Questions tagged [cosine]

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36 views

Ideal low pass filter output at given sampling frequency

Consider the signal $\cos(30t)$ sampled at $w_s=40 rad/s$ using a unit impulse train. The sampled signal is filtered with an ideal low pass filter with unity gain and cutoff frequency $w_c = 40rad/s$. ...
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1answer
69 views

Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$

Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$ I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
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1answer
24 views

time scaling and shifting of cosine in Fourier transform

I've met some problems when calculating the Fourier transform of $\cos(at+b)$. I want to use the shifting and scaling properties to solve this problem. First, when I look up in the book and some ...
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3answers
70 views

Nyquist Rate of cosine modulated function

Here's my understanding: $$y(t) = x(t)~ \cos(\Omega_0 t)$$ I take the Fourier transform of y(t) and I get this result: $$Y(\Omega) = \frac{1}{2}X(\Omega - \Omega_0) + \frac{1}{2}X(\Omega + \...
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2answers
132 views

Running Integral of sine and cosine functions

In typical signal processing course we were taught that the integral of signal $x(t)$ is given by $$y(t) = \int_{-\infty}^{t}x(\tau) d\tau$$ How can we use this definition to evaluate the integrals of ...
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1answer
41 views

harmonic waves as integer multiple in spectrum

i have a motor that is rotating with a certain frequency. If i check the frequency spectrum it contains a peak on 150 hz. Also i have peaks at 300,450,600 ... i guess that those peaks are harmonics. ...
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1answer
33 views

Difference between frame rate and sampling rate?

Below are the two different methods of generating time to create an audio sine wave. While framerate is being used as steps in one method, the inverse of sampling rate is being used as steps in the ...
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5answers
1k views

A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t) $$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than ...
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2answers
58 views

Sampling $x(t)=\cos(4\pi t)+\cos(2\pi t)$

Imagine that we sample the signal $x(t)=\cos(4\pi t)+\cos(2\pi t)$ with a certain sample frequency $f_s$ and we obtain $x[n]$. Now, by ideal interpolation, we get $y(t)$ from $x[n]$. How can we know ...
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0answers
13 views

What wavelet should i use to analyze harmonic function?

If i have the following signal: $$ s(t) = cos\left [ t\cdot \left (\frac{a}{2}t+b \right ) \right ] $$ What is the best family of wavelet to analize the signal, and what is its scale range? Do i ...
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1answer
67 views

When can a windowed cosine be considered band-limited signal?

I have an exam in the following days and i have no clue of what is the response to this question in the exam: given this signal: $$g(t) = H\left(t+\frac{T}{3}\right) f(t) - H\left(t-\frac{2T}{...
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1answer
53 views

Amplitude modulation in pure sine wave [duplicate]

I am generating sine wave in MATLAB with following code ...
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2answers
85 views

How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?

While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch filter: https://www.researchgate.net/...
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1answer
101 views

What are the cosine functions in JPEG's DCTII table?

As I understand it from this video, in a JPEG image an 8x8-pixel block is made up of weighted cosine waves, calculated using DCTII. There are lots of visualizations of these waves, such as this one ...
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1answer
69 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}...
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3answers
164 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 ...
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1answer
263 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). ...
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1answer
169 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 <...
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1answer
192 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: ...
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2answers
46 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\...
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2answers
46 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) ...
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1answer
520 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: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
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2answers
75 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 ...
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1answer
602 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;...
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1answer
75 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.: $$v(t) =\widetilde{v_{dc}} + \sum_{n=1}^{\infty}\sin(\omega_nt+\phi_n)$$...
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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 ...
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1answer
84 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 $\...
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1answer
1k 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 ...
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1answer
1k 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 ...
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2answers
88 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 ...
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2answers
2k 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 ...
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1answer
51 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 ...
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0answers
764 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 ...
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2answers
2k 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 ...
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0answers
554 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 ...
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2answers
866 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 ...
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1answer
950 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...
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1answer
881 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 ...