0
votes
1answer
57 views

Looking for a nice expression of these functions in terms of trig functions

I have come across three sinusoidal functions f1, f2, and f3 which, up to scaling and translation, are very close to each other. When normalized and plotted together, they are hard to tell apart. ...
0
votes
3answers
35 views

3 points on “horizontal” sinusoid, what is its period?

Imagine you have 3 points that are all a distance of 1 separated from each other. How do you find the sinusoid that goes through these 3 points if you also know that the sinusoid is not at a strange ...
2
votes
1answer
42 views

Decomposition of $a\sin(\varphi t)+b\sin(\vartheta t)$ into AM and carrier

I feel like this should not be so hard, but I am somehow stuck. I would like to decompose the signal $$a\sin(\varphi t)+b\sin(\vartheta t)$$ into an amplitude modulation and a periodic carrier ...
1
vote
1answer
20 views

find period of discrete cosine

let us consider following we should find period of this discrete signal,for periodicity we should have $x[n+kN]=x[n]$ or $10\cos(0.088\pi(n+kN) +\phi)=10\cos(0.088\pi n+\phi)$ or $0.088\pi ...
2
votes
1answer
46 views

Trigonometric regression

What methods are performed for regression with trigonometric functions? E.g. : Sequence: $$-1, 0, 1, -1, 0, 1, \text{.....}$$ Regression: ...
1
vote
1answer
92 views

Rational approximation of $\tanh\,(\sqrt[4]{s}$)

I'd like to find a rational representation of $$f(s) = \frac{\tanh\,\sqrt[4]{s}}{\sqrt[4]{s}}= \frac{a_0 + a_1 s + a_2 s^2 + ... + a_n s^n}{b_0 + b_1 s + b_2 s^2 + ... + b_m s^m} $$ For the case ...
0
votes
0answers
30 views

Phase vocoder equation

I know I can adjust the frequency of a waveform using a modified version of the sine wave equation amplitude*cos(2*pi*frequency*time+phase) this will allow me to adjust the frequency of a signal. ...
1
vote
0answers
59 views

what does the sine function tell you about an input

Intuitively, I'm trying to understand the significance of the input in a sine function. I'm currently, trying to develop intuition behind sinusoids and what the input tells you about the output and ...
0
votes
1answer
37 views

Arcsine for a value

I want to exactly determine the arcsine (sine inverse) for a value. Say I take $\sin$ for $60000$, which is approximately $-0.866$. I want to get back $60000$ from this. Taking a sine inverse will not ...
1
vote
2answers
47 views

What calculation remains constant for discretely sampled points of a sinusoid on a window of 1/4th its period?

I have a univariate time series that consists of discretely sampled (equally spaced) points of a sinusoid. If you have a window that slides over these points (like this animation) with a length of ...
1
vote
1answer
111 views

Finding period of a periodic function

I am having some trouble finding the period of this function: $$W(\omega) = \frac{\sin[(2N +1)\omega \Delta t / 2]}{(2N + 1)\sin[\omega \Delta t /2]}$$ Here $N$ is an integer, $\omega$ is angular ...
1
vote
1answer
38 views

CT Fourier Transform

I need to find the Fourier Transform of the given signal below; $$ x(t) = \frac{\sin(\pi t)}{\pi t} \frac{\sin(2\pi t)}{\pi t}.$$ I know that if $ x(t) = \frac{\sin(Wt)}{\pi t} $ , then $ X(w) = ...
0
votes
3answers
379 views

Fourier Series coefficients/Trigonometric functions

I need some help about finding the Fourier Series coefficient of the given signal; $$ x(t) = \sin(10\pi t + \frac {\pi}{6} ) $$ I know that, $$ a_{k} = \frac{1}{T}\int_{0}^{T} x(t)e^{-jkw_{0}t}dt $$ ...
17
votes
3answers
585 views

Fourier transform of $\left|\frac{\sin x}{x}\right|$

Is there a closed form (possibly, using known special functions) for the Fourier transform of the function $f(x)=\left|\frac{\sin x}{x}\right|$? $\hspace{.7in}$ I tried to find one using ...
0
votes
1answer
63 views

Amplitude versus time producing unexpected patterns.

I am writing a program to generate audio frequencies in multi-channel PCM format. This question may be more suited on an audio forum but I would like to know what is going on mathematically. My ...
4
votes
2answers
82 views

Reduce formula using Euler's?

I am performing a self-study, and I am lost as to a derivation that has taken place. I basically started with this equation: $$ \Upsilon(\phi) = e^{-j\frac{N-1}{2}\phi} \ \Big[ \frac{1 - e^{j N ...
1
vote
0answers
221 views

How can I find the compact trigonometric Fourier series from these signals?

I've been stuck on this for a while, but how exactly would I go about calculating the compact trigonometric Fourier series for both of these signals? I have a general formula down for it, but I just ...
3
votes
2answers
2k views

How do you calculate the frequency perceived by humans of two sinusoidal waves added together?

I'm not sure if this is on topic or not. The tag may also not actually fit. If you add together two sinusoidal waves of different frequencies, how do you calculate the frequency of the resulting ...
18
votes
8answers
2k views

Rapid approximation of $\tanh(x)$

This is kind of a signal processing/programming/mathematics crossover question. At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to ...
5
votes
3answers
478 views

Period of a product of $\sin$ and $\cos$

I want to find the period of $\sin(t) \cos(\pi t)$. I started off by transforming that into $\frac{1}{2}\left [ \sin((\pi +1)t) - \sin((\pi - 1)t\right ]$, but then I get stuck. How do I find the ...
1
vote
1answer
880 views

Combining Sine Waves on Chart

I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the ...
2
votes
3answers
484 views

Simplifying the expressions for the magnitude and phase of a Fourier transform

$$h[n] = 2( \delta[n-2]-\delta[n-1]-\delta[n-3])$$ i computed my frequency response and i have this now: $$H[e^{j \omega}] = 2[ e^{-2 j \omega} - e^{-j \omega}-e^{-3 j \omega}]$$ $$H[e^{j \omega}] = ...