# What is Sinusoids: Definition and 38 Discussions

A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter, and having a wall one endothelial cell thick. They are the smallest blood vessels in the body: they convey blood between the arterioles and venules. These microvessels are the site of exchange of many substances with the interstitial fluid surrounding them. Substances which cross capillaries include water, oxygen, carbon dioxide, urea, glucose, uric acid, lactic acid and creatinine. Lymph capillaries connect with larger lymph vessels to drain lymphatic fluid collected in the microcirculation.
During early embryonic development, new capillaries are formed through vasculogenesis, the process of blood vessel formation that occurs through a de novo production of endothelial cells that then form vascular tubes. The term angiogenesis denotes the formation of new capillaries from pre-existing blood vessels and already present endothelium which divides.

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1. ### A Fitness function for window length of filter

Fitness function for window length of filter On a sinusoidal signal with amplitude 1, and period P, an exponential moving average (EMA) (with alpha = 1/n), and a linear weighted moving average (LWMA) (with window length n) are calculated; when you subtract the EMA from the LWMA, it can be seen...
2. ### Aliasing, Continuous sinusoids and discrete sinusoids....

Hello, I understand that continuous sinusoids can have any arbitrary frequency ##f## and are always periodic with period ##T=1/f##. A continuous sinusoid looks like this: $$x(t)= sin(2\pi f t+\theta_0)$$ On the other hand, discrete-time sinusoids are not always periodic. They are periodic only...
3. ### MHB When do the combined heights of two Ferris wheels reach 27.5m?

So I have figured out two equations model a Ferris wheel ride(two different ferris wheels). F1 = Ferris wheel one F2= Ferris wheel two F1, h=-12\cos\frac{\pi}{10}t+12.5 F2, h=-12\cos\frac{\pi}{30}t+15 Now from these two equations, I want to know when F2+F1= 27.5m i.e I want to find the...
4. ### Calculate the phase angle between two sinusoids

I am trying to do exactly what was stated, by finding it with calculations only, so, without having to draw the curves. Is that possible? Here is my attempt: v1(t) = -10cos(wt + 50) and v2(t) = 12sin(wt-10) v1(t) = -10cos(wt + 50) becomes v1(t) = -10sin(wt+50+90) = v1(t) = -10sin(wt+140) Now...
5. ### Sinusoids as Phasors, Complex Exp, I&Q and Polar form

Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...
6. ### I Sinusoids as Complex numbers (multiplication query)

DSP Guide .com has the highly rated textbook for digital signal processing. Chapter 30 pg 561 on Complex Numbers http://www.dspguide.com/ch30.htm (chapters are free to download) Hes talking about representing sinusoids with a complex number. Author states "Multiplying complex numbers A and...
7. ### I Can an FFT be used to extract individual sinusoids from a set of data points?

Hello, Thank you for taking time to read my post. Background: I have a accelerometer project that I am playing with that gives me the acceleration of the object. I can plot this data and it looks very nice. I want to integrate this to get the velocity and then integrate it again to get the...
8. ### Rewrite the given function as a sinusoid - why so different

Homework Statement Hello! I am at the inverse trigonometric functions section, and the following exercise asks to rewrite the given function as a sinusoid of a form S(x) = A sin(ωx + φ). I thought I have understood the approach to solving such tasks, and it went pretty smoothly, until I hit...
9. ### Difference between phase angles

Homework Statement [/B] imgur: http://i.imgur.com/9ktFGSs.pngHomework EquationsThe Attempt at a Solution [/B] I came up with both 150 and 210 as the difference between the phase angles. I chose 150. If you draw the vectors and compare their angles, the angular difference between them could...
10. ### Vout = (a+jb)Vin, what do A and B stand for?

Homework Statement I was given a graph with two waves on it, the input and output wave. I found the frequency of the waves, change in magnitude and change in phase. The last question asks me to write the transformation from input to output as a phasor and he gave the relevant equation below...
11. ### Are all discrete sinusoids distinct?

For the discrete complex sinusoid with period N, how many distnict sinusoids are there? And why?
12. ### Why did Fourier choose sinusoids as the basis functions in Fourier series?

