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Questions tagged [cosine]

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0
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1answer
54 views

Sum of cosines as squashed as possible

I have 10 cosine waves of the form $\cos(2\pi(x f_n+\varphi_n))$, where $f_n$, the frequency, is an integer from 1 to 10 and $\varphi_i$, the phase, is a number from 0 to 1: $$s(x) = \sum\limits_{n=1}...
0
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3answers
96 views

“Sinusoidal” in DSP terminology

This is probably a bad question but I'll ask anyway because I'm often confused by it. Many textbooks explain how the movement of $z$ around the unit circle can be broken up into a sine wave along the ...
0
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0answers
30 views

Practical Signal Processing by Mark Owen Exercise 2.1. and 2.2

The following exercises don't have answers in Practical Signal Processing by Mark Owen. What is the author looking for here? A mathematical proof? 2.1 A cosine wave of frequency f is sampled at $t = ...
6
votes
1answer
200 views

Optimal amplitude of an $m$-bit sinusoid

A continuous-time sinusoid of zero-to-peak real amplitude $A \le 2^{m-1}-0.5$ (e.g., for $m=16$, $A \le 32767.5$) is quantized to $m$-bit resolution by rounding it to the nearest integer (Fig. 1). ...
-1
votes
1answer
46 views

Displaying Cosine Signal in Python [closed]

I am new to signal processing concept, so this can be easy question. Actually, I want to display cosine signal by using python scipy.signal module. The method <...
0
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1answer
42 views

How do I find the frequency of a particular bin in a cosine transform, and two other questions

I have a discrete series of values and I have applied a Discrete Cosine Transform to it, obtaining values like: ...
0
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2answers
37 views

How to make sure that a sinusoid wave with different subsequent frequencies matches up?

A very basic formula to transform a sequence of notes into a signal would be: $$ x(t) = A\cos( 2 \pi (2^{current\_note}/12) t) $$ where $current\_note$ is $notes[\lfloor t / period\_per\_note\...
1
vote
2answers
40 views

Rearranging exp terms

I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but I‘m not able to spot my mistake. I know the solution (since i looked it up with wolfram alpha) ...
2
votes
1answer
160 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$ x(t) = cos(\omega_x \cdot t) = \frac{1}{2} \cdot \left( e^{j\...
1
vote
2answers
50 views

Fourier series of $cos(\omega_0 t)$ in continuous time

Can any one please help me with understanding how we can calculate the Fourier series of Cos(w0t) using the formula: I saw that they did the following calculus, but I Don't really understand how we ...
1
vote
1answer
309 views

Why MATLAB fft cos makes imaginary parts?

The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(7); fs=128; t=-4*pi:1/fs:4*pi-1/fs;...
0
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1answer
65 views

Extracting a DC value from a sum of sinusoids

I guess it might be a basic questions but here it goes anyways. How could I extract a DC value from a sum of sinusoids, i.e.: $$v(t) =\widetilde{v_{dc}} + \sum_{n=1}^{\infty}\sin(\omega_nt+\phi_n)$$...
7
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3answers
2k views

Replacing “e” in Euler's formula with another number

Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$. I tried this idea in ...
0
votes
1answer
71 views

How does the 'phase' of a cosine wave become 'pi' when it transitions from positive to negative?

I was watching this video lecture on filters where this professor says that: The phase of a cosine wave $\cos(\omega)$ is 0 till $\omega=\pi/2$. As soon as $\omega$ goes beyond $\pi/2$, i.e when $\...
0
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1answer
599 views

Combining 2 sinusoids of equal amplitude with different frequencies into 1 new “wave”

This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave ...
0
votes
1answer
889 views

Linear prediction (LPC) of Sine wave samples around maximas

I think I missed class when this was explained ... Anyway as part of a bigger project I have to implement a LPC to predict 2-3 future values of a sinusoidal process. I wrote a small Matlab m-file to ...
0
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2answers
75 views

Simulating spatial perception - with cosine wave based sound - in MATLAB

I'm trying to create cosine wave, one for the right channel and another for the left. The one on the left is to be moved in phase to simulate change to the spatial perception of the tone. A delay in ...
1
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2answers
1k views

Moving Average of sinusoid

If you calculate a simple moving average over a window length that is equal to the period of the sinusoid, you get a straight line (=0 because the wave is symmetric around the X-axis): the wave has a ...
1
vote
1answer
41 views

How would Fourier and Cosine Transforms responds to summation of cosines with same frequency but different phases?

For example, if I have two signals, $\cos(2\pi ft+\frac\pi4)+\cos(2\pi ft+\frac\pi3)$, what would be different in both transforms (Fourier and cosine) how would the spectrum changes? And What would ...
0
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0answers
489 views

Sine wave phase shift from Fourier Transform

This is probably a really basic question but I'm a little stumped and would appreciate some practical input on how to go about doing this rather than reading dockets of equations semi-related to what ...
1
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2answers
1k views

recovering phase of sine signal from FFT

I have a simple sine function as $sin(2\pi ft + \phi)$. I want to obtain the phase signal $\phi$. I tried to use FFT to calculate $\phi$. In matlab I do the following ...
0
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0answers
489 views

For discrete signals, why does phase change not correspond to time shift?

I'm going through a Signal Processing lecture where the professor mentions this fact and the argument given is: Suppose you have a sinusoidal signal: $Acos(\omega t)$ Now if you change the phase of ...
1
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2answers
620 views

Validating cross corrolation between sine and cos, shouldn't pahse lag be pi/2?

I am trying to use cross correlation instead of FFT to find lags between 2 signals. I am trying to understand cross correlation by using it on sin and cos and expecting phase lag to be pi/2 but it is ...
3
votes
1answer
437 views

Sinusoid with increasing frequency

How would you describe this signal? It's like a sinusoid but as if its frequency was constantly increasing: could you write down a mathematical description? Thanks. And no, this is not homework...
1
vote
1answer
828 views

Additional prefix and suffix required when windowing an OFDM symbol?

To reduce out of band energy, it is common to apply a Raised Cosine filter to the front and back of an OFDM symbol. It is also common to overlap the windowed portions of adjacent symbols to eliminate ...