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
79 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
57 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
36 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
45 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
108 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
358 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
573 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
81 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
220 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
471 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
877 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
480 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}] = ...