Questions tagged [cosine]
The cosine tag has no usage guidance.
53
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The benefit of Eigendecomposition of DCT and DST
I am Ph.D in pure mathematics and interested in signal processing.
Theoretically, any illustration of the eigendecomposition of the discrete trigonometric transforms (DTTs) is worthwhile.
Q. What real ...
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Error in complex signal with imperfect quadrature phase and amplitude (textbook question)
I am working on the following problem:
I have a solution that I am pretty confident is correct as have checked the output in python. However, it is long and the entire time I was answering the ...
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How do I match a filter to an AWGN channel?
I have the task to find a transition that fulfills the first Nyquist Criterion. After that I am supposed to match that filter to an AWGN channel. For the first part I thought a raised cosine ...
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2
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An new arranging of the discrete Sine transforms
Let $n$ be even and consider the non-normalized discrete Sine transform of type 5 which is
$$S=\left(\sin(k+1)(l+1)\frac{\pi}{n+\frac12}\right)_{k,l=0}^{n-1}$$
Let us denote $s_{-,l}$ by the $l^{th}$...
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Strange Look to Sampled Sinusoid [duplicate]
Ok so as part of a project for school I have been designing an FIR bandpass filter. The output should have been a signal which looks like a sampled sinusoid but there was a strange alteration on the ...
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771
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Envelope detection using hilbert transform
I have a sine wave of frequency 1kHz sampled at 16kHz. I need to find the envelope of this signal using hilbert transform in MATLAB.I have used the inbuilt function abs(hilbert(input_signal)) and got ...
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How to create a signal m(t)?
I have this signal $m(t)=8\sin(9\pi t)\sin(8\pi t)$, my teacher gave as explain $2\sin x \sin y=\cos(x-y)-\cos(x+y)$. So how to create and get this signal $m(t)=a\cdot\cos(2\pi f_c t)$.
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Integration of Sinusoidal functions
Since Differentiation of a sinusoidal function of a certain angular frequency gives a sinusoidal function of the same frequency, does the statement "Integration of a sinusoidal function of ...
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Z-transform of $\cos(\omega_0 n(n+1))u[n]$
I'm doing some research on Zadoff-Chu sequences and as a part of it I wanted to find the Z-transform of:
$$\cos(\omega_0 n(n+1))u[n]$$
Wolfram Alpha / Mathematica couldn't help out. I couldn't find a ...
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Filtering a sum of cosines
The block diagram below represents a linear modulation system operating at the frequency of $1000 Hz$, $f_C = 1000 Hz$, transmitting the message $m(t) = 2\cos(400πt)$
At point B, i got the signal: $$...
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What type of data need to be used for multiplication of sine and cosine signals in mixer?
I want to multiply sine and cosine signals(have same frequency).
I've sampled the signals and converted to digital .
Samples can range from 0 to 4096.
like 4095, 4078, 4028, 3945, 3832, etc...
I want ...
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3
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345
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Unexpected imaginary part in the fft of a zero-padded cosine
I simulated a cosine waveform $ y = \cos(\omega t) $ and I applied the FFT algorithm to it. As expected, I have a frequency peak at $\pm \omega$ only in the real part, and nothing in the imaginary ...
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DTFT of sine wave using freqz
As mentioned in the title, is it possible to use freqz to find the DTFT of a sine wave? I am confused about what the 'a' and 'b' vectors would look like, since there are only impulses in the numerator....
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Setting up RRC filter and useful equations
I have looked at previous answers but cant seem to get everything I need in one place to help me and my textbook doesnt explain this in practical terms.
Signal Parameters:
$F_s = 44100$
$R_s = 300$
$...
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Discrete time sine wave generation near nyquist
I'm trying to wrap my head around how to generate sine-waves out of a DAC near the Nyquist frequency (or determining how close I can get for reliable results). So if I want to generate a 499 Hz sine ...
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Optimization of harmonics calculation
I need to compute the sine and cosine of an argument along with n "harmonics"
\begin{matrix} \sin(x) & \cos(x) \\
\sin(2x) & \cos(2x) \\
\cdots \\
\sin(nx) & \cos(nx)
\end{...
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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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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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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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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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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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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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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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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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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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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:
$$g(t) = H\left(t+\frac{T}{3}\right) f(t) - H\left(t-\frac{2T}{...
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107
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Amplitude modulation in pure sine wave [duplicate]
I am generating sine wave in MATLAB with following code
...
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How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?
While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch filter:
https://www.researchgate.net/...
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What are the cosine functions in JPEG's DCT-II table?
As I understand it from this video, in a JPEG image an 8x8-pixel block is made up of weighted cosine waves, calculated using DCT-II. There are lots of visualizations of these waves, such as this one ...
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Sum of cosines as squashed as possible
I have 10 cosine waves of the form $\cos(2\pi(x f_n+\varphi_n))$, where $f_n$, the frequency, is an integer from 1 to 10 and $\varphi_i$, the phase, is a number from 0 to 1:
$$s(x) = \sum\limits_{n=1}...
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"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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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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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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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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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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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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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:
$$\begin{aligned}
x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
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Fourier series of $cos(\omega_0 t)$ in continuous time
Can any one please help me with understanding how we can calculate the Fourier series of Cos(w0t) using the formula:
I saw that they did the following calculus, but I Don't really understand how we ...
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Why MATLAB fft cos makes imaginary parts?
The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(7);
fs=128;
t=-4*pi:1/fs:4*pi-1/fs;...
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Extracting a DC value from a sum of sinusoids
I guess it might be a basic questions but here it goes anyways.
How could I extract a DC value from a sum of sinusoids, i.e.:
$$v(t) =\widetilde{v_{dc}} + \sum_{n=1}^{\infty}\sin(\omega_nt+\phi_n)$$...
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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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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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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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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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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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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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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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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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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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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 ...
