawson Steve Lawson

Anonymous

Post #2
21664571 31 Oct 2012 12:33

Or you could convert the constant angles to radians -- depending on whether you want to take the sin of the values in degrees or in radians.
#3 21664572 31 Oct 2012 12:38

Rick Rude Rick Rude

Anonymous

Post #3
21664572 31 Oct 2012 12:38

Hi Steve,

I just love college how they teach you all this stuff then it comes to the assignment and you feel lost.

So the equation: r = 80sinwt What on earth do i do with this?. My example shows 50sinƟ. as i did a full cycle i used Ɵ as the angle 0,30,60,90,120 ect 360

so 50sin0 = 0, 50sin30 = 25 ect ect

but in this question i just don't have the information to start with.
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#4 21664573 31 Oct 2012 12:43

Steve Lawson Steve Lawson

Anonymous

Post #4
21664573 31 Oct 2012 12:43

Hint: 1 radian = 57.2957795 degrees
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#5 21664574 31 Oct 2012 12:54

Rick Rude Rick Rude

Anonymous

Post #5
21664574 31 Oct 2012 12:54

so 40 degrees:

pi = 180 degrees

40 * (pi/180)
= (2pi)/9 = 0.6981

pi = 180 degrees

15 * (pi/180)
= (1pi)/12 = 0.2617

Looking at this i think i may need this in a degree answer as i need to plot a graph to show the waveform.
#6 21664575 31 Oct 2012 13:17

Steve Lawson Steve Lawson

Anonymous

Post #6
21664575 31 Oct 2012 13:17

Looks good to me.

You could plot voltage vs radians ;)

Or, just convert the 'wt' terms to degrees.
#7 21664576 31 Oct 2012 13:22

Rick Rude Rick Rude

Anonymous

Post #7
21664576 31 Oct 2012 13:22

the wt terms are the one thing that is confusing me, as i have converted the angles to radians. i Just don't understand th wt meaning. I feel i need a number in there but i don't understand what i need to do.

Also as in my example with the full cycle, would this be required 0 degree to 360....
#8 21664577 31 Oct 2012 13:35

Earl Albin Earl Albin

Anonymous

Post #8
21664577 31 Oct 2012 13:35

College, this is high school Trig stuff. You should know, "wt," and be able to convert radians and degrees.

The Vol thing, I would disregard with an explanation that it is incorrect in the present form. This equation can be plotted using Excel. You simply create one column for the f*t product since you did not state what the frequency is, you go from o - 1, making the argument 0 - 2pi, +/- the pghase shift given in degrees.

Then add three more columns for each sin function then one last column where you sum each of the evaluation point. How many, that's up to you, 25, 50, up to you since it isn't given.

Last you plot the first column (x axis), the argument, then the last column (y axis) the summed evaluation points.
#9 21664578 31 Oct 2012 13:54

Rick Rude Rick Rude

Anonymous

Post #9
21664578 31 Oct 2012 13:54

Hi,

Thanks for the information, yes i can convert this, i just confused my self. from looking around i believe that the wt = frequency and t = time.

as a sinusoidal supply waveform has a frequency in the uk of 50hz i think my equation should look like this:

80sinwt

80sin( 50hz x 10s) and the only thing that changes is t, if i go to 60 seconds (Graph) i will see the wave form over the 1 minute marker.

No if i am barking up the wrong tree please say
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#10 21664579 31 Oct 2012 14:37

Earl Albin Earl Albin

Anonymous

Post #10
21664579 31 Oct 2012 14:37

No the time scale is 1/50Hz or 20mS, which will take the argument (2*pi*w*t) from 0 to 2pi, which will show one complete cycle, which is really all you need because the rest just repeats.

Beside if the time scale is 60S which it isn't, what difference does that make?

Break up your increments into say 400uS, and have 50 increments in time which, 400uS * 50 is what, 20mS, which is 1/50 Hz.

Have one column with 50 time increments of 400uS,

400uS
800uS
1200uS
etc
etc

the 2nd column is

400uS * 1/50
800uS * 1/50
1200uS * 1/50
etc,
etc,

Th 3rd column evaluates the 2nd column, X*sin ( ...)

10 minutes you have a plot.
#11 21664580 31 Oct 2012 18:02

Steve Lawson Steve Lawson

Anonymous

Post #11
21664580 31 Oct 2012 18:02

bq). ...from looking around i believe that the wt = frequency

wt is not the "frequency"

w stands for the angular frequency in radians per second. Multiply that by the time and you get the phase angle at that moment.

BTW: It's important to make a distinction between "frequency" and "angular frequency".

w: angular frequency in radian per second
v: frequency in cycles per second.

There are 2pi radians per cycle. That is the conversion factor between the two.
#12 21664581 31 Oct 2012 19:59

Earl Albin Earl Albin

Anonymous

Post #12
21664581 31 Oct 2012 19:59

Admin:

I need you to step in here and do something to sanction this person's deliberate provocative comments (lisichka Lisichka ). We don't need this sort of disrespect in the forum and absolutely should not be tolerated.

Otherwise I have an open invitation for lisichka Lisichka at Gold's Gym.

Advise ASAP.

Earl
#13 21664569 08 Nov 2012 04:38

Rick Rude Rick Rude

Anonymous

Post #13
21664569 08 Nov 2012 04:38

H
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Topic summary

✨ The discussion focuses on understanding and analyzing sinusoidal waveforms in signal processing, specifically the interpretation of the term "wt" in the equation r = 80sin(wt). "wt" represents the product of angular frequency (ω, in radians per second) and time (t), yielding the instantaneous phase angle in radians. It is emphasized that angular frequency differs from frequency (f, in cycles per second), with the conversion factor being 2π radians per cycle. To work with angles in degrees, constant phase shifts (e.g., 40° and -15°) should be converted to radians or vice versa, depending on the calculation or plotting requirements. For waveform plotting, it is recommended to generate time increments corresponding to one full cycle period (e.g., 20 ms for 50 Hz frequency), calculate the phase angle ωt for each increment, evaluate the sine function, and sum multiple sinusoidal components if needed. The confusion about the term "Vol" (possibly open loop voltage) and its multiplication factor was noted as likely incorrect or irrelevant for the waveform analysis. Practical advice includes using spreadsheet software like Excel to tabulate time, phase angle, individual sine values, and their sum for visualization. The importance of understanding basic trigonometry and signal parameters for waveform synthesis and analysis is highlighted.

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How to Analyze and Synthesize Complex Waveforms in Signal Processing?

FAQ

TL;DR: To model AC signals, use ωt as phase; “w stands for the angular frequency in radians per second.” There are 2π radians per cycle. Convert units consistently to analyze, synthesize, and plot one clean 20 ms cycle for 50 Hz signals. [Elektroda, Steve Lawson, post #21664580]

Why it matters: This FAQ helps students and engineers avoid unit mix-ups when building and plotting sinusoidal waveforms.

Quick Facts

1 radian = 57.2957795 degrees; keep units consistent across your equation and plots. [Elektroda, Steve Lawson, post #21664573]
There are 2π radians per cycle; ω relates to f by a 2π factor. [Elektroda, Steve Lawson, post #21664580]
A 50 Hz mains cycle lasts 20 ms; plotting one cycle shows the entire repeating shape. [Elektroda, Earl Albin, post #21664579]
Example conversions: 40° ≈ 0.698 rad; 15° ≈ 0.262 rad for phase terms. [Elektroda, Rick Rude, post #21664574]
You can plot voltage vs radians directly or convert ωt to degrees first. [Elektroda, Steve Lawson, post #21664575]

What does wt mean in a sine like v(t) = A·sin(ωt + φ)?

wt is the instantaneous phase from angular frequency ω (radians/second) multiplied by time t. That product gives the angle used by the sine. As Steve explains, frequency f (cycles/second) is distinct from angular frequency. Quote: “w stands for the angular frequency in radians per second.” [Elektroda, Steve Lawson, post #21664580]

How do I convert between degrees and radians for phase?

Use radians = degrees × π/180 and degrees = radians × 180/π. Keep the same unit across ωt and any constant phase φ before evaluating sin(). A common check: 1 radian ≈ 57.2957795°. [Elektroda, Steve Lawson, post #21664573]

How do I handle phase offsets like +40° or −15°?

Convert the offsets to radians if ωt is in radians, or convert ωt to degrees if you prefer degrees. Example conversions shown: 40° ≈ 0.6981 rad and 15° ≈ 0.2617 rad. Apply the sign to φ inside sin(ωt + φ). [Elektroda, Rick Rude, post #21664574]

Is ω the same as frequency f?

No. Frequency f measures cycles per second, while ω is angular frequency in radians per second. They are related by ω = 2πf because each cycle spans 2π radians. Mixing them causes a 2π scale error. [Elektroda, Steve Lawson, post #21664580]

How long is one 50 Hz cycle and why plot only one?

One 50 Hz cycle is 1/50 s = 20 ms. Plotting one cycle is enough because the waveform repeats each cycle. Set your time axis from 0 to 20 ms to capture a full period cleanly. [Elektroda, Earl Albin, post #21664579]

What’s a simple 3‑step way to plot a phased sine in Excel?

Create a time column from 0 to 20 ms in 50 steps of 0.4 ms.
Compute the argument column as ωt ± phase, keeping consistent units.
Compute A·sin(argument) and chart argument (x) vs result (y). [Elektroda, Earl Albin, post #21664577]

Do I need to plot 0–360° or 0–2π?

Either works, but keep it consistent. You can plot voltage versus radians directly, or convert the ωt terms to degrees first. Do not mix units within the same equation or chart. [Elektroda, Steve Lawson, post #21664575]

What does the “Vol” term in some equations mean?

In the thread, “Vol” appears ambiguous. Treat it as incorrect in that form and proceed without it, documenting why you removed it. Use a clear amplitude A instead. [Elektroda, Earl Albin, post #21664577]

How should I choose the sampling step for plotting?

Use a small, regular step that divides the period cleanly. Example: for 50 Hz, 0.4 ms steps yield 50 samples per 20 ms cycle, producing a smooth plot and simple math. [Elektroda, Earl Albin, post #21664579]

What’s a common mistake that breaks the waveform?

Confusing frequency f with angular frequency ω. Using f inside sin() without converting to ω under-scales the phase by 2π and distorts timing. “It’s important to distinguish frequency and angular frequency.” [Elektroda, Steve Lawson, post #21664580]

How do I compute phase at a specific time t?

Multiply angular frequency by time, then add any phase offset: θ(t) = ωt + φ. Evaluate sin(θ) using the same angle unit throughout. This directly yields the instantaneous voltage when scaled by amplitude A. [Elektroda, Steve Lawson, post #21664580]

Should sin() use degrees or radians in my calculator or code?

Use whichever your tool expects, but match your inputs. Either convert constants to radians and keep ωt in radians, or convert ωt to degrees. Consistency prevents phase errors and misaligned plots. [Elektroda, Steve Lawson, post #21664571]