Fourier said that any periodic signal can be represented as sum of harmonics i.e., containing frequencies which are integral multiples of fundamental frequncies. Why did he chose the basis functions i.e., the functions which are added to make the original signal to be sinusoidal? I know...
13. ### MHB Convert V: 10< 90 Degrees + 66 - j10V at 10k Rads/s

Question: Convert V = 10< 90 degrees + 66 - j(10 V) at angular frequency = 10k rads/s. I am stuck here 10(cos(90)+ j(sin(90)) + 66 - j(10) which would then be: 0 + j + 66 - j(10)
14. ### What is the Sum of Discrete Sinusoids?

Homework Statement Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero. Homework Equations sin[8*\pi*n/5]+sin[12*\pi*n/5] n is an integer. The Attempt at a Solution n----sin[8*\pi*n/5]----sin[12*\pi*n/5] 0 ----...
15. ### Alternating current, voltage, sinusoids

Homework Statement Consider v1 = 30 sin(ωt + 10º) and v2 = 20 cos(ωt - 40º) A: v1 is in advance to v2 B: v1 differs 50º from v2 C: v2 is in advance to v1 D: v1 is in quadrature to v2 Homework Equations The Attempt at a Solution I think the correct answer is A because v1's angle is nearer...
16. ### Summing sinusoids of different frequency

I'm curious if there is a way to combine sinusoids of multiple frequency into a single sinusoid? For example, I'm looking for a way to combine: Acos(2παt + φ) + Bcos(2πβt + χ) where A, α, φ, B, β, χ are scalar constants and α & β represent the frequency. I'd even be interested in a less...
17. ### Engineering Sinusoids- Fundamentals of Electric Circuits

Find the phase angle between i_1= - 4 sin(377t+55) and i_2= 5 cos(377t-65) The Attempt at a Solution Ok, so I converted i_1= 4 cos(377t+145) and i_2=5cos(377t-65) According to lectures in class the 'most' negative leads. So in this case i_2 leads by -65-145=210. However, if you look at the...
18. ### Solving Fourier Sinusoids using DFT and ω = π/6 | Homework Statement

Homework Statement The entries of the time-domain vector: x(1) = [2 1 -1 -2 -1 1 2 1 -1 -2 -1 1] ; N = 12 are given by 2cos(ωn) where n = 0:11. what is the value of ω? express x(1) as the sum of two Fourier sinusoids. By considering the appropriate columns of the Fourier matrix V...
19. ### Sinusoids and Phasors (Micro-Cap)

Homework Statement Hi, I've been trying to figure this out for a while, its really annoying because it should be straight forward but its troubling me a lot. The exercise is a practical on Sinusoids and Phasors. We are given the circuit and have to first calculate the voltage and...
20. ### Fitting points to skewed sinusoids

Fitting points to "skewed" sinusoids Hello, I have a problem related to least square fit of data. Let me start from a step back. I have a set of points, given as x-y coordinates. x represents an angle and y the corresponding value of a function. I am fitting sinusoids to those data points...
21. ### Receiving 3 Sinusoids Wirelessly: Is It Possible?

Hi, if we transmit 3 different pure sinusoids with different frequencies using 3 transmitters at the same time in the air (wireless), is this possible for a single receiver to receive all the 3 signals at the same time, so we many know frequency components of the signals using FFT? If yes...
22. ### How sinusoidal oscillators produce sinusoids?

Why/How does a linear oscillator give >>>sinusoidal<<< output? I am basically confused how the sinusoidal signal output generates from a random noise? Why sinusoidal and not something else? Can this be explained from the characteristic equation/circuit poles?
23. ### Aliasing and discrete sinusoids

Hello Forum, a continuous time, continuous amplitude sinusoid like sin(2pi*f*t) is 2pi periodic: sin(2pi*f*t)=sin(2pi*f*t+m*2pi) where m can be any positive or negative integer. Let's sample the sinusoid at a sampling frequency fs (sample interval is ts=1/fs) and get the discrete signal...
24. ### Peroid of a summation of sinusoids

Homework Statement I have the following function, f(t) = 2048 + 700cos(31.25*2\pi t) - 1100sin(125*2 \pi t) and I need to find 48 data points spread evenly between one peroid of the waveform. How would I go about doing this? Homework Equations The Attempt at a Solution...
25. ### Help with graphical technique of adding 2 sinusoids

Homework Statement I have a problem understanding how equation 9.11 (see attached) works with Fig. 9.4 (a). Any help would be appreciated. Homework Equations The Attempt at a Solution
26. ### Finding fundamentals of a wave from a product of two sinusoids

Homework Statement Find the amplitude, frequency and period of a particle whose distance from the origin is described by x=4cos(5t)sin(8t) Homework Equations The Attempt at a Solution Would sin x - sin y = 2 cos [(x+y)/2] sin [(x-y)/2] be a worthwhile expression to try?
27. ### Finding phase difference between two sinusoids

Homework Statement I have a graph of two sinusoids which I need to find the frequency of and phase difference between the two. I have the frequency easily enough, I hope, and I found what I believe is the actual formula for each wave. But I have no clue as to finding the difference. Homework...
28. ### Solve V = 5 + 12*j in Form v(t) = A*cos(w*t) + B*sin(w*t)

Homework Statement If V = 5 + 12*j then write v(t) in the form v(t) = A*cos(w*t) + B*sin(w*t) w = 10000 rad/s Homework Equations N/A The Attempt at a Solution I can easily put it into the form v(t) = C*cos(w*t + phi) and I can probably get the above form using a trig identity (haven't...
29. ### How Do Sinusoids Combine to Create Complex Waveforms?

I am taking a circuits class. The professor has given us a waveform. I was trying to figure out what it takes to create the waveform. The professor give us a hint that it was a combination of sinusoids. I am at a loss. The wave appears to have a DC offset of -2. The wave appears to have...
30. ### Complex Sinusoids Homework: 3.4 x(t) = sin^3(17\pi t)

Homework Statement 3.4 Consider the signal x(t) = sin^3(17\pi t) (a) Express this signal in terms of a sum of complex exponentials. (b) Simplify this formula to the sum of sines and/or cosines. (c) What is the fundamental period of x(t)? (d) Sketch the spectrum for x(t). (e) Sketch one...
31. ### Modulation of Sinusoids in Matlab (Frequency Domain Problems)

The Problem Hi, I am trying to modulate two sinusoids in Matlab. I have some and some , where fx and fc are different frequencies. I then modulate them together, using dot multiplication, . I then plot each in the time domain using and I obtained the correct solution. The problem comes with...
32. ### Are Complex Sinusoids an Orthogonal Basis for L^2(\mathbb{R}) Space?

Hello, Let's consider the L^2(\mathbb{R}) space with an inner product, and the complex sinusoids in the interval (-\infty,+\infty). Is it correct to say that the complex sinusoids form an orthogonal basis for this space? One would need to have: \int_{-\infty}^{+\infty}e^{ipx}e^{-iqx}dx=0 for...
33. ### Adding Sinusoids of differing Magnitute & Phases

Homework Statement Find A and \theta given that: Acos(\omega t + \theta) = 4sin(\omega t) + 3 cos(\omega t) Could someone elaborate on how to solve this. I mean it looks to me that one simply takes the magnitude of the coefficient and the inverse tangent of the same coefficients. But I feel...
34. ### Intersections betweens sinusoids

I'm facing the following problem which sounded simple but apparently it is not (at least for me): I have two sinusoids: different amplitude, different frequency, different phase difference and I want to find the intersection points, which is equivalent to solving the following equation in...
35. ### Sinusoids represented by Phasors

1. Find the sinusoids represented by these phasors: (a) I = -3 + j4 A 3. well to convert first to polar they got the following they didnt show their steps: I = 5 <126.87 then they said i(t) = 5 cos(wt + 126.87) What I don't get is the fact that how they got 126.87...
36. ### Confused about how to solve this problem combining sinusoids

Homework Statement The textbook problems states: y=cos3x +sin3x and you are to combine it to a single cos function and tell what effect the 3 has. The answer in the back of the book is given as sqrt2*cos(3x-pi/4) and that the 3 means the wave has a horizontal dilation of 1/3...
37. ### Solving Sinusoids: Expressing 8.5sin(290t+325) in Different Forms

Homework Statement Express 8.5sin(290t+325) as C1cos(wt)+C2sin(wt) Homework Equations The previous parts of the problem actually ask to find the wave equation itself and write it in different forms. So the above wave equation can also be expressed as 8.5cos(290t-125) or as...
38. ### Math Help: Understanding Sinusoids

I do not understand how to find the period of a sinusoid. I don't know when I should use degrees or just numbers. I don't understand when there is a graph that looks the same yet the answers come out with degrees such as y=2sin(fada+45degrees) and another will come out y=10+2sin4fada. :confused: